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Predictors and consequences of involvement in physical activity : a causal model of the 1981 Canada Fitness.. Haag, Gerald Gunnar 1989-12-31

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PREDICTORS AND CONSEQUENCES OF INVOLVEMENT IN PHYSICAL ACTIVITY: A C A U S A L M O D E L OF T H E 1981 C A N A D A FITNESS SURVEY By Gerald Gunnar Haag B. P.E. University of B r i t i s h C o l u m b i a  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF " THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION  in THE FACULTY OF GRADUATE STUDIES SCHOOL OF PHYSICAL EDUCATION AND RECREATION  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October 1989 © Gerald Gunnar Haag, 1989  In  presenting  degree freely  this  thesis  in  partial  fulfilment  at the University  of  British  Columbia,  available  copying  of  department publication  this or  for reference thesis by  of this  and study.  for scholarly  his thesis  or  her  of  I agree  I further  purposes  gain  agree  requirements that that  shall  It  is  Department  of  ^VAJ  <,'.  not be allowed  ^Aoxl\-^ov\ <^cV W v t ^ Q v N  The University of British Columbia Vancouver, Canada  DE-6 (2/88)  advanced  shall  make  it  permission for extensive by the head  understood  permission.  for an  the Library  may be granted  representatives.  for financial  the  that without  of my  copying  or  my written  Abstract  Involvement in physical activity (IPA) represents a complex lifestyle behavior. In order to gain a better understanding of the concept of I P A and the relationships with other factors, two comprehensive theoretical models of predictors and consequences of I P A were tested. T h e 1981 Canada Fitness Survey ( C F S ) provided an extensive database including physical activity measures. A subsample of 3055 20- to 40-year old Canadian males was chosen for all analyses.  Forty-six observed variables were initially selected  from the C F S to measure the abstract concepts of past experience, attitude, motivation, social status, barriers, modifiers, I P A , physical fitness, and psychological fitness. Causal modeling techniques were applied to test the conceptual model of fitness, presented in the C F S manual (model I), and a model of I P A developed by the author from a review of the literature (model II). The measurement model and structural equation model were tested for each model with the L I S R E L computer program. Both models revealed a good fit to the data (GFI=.95 and GFI=.93, respectively). M o d e l I was not based on strong theory and required a large number of modifications. The test of model II was much less difficult and produced larger structural path coefficients.  Results from model II indicate that  motivation is the strongest predictor of I P A , followed by barriers and social status. Past experience and I P A improve physical fitness. Attitudes and past experience could not predict I P A and neither I P A nor physical fitness affected psychological well-being. Causal modeling appears to be a very powerful and promising statistical method for testing hypothetical models with observational data. However, its mathematical complexity and novelty create various problems with applications. A flowchart of suggested procedures is given.  ii  Table of Contents  Abstract  ii  List of Tables  vii  List of Figures  viii  Acknowledgement  ix  1 Introduction  1  1.1  Canada Fitness Survey  2  1.2  Model I  5  1.3  Model II  5  1.4  Uni- vs. Multivariate Analysis  8  1.5  Causal Modeling  11  1.6  Purpose  14  2 Methods and Procedures  15  2.1  Data  15  2.2  Involvement i n Physical Activity  16  2.3  Operationalization of Variables  26  2.3.1  Attitude  26  2.3.2  Barriers  28  2.3.3  Modifiers  29  2.3.4  Past Experience  30 iii  2.3.5  Motivation  30  2.3.6  Social Status  31  2.3.7  Physical Fitness  31  2.3.8  Psychological Fitness  32  2.4  Practical Versions of Models I and II  33  2.5  Causal Modeling  33  3 Results and Discussion 3.1  3.2  3.3  3.4  40  Model I  40  3.1.1  Measurement M o d e l  43  3.1.2  Structural Equation M o d e l  49  3.1.3  Categorical Data Treatment  54  3.1.4  Non-Normal D a t a Treatment  57  3.1.5  Summary  60  Model II  62  3.2.1  Measurement M o d e l  62  3.2.2  Structural Equation Model  68  3.2.3  Summary  73  Predictors and Consequences of I P A  74  3.3.1  Model I  74  3.3.2  M o d e l II  78  3.3.3  Comparison of Models  84  Recommended Causal Modeling Procedures  85  3.4.1  General Guidelines  88  3.4.2  A List of "Tricks"  95  iv  4 Summary and Conclusions  97  4.1  Physical Activity Behavior  98  4.2  Causal Modeling  99  4.3  Recommendations for Future Research  100  Appendices  101  A Literature Review - Physical Activity  101  A.l  A.2  Determinants of Physical Activity  103  A.1.1  Past Experience .  '  A . 1.2  Attitude  107  A . 1.3  Motivation  109  A . 1.4  Knowledge  Ill  A . 1.5  Social Support  112  A . 1.6  Barriers  113  A . 1.7  Demographics  115  A . 1.8  Biological Traits  116  A . 1.9  Models of Exercise Behavior  117  Outcomes of Physical Activity  120  A.2.1  Physical Benefits  120  A . 2.2  Psychological Benefits  .  123  A . 3 Summary  126  B Causal Modeling B. l  106  128  T h e Theory  129  B. l . l  Model Selection  129  B.1.2  T h e L I S R E L Model  131  v  B.2  B.1.3  M o d e l Identification  137  B.1.4  Estimation of the Model  138  B.1.5  Assessment of F i t  139  B.1.6  Other Models  144  B.1.7  Categorical Data  145  B.1.8  Non-Normal Data  146  General Procedural Guidelines  146  B.2.1  Measurement Model  147  B.2.2  Structural Equation M o d e l  148  B.2.3  Respecification  149  C Questionnaire of the 1981 Canada Fitness Survey  151  D SPSS Control Commmands  163  Bibliography  172  vi  List of Tables  2.1  Means and Standard Deviations for Various Activity Categories  24  2.2  Operationalized Variables for Model I  34  2.3  Operationalized Variables for Model II  35  3.4  Descriptive Statistics for Manifest Variables i n Model I (n=3032)  3.5  Correlation M a t r i x for Manifest Variables i n Model I  42  3.6  Steps for the Development of Measurement Model I  44  3.7  Steps in the Development of Structural Equation Model I  51  3.8  Steps in Categorical D a t a Treatment for Model I  56  3.9  Steps in Non-Normal D a t a Treatment of Model I  59  3.10 Summary of Solutions for Structural Equation Model I  61  3.11 Descriptive Statistics for Manifest Variables of Model II  63  3.12 Correlation M a t r i x of Manifest Variables from M o d e l II  64  3.13 Steps in Development of Measurement M o d e l II  65  3.14 Alternate Tests of Measurement M o d e l II (MMII5)  95  vii  . . . .  41  List of Figures  1.1  Theoretical Model I (from C F S D a t a Tape Manual)  1.2  Theoretical Model II (based on the literature review in A p p e n d i x A )  2.3  Testable Version of Model I  36  2.4  Testable Version of Model II  37  3.5  Parameter Values for F i n a l Measurement Model I  50  3.6  Parameter Values for Final Version of Structural Equation M o d e l I  3.7  Parameter Values for Final Version of Measurement M o d e l II  69  3.8  Parameter Values for Final Version of Structural Equation M o d e l II . . .  72  3.9  Flowchart of Suggested General Causal Modeling Procedures  89  vm  6 . .  . . .  9  53  Acknowledgement  T h e three members of my committee have been very supportive over the last year, and I would like to thank them very much for their help. Dr.  K. Coutts gave useful suggestions with respect to the hypothetical concepts  relating to physical activity that were defined in this study. Dr. J . Steiger offered support and helpful suggestions about various aspects of causal modeling, the statistical methodology applied in the study. D r . R. W . Schutz has shown continued support as my advisor w i t h a l l aspects of m y study. He gave numerous suggestions relating to the theoretical models, their measurement and many different statistical procedures. He showed interest and offered help with tests of hundreds of models. I was able to use his personal I B M computer for several analyses. I would like to thank Dr. Schutz very much for his patience, his tolerance, and all the time he spent helping and educating me. His support in virtually all aspect of life from the time I arrived from Germany to the completion of my Master's degree has been much appreciated and will never be forgotten. D r . G . Sinclair deserves thanks for his helpful comments. Finally, I was very fortunate to receive support from Deborah K i l l a m during the last stages of my thesis, and I would like to thank her very much.  ix  Chapter 1  Introduction  M a n y people find enjoyment i n being physically active. Even though opportunities to engage i n various forms of recreational physical activities are available, there still is a significant proportion of the Canadian population that is completely sedentary. W h y are some people physically active while others are not ? W h a t are reasons for involvement in physical activity ? The general consensus among public and media is that exercise is good for you. This claim has been extensively substantiated for physical fitness as a consequence of physical activity.  Psychological well-being or mental fitness appears to be a benefit of  involvement i n physical activity as well, although a large proportion of research i n this area is lacking validity due to insufficient research designs. How strong is the association between involvement i n physical activity and major outcomes of physical activity ? Leisure time physical activity is the central focus of this study. Involvement in physical activity (IPA) represents an important lifestyle behavior. In order to get an understanding of the concept of I P A , its role for the individual and complex interrelationships  with  other important concepts, I P A needs to be examined i n terms of both its causes and effects.  Such an analysis can identify predictors of involvement as well as important  benefits of physical activity.  These results produce important knowledge, which can  then be applied to the design of fitness programs, national sport-for-all programs, fitness promotion campaigns and motivational techniques to enhance fitness behavior. Potential target groups can be defined by identifying characteristics of individuals who generally  1  Chapter 1. Introduction  2  exercise very little or not at all. Information about the strength of the exercise-fitness relationship can be used to promote physical activity. Unfortunately, most of the empirical research conducted i n the area of physical activity has been restricted to focus on either predictors of I P A , or the outcomes of I P A , but never have both been examined i n a single comprehensive model. One of the goals of this study was to develop and test such a model. In addition to the rather specific focus of these studies, other factors limit the generalizability of results. Most studies concerned with the effects of physical activity use small samples from specific populations in quasi-experimental designs. Hayes (1986) reports that control groups are often missing and he suggests the use of survey data. In order to identify the general principles related to I P A and i n order to generalize results from tests of a comprehensive model of I P A , a survey based on a large sample and measuring many variables is necessary. Fortunately, such a survey has recently been conducted i n Canada.  1.1  Canada Fitness Survey  Canadians have shown an increasing interest i n physical activity and its effects on physical fitness and health i n the past two decades. T h e government, industry and private organizations have promoted the inclusion of regular exercise in lifestyles of the general public and offered suitable physical activity programs. T h e designers of such recreational activity programs have, however, very limited knowledge about physical activity habits of Canadians and of factors influencing these habits. Even though some national surveys, such as the 1978 Canada Health Survey, contained information about physical activities, they only provided a static picture of a small number of variables; therefore, developments or trends over time could not be assessed. In  Chapter 1.  Introduction  3  order to bridge this knowledge gap, the Minister of Fitness and Amateur Sport approved the Canada Fitness Survey i n 1980, upon proposition from the National Conference of Fitness and Health, which was held i n 1972. It was established as a permanent institution providing periodic assessments of Canadians' physical activity habits and related information. T h e major purposes of the Canada Fitness Survey ( C F S ) were to establish fitness norms, obtain baseline information and assess trends by comparison with results from repititions of the survey. The first administration of the C F S took place from February to July, 1981, covering spring, summer and fall i n order to account for any seasonal differences. A C F S questionnaire and physical fitness test procedures were developed and data were collected throughout Canada. T h e sample was stratified, multistage and clustered, and consisted of 23,400 Canadians aged 7 to 69. Trained interviewers asked all members of a chosen household that were present to fill out the questionnaire and perform the physical fitness tests. Conservative screening methods prevented a number of subjects from taking the physical fitness tests; the remaining sample, for which both questionnaire and physical fitness data are available, consists of 14,365 subjects.  A discussion of data collection  procedures, data processing and survey errors, as well as a complete description of the data tape and variables can be found i n the 1981 C F S Data Tape M a n u a l (1987). This first administration of the C F S is one of the most comprehensive fitness and lifestyle surveys conducted anywhere i n the world. From the wide variety of variables available from the questionnaire and physical fitness test the Canada Fitness Survey has extracted valuable information about lifestyle habits, such as exercise, eating, smoking, drinking and sleeping, about attitudes towards, knowledge of and barriers to physical activities, and about various demographic characteristics. Analyses of physical activity patterns for activities ranging from jogging to gardening have been performed by the C F S as well.  A number of reports have been  Chapter 1.  Introduction  4  published which give a detailed descriptive overview of the data such as "Fitness and Lifestyle in Canada" or "Canada's Youth and Fitness" ( C F S , 1983).  Bimonthly one-  page summaries of a specific aspect of the data, entitled "Highlights", have also been published between A p r i l 1983 and June 1985. These publications give informative descriptions of various types of physical activities and a large number of tables and crosstabs show outcomes such as gender, regional and age differences. Most of these government publications are aimed at informing the general public; they report analyses of the data and results on a descriptive level only. Since the release of the C F S data tape in 1983, a number of researchers i n the area of physical activity have used results from the Canada Fitness Survey for publications or have subjected the data to secondary analyses as part of further research.  Several  authors have explained the nature and usefulness of the C F S and have reported some of the key results (Ferris, Kisby, Craig & Landry, 1987; Ferris, L a n d r y & Craig, 1987; Gilmore, 1983; Hunter,1985; Newton, 1984; Peepre, 1984; Shepard, 1986; Stephens, 1983; White, 1983). W h i t e (1983) desribed the potential use of the C F S for health research and identified the elderly and economically disadvantaged groups as displaying the greatest need for involvement in physical activity at the moment, based on preliminary results from the C F S . Shepard (1986) compared anthropometric and physical fitness data from the 1981 C F S with data from several similar surveys from other Western countries. He concluded that despite response rate and other sampling problems the Canada Fitness Survey "has practical value i n providing a benchmark of physical condition for the year 1981" (p. 299). These publications provide useful descriptive information about physical activity patterns and related variables. However, no attempt has been made to explore relationships between these variables and involvement in leisure time physical activity.  Chapter 1.  1.2  Introduction  5  Model I  In the 1981 C F S D a t a Tape M a n u a l a conceptual " M o d e l of Fitness and its Interrelationships" (p. 4) was developed i n order to select variables to be included i n the survey (see Figure 1.1). In this theoretical model (Model I) fitness is identified as the main dependent variable or the most important outcome. It consists of a psychological and physical component, which may be interrelated. T h e amount of physical activity determines the degree of fitness, but this relationship is complicated by modifying factors such as nutrition, tobacco and alcohol use. In Model I the two determinants of involvement in physical activity are attitude and knowledge. According to the manual, attitudes are formed as a result of complex interactions between motivation and knowledge. Attitudes that are relevant with respect to physical activity are: attitudes towards initiating activity, towards sustaining activity, towards fitness, and towards consequences of fitness. Knowledge, on the other hand, is required for forming positive attitudes.  Barriers to  activity, such as lack of time, cost or inadequacy of facilities might have a significant effect on the relationship between attitudes and involvement i n physical activity. Model I represents a conceptual model of fitness consisting of variables and relationships based on the 1981 C F S D a t a Tape Manual.  1.3  Model II  The authors of the Canada Fitness Survey neither intended nor actually did develop a theoretical basis for their abstract model.  In order to understand what determines  involvement i n physical activity and what the outcomes of physical activities are, such a theoretical basis is necessary. aspects:  This requirement manifests itself particularity i n two  Chapter 1.  Introduction  7  1. T h e use of any statistical methodology for the test of a model of I P A can only be justified on the grounds of such a theory. 2. A n y interpretations of results from statistical tests are very difficult to make and not legitimate without a theoretical base. Therefore, a new model of I P A based on existing theories had to be developed. A l though a number of researchers have attempted to explain involvement i n physical activity within the context of behavioral models, most studies have been limited to examining the relationships between physical activity and a small number of variables. The effects of exercise upon the human system have been studied by many sport sciencists and a direct relation between physical activity and general well-being has been well established. T h e identification of determinants of I P A represents a much more complex issue. This is a common phenomenon i n social sciences since outcomes of behavior are generally much easier to measure and understand than predictors of behavior. It appears as if exercise as a common human behavior is caused by a complex psychological process, involving many variables. Despite this complexity and problems with implementing experimental research designs, several researchers have identified factors that are directly associated with I P A . A detailed review of the literature examining predictors and outcomes of involvement in physical activity is given in A p p e n d i x A . Based on the findings summarized i n this literature review a hypothetical model of involvement in physical activity was developed. Since the intent of this study was to develop a general model of I P A , no specific psychological or social behavior theory, such as the theory of reasoned action or the Health Belief Model, was adapted.  Components of these models were combined with factors  that have been shown to be associated with I P A in order to form a general model of I P A . Figure 1.2 shows a schematic representation of Model II, the hypothetical model  Chapter 1. Introduction  8  developed i n this study. Since some social behavioral theories emphasize the importance of distinguishing between behavioral intention and actual behavior, both concepts were included in the model.  Intention to exercise is hypothesized to be determined by past experience, at-  titude, motivation, social support and demographics. Involvement in physical activity, which represents the observed behavior, can be predicted from intentions to exercise, social support and barriers to physical activity, according to the model. I P A is hypothesized to directly predict physical fitness and psychological fitness. Physical fitness may influence psychological fitness. T h e amount of past experience with physical activity may have a direct effect on physical fitness. The goal of this study was to test M o d e l I, the Canada Fitness Survey conceptual model of fitness, and M o d e l II, the hypothetical model of I P A developed from the review of literature, with data from a subsample of the 1981 Canada Fitness Survey.  1.4  Uni- vs. Multivariate Analysis  Most of the studies reviewed i n Appendix A applied univariate methods for data analysis. Statisticians, psychometricians and sociometricians have advocated the usefulness and appropriateness of multivariate techniques for analyzing multivariate datasets.  Tucker  (1987), for example, reports that no causal inferences can be made from a large portion of the existing sport scientific literature and suggests the use of multivariate methods. Schutz and Gessaroli (1987) and Schutz (1988) have suggested the application of multivariate data analysis procedures to experimental designs and to comparative research in physical education and sport. Schutz argues, that in order to study complex interrelationships among a number of variables, new multivariate techniques such as structural  Chapter 1.  Introduction  Chapter 1. Introduction  10  equation modeling, log-linear analysis and all possible subsets regression can produce important results which univariate techniques cannot reveal. In their study of processes underlying involvement i n physical activity G o d i n et al. (1987) identified three major factors that "can explain our lack of fundamental understanding of exercise behavior" (p. 146): 1. Most studies have inappropriately omitted development or adaptation of a theoretical model. 2. Prospective designs have to be employed i n order to establish causal order within relationships. 3. Multivariate statistical techniques have been largely ignored. G o d i n et al. applied path analytic procedures based on an intricate theoretical model i n order to overcome these weaknesses. In a review of the literature on determinants of physical activity Dishman et al. (1985) concluded that methodological diversity and inadequacies increased the difficulty of making generalizations about the existence of determining factors. Dishman (1982) also discussed research designs for the study of exercise adherence and suggested that a multivariate prediction model based on interval data should be developed when attempting to predict behavior. Gottlieb and Baker (1986) state that the fact that many psychosocial studies have been limited to examining a single behavior and/or independent variable, and this "has constrained our ability to develop a multilevel causal model for understanding lifestyle health behavior" (p. 915). The presented models of I P A , M o d e l I and M o d e l II, consist of a number of abstract concepts and hypothesized causal relationships.  These concepts can be measured by a  Chapter 1. Introduction  11  number of variables from the 1981 Canada Fitness Survey.  A multivariate statistical  technique should be applied i n order to test the validity of these models.  Causal Modeling  1.5  Causal modelling has recently been developed and become available as an empirical procedure for the evaluation of complex multivariate interrelationships.  Linear Structural  Relations ( L I S R E L ) , Structural Equation Modeling, Analysis of Covariance Structure, P a t h Analysis and Confirmatory Analysis all represent similar statistical procedures designed to test the fit between a theoretical model involving relationships and empirical data.  Latent or unmeasured abstract variables such as the concepts i n Model I and  M o d e l II can be denned and the strength of causal links between them can be tested and assessed. Manifest or directly measured variables represent indicators of these latent constructs, which illustrates that causal modeling has been developed as an extension of exploratory factor analytic methods in order to evaluate hypothetical structures i n a confirmatory sense. These techniques have been called the greatest promise and the most important statistical revolution i n the social sciences by psychometricians such as Bentler and Cliff (in James, 1982). Anderson and Gerbing (1988) state that confirmatory methods allow the researcher to assess theoretical models which can further theory development. According to Bentler (1987) the major advantages of applying structural equation modeling techniques i n social and behavioral sciences are that mathematical models can be used to conceptualize problems and data i n a research area and that inferences about the plausibility of these models can be made. However, Fassinger (1987) concludes that causal modeling procedures are very useful  (  Chapter 1.  Introduction  12  but difficult in their application due to the mathematical complexity of the methodology.  There have also been warnings about inadequate uses (e.g. Billings & Wooten,  1978; Cliff, 1983; James et al., 1982).  Especially when disregarding some of the un-  derlying assumptions of the methodology there is an inherent danger of not identifying causal relationships that exist i n reality as well as drawing invalid inferences about causal relationships that do not exist i n reality. The summer 1987 issue of the Educational Statistical Journal contains very interesting discussions about the usefulness of and dangers associated with the use of structural equation methods. Freedman (1987) used an example of an application of causal modeling in order to explain the limits of this statistical method for analyzing complex phenomena. He gives a review of literature on problems with causal modeling and describes arguments for various positions on the use of this sophisticated methodology. His major criticisms with respect to its usefulness for the social sciences are based on the general question whether causal inferences can be drawn from observational data and on the lack of theoretical bases for hypothetical models i n applied studies. T h e problem associated with drawing causal inferences from non-experimental data has been discussed by statisticians (e.g. Cliff, 1983; Dillon & Goldstein, 1984) and philosophers (e.g. Hiibner, 1988) for a long time, and represents a much more fundamental metaphysical question. It is important to note that cause and effect relationships between variables are derived from theory, which is not based on statistics.  Classical  thinkers have established basic conditions for the implications of causality, one of which is that to prove causality it is necessary to rule out all other possible causal variables or factors. In general, we cannot meet these conditions in testing causal models, and therefore, causal modeling does not allow the researcher to make definitive inferences about the existence or direction of causal relationships. However, the strength of hypothesized relationships between latent variables can be evaluated by comparing path coefficients.  Chapter 1. Introduction  13  Freedman's second major point, the lack of profound theoretical foundations for hypothetical models, is a problem that could partially be controlled by improved education and guidance for the applied social scientist.  Freedman concludes that a clear state-  ment of the assumptions and drawing conclusions i n light of these assumptions could diminish these problems. Muthen (1987) believes that the main problem with structural equation modeling has been bad applications, which have been mainly due to insufficient experience and guidance.  In his reply to Freedman he states, that by offering better  methodological training, credibility of structural equation modeling as a powerful and appropriate statistical technique for the analysis of social science data could be established. Rogosa (1987) emphasizes the importance of developing a statistical model for processes represented by social science data. He argues that most applications of causal modeling procedures do not support scientific conclusions and simply consist of "tossing the data at available statistical methods" (p. 185). Social scientists should search for qualitative theory and not for quantitative specification. According to Achen (1987) path analysis is a legitimate and useful tool i n undertaking such a search, and Dillon and Goldstein (1984) note that " a priori theory is absolutely necessary for covariance structure analysis" (p.489). From these discussions of dangers and advantages of causal modeling as a statistical techniques it seems reasonable to conclude that at this point i n time it represents one of the most powerful and useful methodologies for the evaluation of hypothetical models based on observational data, if, and only if, the model is soundly based on scientific theory and limitations due to underlying assumptions are stated and recognized. There have been a number of attempts to summarize information about causal modelling (e.g. Everitt, 1982; James et al., 1982; Joreskog, 1978; Long, 1983; Mulaik, 1972). However, terminologies and approaches vary considerably throughout this literature, presenting the researcher wishing to apply structural equation modeling techniques with the  Chapter 1.  Introduction  14  challenge of choosing a correct and useful methodology. There appears to be no one correct approach; i n fact many aspects of causal modeling are more an art than a science, which is partially what makes its application so fascinating. Most of the available techniques are very new. Although not mentioned by the investigators, who have developed some of the methodologies and computer software packages, the practical application of these statistical procedures often presents tremendous problems. Analytical procedures for minimization of the loss function from the estimation process are very complex and sensitive. Especially when evaluating more complex functions, they sometimes do not converge and yield invalid results. Although there are other problems such as invalid standard errors and software "bugs", they can be minimized by using different computer programs. Despite the problems with applying causal modeling, it seems to be a very powerful statistical methodology that is useful and appropriate for the analysis of complex models of I P A .  1.6  Purpose  T h e purpose of the study is to test the conceptual model of fitness presented i n the Canada Fitness Survey D a t a Tape manual (model I) and a hypothetical model of predictors and consequences of involvement i n physical activity (model II) using data from a subsample of 20 to 40-year old males from the 1981 Canada Fitness Survey by applying appropriate causal modelling techniques. T h e appropriateness of models will be evaluated and results will be interpreted i n light of hypothesized relationships.  Chapter 2  Methods and Procedures  2.1  Data  A l l data subjected to statistical analyses were taken from the household-based sample of the 1981 Canada Fitness Survey. Data were collected from randomly selected households across Canada. Every person present in the household was asked to fill out the C a n a d a Fitness Survey Questionnaire (see A p p e n d i x C ) and to complete the Canadian Standardized Test of Fitness ( C S T F ) . After thorough editing it was stored on microdata tape, a copy of which is available and accessible at the data library of the Computing Center of the University of British Columbia. Age and gender have repeatedly been shown to account for a large proportion of the variance in participation in exercise programs (e.g., Dishman et al., 1987) and similarity i n involvement in leisure time physical activity.  Since the intent of this study was to  identify important predictors of I P A and not to reassess age and gender differences, a subsample of the Canada Fitness Survey sample was selected in order to control these factors, namely male subjects aged 20 to 40 years. The total resultant sample size was n=3055. A n SPSS control command file was created to read data for these subjects from the datatape and to store it for subsequent analysis.  The correctness of the format was  checked several times before the complete set of data was read from the tape. The final data check consisted of descriptive analysis of all variables and comparisons with the raw  15  Chapter 2. Methods and Procedures  16  data.  2.2  Involvement in Physical Activity  The measurement of involvement i n physical activity has presented a problem to sport scientists and epidemiologists ever since it has been considered an important part of our lifestyle and a topic of study.  Montoye and Taylor (1984) give a good review of  available physical activity assessment methods and problems associated with each of these methods. The procedure of selecting the best physical activity assessment method can be characterized by a tradeoff between cost and quality. Even though m a x i m u m objectivity and accuracy is desirable, more subjective methods such as self-report procedures have to be chosen i n larger studies and population surveys due to practical and financial reasons. Blair (1984) identifies some of the important issues with respect to exercise assessment: • Data Treatment: The estimation of group means may be useful for assessing exercise habits of large samples i n research studies, but accurate information about the single individual is more appropriate i n clinical settings. •  Type of Exercise: Even though the measurement of vigorous physical activity is relatively easy and useful i n studies related to heart disease, moderate physical activity should not be disregarded when studying other factors such as predictors or benefits of physical activity.  •  Time of Activity:  Despite the fact that most jobs have become more and more  sedentary, it might be necessary to assess occupational activity patterns as well as leisure time activity patterns i n the study of specific groups. • Accuracy of Measurement: T h e estimation of daily caloric expenditure appears to  Chapter 2. Methods and Procedures  17  be relatively accurate, but unfortunately still relies on imprecise methods. Classification  of subjects into activity categories is a useful and much simpler method of  assessing physical activity habits, but the method might not be sensitive enough to changes in physical activity patterns. • Length of Assessment: Since health benefits of physical activity result from regular exercise over an extended period of time, assessment of these activities over several months would be desirable, but unfortunately that is very impractical in most studies. Physical activity assessment methods range from direct observation, which is objective but excessively costly and impractical, to respondent recall surveys, which are only a reliable measure of frequent activities and are very likely to be affected by social desirability bias. Recall surveys are most commonly used i n studies of physical activity habits. Brooks (1987a) describes problems with present assessment sytems: "inadequate measurement of time allocations to physical activity, lack of cost efficient sampling techniques, lack of consistency in survey techniques, and unsophisticated analytic strategies" (p. 455).  She suggests that an instrument providing valid and reliable data on physical  activity involvement patterns has to be found and that sampling methods have to be adjusted i n order to account for variations over time. Brooks (1987b) states that recall methods are not very accurate and tend to overestimate actual levels of participation. She presents and discusses the viability of time diaries for the assessment of leisure time physical activity (1987a). Blair (1984) suggests the use of activity pattern questionnaires, but i n a review of 13 population surveys Lupton et al. (1984) note that most collected survey data assesses only participation i n specific forms of exercise. B o t h researchers suggest the use of more  Chapter 2. Methods and Procedures  18  detailed methods. Laporte, Montoye and Casperson (1985) argue that physical activity habits are very difficult to measure due to their complex nature and many interrelated dimensions of activity. Although a number of different methods have been applied to measure activity patterns, their validity and reliability has not been determined and they only seem to capture a certain aspect of physical activity habits. Laporte and his co-workers conclude that at present recall procedures seem to be the best available method for population studies. Since involvement i n physical activity is the main focus of this study and the central component of both models, its accurate assessment appears to be necessary i n order to make valid interpretations of relationships with other variables. Fortunately, the Canada Fitness Survey designed a very detailed recall procedure for assessing physical activity patterns, which was implemented i n the 1981 C F S . In the questionnaire subjects were asked to identify activities which they were participating i n on a weekly basis, within the last month, and within the last year i n three different sections of the questionnaire (see C F S questionnaire i n Appendix C ) . Frequency as well as average intensity and duration were recorded. The weekly activity section (page 1 of the questionnaire) was designed to assess those physical activities which were performed on a very regular basis (i.e., at least once a week). T h e frequency of activities were indicated for each month of the year, accounting for possible seasonal differences due to the nature of the activity or other factors. O n page 2 of the questionnaire, subjects were asked to report all activities performed i n the previous month.  Activities that respondents participated i n within the last year  were indicated on page 3 of the questionnaire, where a list of twenty common activities, ranging from walking for exercise to ice skating, as well as additional space for other not so common activities, was provided. Subjects had to report the frequency of each actvity  Chapter 2. Methods and Procedures  19  for every month of the last year. Each activity could only be indicated i n one of these three sections. The C F S used the concept of Metabolic Expenditure as a measure of physical activity:  ME = FREQ where  ME  * INT * DUR  represents metabolic expenditure  F R E Q is the frequency of participation i n an activity per month INT  is the intensity of an activity, which is represented by an assigned M E T S value  DUR  is the duration of participation i n an average activity session i n hours  Metabolic expenditure M E T S values were developed by Bouchard, Godin, Landry, Shepard and Skinner to represent the physical effort an individual undertakes when participating i n a physical activity.  They were adapted by the C F S as described i n the C F S  data tape manual (1981). Values were assigned based on the activity and reported intensity. Walking for exercise, for example, was assigned M E T S values of 3, 4 and 5, whereas values for bicycling were 3, 7 and 10 for light, medium and heavy intensity, respectively. The only general measure of involvement i n physical activity that the Canada Fitness Survey derived from the detailed data is the activity scale, which classified respondents into the following three categories: • active: average of 3 or more hours of physical activity per week for 9 or more months • moderate: average of 3 or more hours of physical activity per week for less than 9 months or average of less than 3 hours of physical activity per week for 9 or more  Chapter 2. Methods and Procedures  20  months • sedentary: average of less than 3 hours of physical activity per week for less than 9 months This measure included all reported leisure activities, but d i d not consider intensity of activities. In order to adequately assess the concept of I P A additional measures of I P A based on the design of the C F S questionnaire had to be developed. Several data checks were undertaken initially i n order to understand and test the rather complicated design of reporting weekly, monthly and yearly activities.  Walking for exercise was used on the  first one hundred subjects as a test example and original assumptions about the design made on the basis of the information given i n the C F S data manual were confirmed. The following procedures were applied for the development of new measures of I P A (for exact mathematical transformations see the SPSS control commands i n Appendix D). Based on the frequencies i n the total population, which are reported i n the C F S data manual, the following twenty-four major activities were identified: Walking for Exercise, Jogging, Running, Bicycling, Golf, Racquetball, Tennis, Baseball, Ice-Hockey, Softball, Swimming, Alpine Skiing, Cross-Country Skiing, Ice-Skating, Roller-Skating, Calisthenics, Exercise Classes, Weight Training, Badminton, Basketball, Football, Soccer, Volleyball, Frisbee. A n average frequency per month was calculated for each activity.  T h e sum of all fre-  quency scores produced a score Y E A R F R E Q , which represents the average occurence of participation i n physical activity per month, based on recall data from the previous year. Additionaly, each frequency score was multiplied by the assigned M E T S value, which represents the intensity of the activity, and by the average duration per session i n hours, to produce a T M E (Total Metabolic Expenditure) score for each activity.  T h e sum of  Chapter 2. Methods and Procedures  21  all T M E scores produced a score Y E A R T M E , which represents the average metabolic expenditure per month, based on recall data from the previous year.  Frequency was  hypothesized to be conceptually different from total metabolic expenditure i n a manner parallel to the distinction between frequency and amount of alcohol (see section 2.2.3). Frequency scores only represent the time an individual invested into physical activity, whereas T M E scores are a reflection of the total effort an individual invests. Initial analyses revealed that several subjects were overanxious and reported being physically active five times a day every day. This can be interpreted as a gross overestimation, perhaps due to a social desirability complex. In order to prevent the distributions of I P A variables to be disturbed by these outliers the following restrictions were applied to indicators of I P A : • Frequency: A n y subject participating i n an activity more than 60 times per month or i n all activities more than 90 times per month was eliminated from the sample. • T M E : A n y subject having a total metabolic expenditure of more than 1500, for example a respondent who cycled at high intensity for more than 150 hours per month, was eliminated from the sample. In model I two additional scores were calculated and included as indicators of I P A . Since recall procedures are more reliable for a shorter time span, summary measures from the previous month only were defined. L M O N F R E Q represents the frequency of all major activities i n the last month, based on data from that previous month.  LMONTME  represents the metabolic expenditure from a l l major activities i n the last month, based on data from that previous month. Before testing model II additional analyses of I P A scores were performed to possibly identify an underlying structure important to the measurement of I P A and in order to get  Chapter 2. Methods and Procedures  22  more information about physical activity habits of Canadians. Four categories of activity types were defined and the selected major activities were assigned to these categories: 1. P A I R : Games played with a partner • Badminton • Golf • Racquetball • Tennis 2. T E A M : Games played as a member of a team • Baseball • Basketball • Football • Ice-Hockey • Soccer • Softball • Volleyball 3. F I T : Activities generally aimed at improving cardiovascular or physical fitness • Calisthenics • Cross-Country Skiing • Cycling • Exercise Classes • Jogging  Chapter 2. Methods and Procedures  23  • Running' • Swimming • Weight Lifting 4. L E I S : Activities that stress enjoyment and social aspects • Alpine Skiing • Frisbee • Roller-Skating • Skating • Walking Categories 1 and 2 were combined into a G A M E category. combined into an A C T I category.  Categories 3 and 4 were  Frequency and T M E scores for all categories were  computed as demonstrated above and compared. Table 2.1 shows means and standard deviations of all seven categories. Even though respondents participated over four times as often i n activities than i n games, the total metabolic expenditure from activities was only twice as high as the total metabolic expenditure from games. T h e last column i n table 2.1 represents the ratio of T M E and F R E Q , which is the product of duration and intensity:  TME IFREQ  = DUR * INT  As shown i n table 2.1, the product of duration and intensity for games is twice as large as that of activities.  Therefore games tend to last longer and are probably of higher  intensity, yielding higher metabolic expenditure.  T h e frequency value for F R E Q F I T  indicates that 20 to 40 year old Canadian males participate i n fitness-oriented activities such as cycling or running over half the time they decide to be physically active.  24  Chapter 2. Methods and Procedures  Table 2.1: Means and Standard Deviations for Various Activity Categories  Category  No of Acti  Freq Pair Freq Team Freq F i t Freq Leis Freq Game Freq A c t i Year Freq T M E Pair T M E Team T M E Fit T M E Leis T M E Game T M E Acti Year T M E  4 7 8 5 11 13 24 4 7 8 5 11 13 24  X 1.39 2.16 9.33 6.04 3.55 15.03 18.24 11.64 19.42 38.49 24.74 31.07 62.70 93.39  s 3.15 4.30 13.35 9.72 5.72 16.94 17.97 33.84 49.63 84.06 62.87 64.45 108.21 132.67  TME/Freq  8.4 9.0 4.1 4.1 8.8 4.1 5.1  The standard deviations are very large, indicating that involvement i n physical activity is quite variable across this sample. T h e distribution of these scores is strongly affected by the large number of completely inactive subjects, that is subjects with scores of zero on I P A variables.  B y inspecting table 2.1 it can be concluded that the total  measures of F R E Q and T M E of all 24 activities combined have the smallest variability, indicated by the lowest coefficients of variation CV  =x/s.  Correlations between all frequency and T M E measures and other variables from models I and II were calculated and some interesting results emerged. T h e Pearson productmoment r between Activities and Games was only .15 for the frequency measure and .14 for the T M E measure, which indicates that they are two distinct concepts. In general, people who play games do not participate i n fitness activities as much and vice versa. Fitness activities correlated much higher with total scores ( r = .95 and r = .88 for F R E Q and T M E scores, respectively) than did games (r = .42 and r - .60 for F R E Q and T M E  Chapter 2. Methods and Procedures  25  scores, respectively). This indicates that most of the variance i n combined activity scores can be accounted for by fitness activities. Correlations with other variables revealed some differences.  For example, measures  for the G A M E category correlated higher with social and personal development reasons for exercise, and measures for the A C T I category correlated higher with health- and fitness-oriented reasons for exercise, which confirmed the conceptual basis chosen for classification of physical activities. Of all the correlations between the manifest variables selected i n models I and II and the derived physical activity measures, the largest were found for the total measures of all twenty-four activities combined i n all cases. T h e derived categories of actvities were therefore not used for the indication of I P A i n tests of the hypothetical models. Based on these preliminary analyses the following measures of I P A were chosen as manifest variables:  Model I • Activity Scale: as defined by the C F S (see above) • Y E A R F R E Q : frequency of all activities based on data from previous year • L M O N F R E Q : frequency of all activities based on data from previous month • Y E A R T M E : total metabolic expenditure of all activities based on data from the previous year • L M O N T M E : total metabolic expenditure of all activities based on data from the previous month • Adherence: Question 10 of the questionnaire, indicating the amount of past experience with physical activity  Chapter 2. Methods and Procedures  26  Model II Only Activity Scale, Y E A R F R E Q and Y E A R T M E were selected as indicators of I P A i n model II, based on results from analyses of model I.  2.3  Operationalization of Variables  A l l abstract concepts defined i n models I and II are represented as latent variables that cannot be measured directly.  Manifest or observed variables h a d to be selected which  are indicators of these latent variables. Concepts such as Attitude are therefore measured and represented by a combination of manifest variables. These manifest variables have to be carefully selected and it should be demonstrated that they measure the concept they are hypothesized to measure. This procedure is known as operationalization of variables. Because the nature of the study required secondary data analysis, the availability of adequate observed variables was limited. T h e Canada Fitness Survey had designed both the questionnaire and fitness test i n order to receive baseline information about fitness and related factors i n Canada.  If a survey would have been designed for this study,  some different variables would have probably been chosen. However, questions from the survey and fitness test measures were quite useful and indicators of most latent constructs in model I and model II could be defined from these variables. T h e following sections describe the manifest variables selected for each of the abstract concepts.  2.3.1  Attitude  Question 5 of the questionnaire consisted of ratings of ten reasons for being involved i n physical activity during leisure time.  Each of the ten items was scored on a scale  of 1 (very important) to 4 (not important at all). Exploratory factor analyses were performed i n order to get more detailed information about different types of attitude.  Chapter 2. Methods and Procedures  27  The Alberta General Factor Analysis Program ( A G F A P ) was applied to the correlation matrix of all ten items and a maximum likelihood analysis with oblique rotation (Promaxtype Procrustes transformation) yielded a clear four factor pattern, which was easily interpretable. Items 1, 4, 5, and 7 all adressed the issue of improving functions of the human body and the first factor was therefore defined as Health and Fitness. T h e second factor clearly represented Social Reasons for involvement i n physical activity, indicated by items 2 and 3. " A challenge to my abilities" and "learning new things" (items 6 and 8) composed a Personal Development factor. Finally, items 9 (fitness specialist) and 10 (doctor) refer  to Specialist's Advice. Since the correlation between the Social and Personal Development factors was relatively high (r=.52), a second exploratory factor analysis restricted to three factors was run with the A G F A P computer program. Again, a clear factor pattern indicated that there are three important factors, which can all be theoretically explained.  Factors 2  and 3 from the four factor solution clearly formed a common factor of personal and interpersonal development. Results from these factor analyses were then used to calculate sum scores for each factor. In model I the three factors Health and Fitness, Social and Personal Development, and Specialist's Advice were selected as indicators of attitude towards physical activity. Since social and personal development were conceptually different in terms of the theory discussed i n section A.1.2, all four factors from the original exploratory factor analysis solution were included as measures of attitude i n model II. Item 7 of question 20 required a rating of how important regular exercise is for a general feeling of well-being; it was also defined as a manifest variable measuring attitude towards physical activity. Three items of question 12 were originally included as indicators of attitude i n model I; they were indications of having no energy, no self-discipline  Chapter 2. Methods and Procedures  28  and no intention to be more physically active. One variable was selected as a measure of knowledge, which is conceptually different from but highly related to attitude, according to the C F S . A l l items of question 14 ("which of the following programs have you heard of ?") were summed, producing a total score of knowledge of fitness programs, which was used i n analyses of model I.  2.3.2  Barriers  Question 12 consists of reasons for not being more physically active, which defines the concept of barriers to physical activity. In model I, the following five items were included as indicators of barriers: • no time to exercise • lack of facilities • illness / injury • lack of skill • cost A rating of perceived health (question 29) was identified as a barrier to physical activity as well. A l l but the latter variable were of dichotomous nature, and produced highly skewed distributions.  T h e amount of information contained i n these variables was very small,  due to the fact that subjects who indicated one barrier were probably not very inclined to identify other barriers as well (illustrated by low correlations between the barriers). In a renewed attempt to operationalize variables to represent the concept of barriers, a sum score of a l l barriers listed i n question 12 was computed and used i n conjunction with a measure of limitations due to health (question 28) as indicators of barriers to physical activity i n model II.  Chapter 2. Methods and Procedures  2.3.3  29  Modifiers  Model I includes the concept of modifiers which can effect the relationship between I P A and fitness. A number of variables are identified as modifiers i n the C F S data manual: Anthropometric variables, perceived state of health and fitness, limitations to physical activity, alcohol and tobacco use, nutrition. Anthropometric characteristics such as somatotype, height and weight seem to be purely biological variables and virtually unrelated to modifiers such as alcohol and tobacco use. One could argue, for example, that somatotype is a direct outcome of I P A i n conjunction with its genetic components, which would not fit the theoretical basis for model I. Perceived state of health and perceived state of fitness is more closely related to the behavior itself than the outcome of behavior, as exemplified i n behavioral models discussed in the literature review. Most behavioral models define these variables to be a measure of motivation, which is an entirely different concept. Limitations seem to be much more related to the behavior as well and represent barriers to the initiation of the behavior rather than modifiers of the relationship between behavior and outcome. The only variables which could be adequately operationalized as modifiers were alcohol and tobacco use. Frequency (days per week) and amount (drinks per drinking occasion) of alcohol (question 23) were defined as two variables indicating alcohol habits. They are conceptually different i n that frequency indicates the general pattern of the alcohol habit, whereas the number of drinks reflects the intensity of this habit.  Three  variables concerning smoking were taken from the C F S (question 24) and transformed into a single variable representing smoking habit with the following categories: 1. never smoked 2. stopped smoking more than a year ago  Chapter 2. Methods and Procedures  30  3. stopped smoking recently 4. smoke occasionally 5. smoke regularly Importance of Rest and Importance of Diet for one's well-being (Items 1 and 2 of question 20) were considered as modifying variables, but both variables were virtually unrelated to smoking and alcohol habits; therefore they were not included as manifest variables representing modifiers. Despite the argument made above, the sum of five skinfolds was originally included i n model I.  2.3.4  Past Experience  The only indicator of past experience with physical activity that could be taken from the C F S was adherence to exercise, which was measured i n question 10 of the questionnaire ("How long have you been doing some activity i n your leisure time at least once a week?"). In model I this variable was combined with measures of involvement to represent a general I P A factor.  In model II, however, adherence was defined as a different concept than  involvement per se, based on research findings discussed i n the literature review.  2.3.5  Motivation  Two items were selected from the C F S as measures of motivation i n model II. Question 11 of the C F S questionnaire requires a rating of one's own fitness, which was defined as perceived fitness. Question 29 represents a measure of perceived health. Measures of perceived health and perceived fitness have been defined as motivational variables i n behavioral models such as the Health Belief M o d e l and were therefore considered to be adequate indicators of motivation.  Chapter 2. Methods and Procedures  2.3.6  31  Social Status  As described i n the review of literature (Appendix A ) , demographic variables seem to play an important role with respect to exercise behavior. However, it is a very difficult task to combine these conceptually different variables into a single factor. T h e interrelationships between demographic variables such as age, marital status, parental status, education, income and occupation are very complex and often nearly impossible to interpret.  A  general state of wealth can be associated with higher income, better education and better occupation.  M a r i t a l and parental status and age represent a state of maturity.  Even  though these two abstract concepts theoretically form two distinct factors, relationships among demographic variables are too complex to reveal such a clean structure. In this study a single factor of demographic variables repesenting a person's status in society was included i n model II. Age, Marital Status, Education and Income were selected as indicators of social status.  2.3.7  Physical Fitness  Several direct and derived measures of physical fitness were available from the physical fitness test of the C F S administration. T h e following were chosen as established measures of different aspects of physical fitness (see Haag, 1975): • Predicted Aerobic Power from steptest: aerobic/cardiovascular • Pushups: muscular endurance, muscular strength • Situps: muscular endurance •  Gripstrength: muscular strength  •  Trunkflexion: flexibility  fitness  Chapter 2. Methods and Procedures  32  • Sum of five Skinfolds: body composition There has been considerable discussion about the validity of the step test, which is defined in the Canadian Standardized Test of Fitness and was administered i n the 1981 Canada Fitness Survey, as a measure of aerobic power; alternate methods such as the Cooper test have been suggested. Although this fact was recognized, predicted aerobic power as estimated from the step test was selected as it was the only available measure of aerobic fitness.  2.3.8  Psychological Fitness  Unfortunately, the only available indication of mental fitness i n the 1981 Canada Fitness Survey is the Bradburn Affect Balance Scale, a ten item scale developed by Bradburn in 1969. Question 25 consists of five items expressing negative feelings and five items expressing positive feelings, which form the negative and positive affect balance scales. Respondents were asked to indicate how often they experience that feeling. McDowell and Prought (1982) examined the scale using data from the 1978 Canada Health Survey. They reveal some weaknesses of the instrument w i t h respect to the independence of the positive and negative affect balance scale, the usefulness and adequacy of the affect balance score, and the validity of specific items. A n inspection of distributional characteristics within the 1981 Canada Fitness Survey data showed that the information contained i n this scale for assessing psychological well-being is limited by the fact that the scale consists of only three possible responses for each item (i.e. "often", "sometimes" or "never").  Despite  the apparent weaknesses of the Bradburn Affect Balance Scale, it was defined to be an indicator of psychological fitness i n models I and II.  Chapter 2. Methods and Procedures  2.4  33  Practical Versions of Models I and II  A l l selected manifest variables are presented i n tables 2.2 and 2.3. Table 2.2 lists all operationalized variables available for testing model I. Table 2.3 lists manifest variables included i n the practical version of the model II, which was developed i n this study. Variables that were used as measures of latent constructs i n the final version of the models after completion of analysis are indicated by an asterisk i n both tables.  On  the basis of these selected variables practical versions of both hypothetical models were defined. T h e testable version of model I is shown i n figure 2.3. It consists of 5 latent and 29 manifest variables. The testable version of model II is shown i n figure 2.4. Twenty-four manifest variables were defined to measure 8 latent variables. N o measures of behavioral intention or social support could be found i n the 1981 Canada Fitness Survey data and these concepts were therefore eliminated from the model. A l l hypothesized causal relationships are based on evidence discussed i n the literature review (see A p p e n d i x A ) .  2.5  Causal Modeling  Causal modeling techniques were used to test the models I and II. Unfortunately, unlike many other statistical methods, causal modeling often requires many successive steps to be taken i n testing a model, rather than just producing statistical test results i n a single computational process. Each step consists of a test of a respecified model. This process of successive analyses of models is completed when an acceptable fit has been found for a model. Based on results from each test, decisions about the nature of the subsequent procedure had to be made. Neither specific statistical procedures based on causal modeling methodolgy nor the number of tests to be performed could be defined  Chapter 2. Methods and Procedures  34  Table 2.2: Operationalized Variables for Model I  Latent  Manifest  ATT  Lifestex Reason Health Reason Social Reason Self No Intention No Energy No Discipline Knowledge  BAR  MOD  IPA  FIT  Time Facilities Illness Skill Cost Perceived Health Alcohol Amount Alcohol Frequency Smoking Skinfolds Importance of Diet Importance of Rest Activity Scale Year Frequency Last M o n t h Frequency Year Total Metabolic Expend. Last M o n t h Total Met. Expend. Adherence Predicted Aerobic Power Pushups Situps Flexibility Gripstrength Bradburn  retained * * * *  * * *  *(FIT)  * * * *  *  *  Chapter 2. Methods and Procedures  35  Table 2.3: Operationalized Variables for Model II  Latent  Manifest  PEP ATT  Adherence Reason Health Reason Social Reason Self Reason Advice Lifestex Perceived Fitness Perceived Health Barriers Health Age Marital Education Income Activity Scale Game Frequency Activity Frequency Game Total Met. Expend. Activity Total Met. Expend. Predicted Aerobic Power Pushups Situps Flexibility Gripstrength Skinfolds Bradburn  MOT  BAR SOC  IPA  PHY  PSY  retained * * * *  * * * * *  * *  *(Tot) *(Tot) *(Tot) *(Tot) * * *  *  Llfestex  •  RHealth  •  RSocial  •  RSelf  •  Nolntent  •  YearTME LmonFreq LmonTME ActSc^""'  • •••••  NoEnergy NoDlsclp  Adh.r.nc.  •  Knowledge Time  •  Facilities  •  Illness  G  Skill  •  Cost  •  PerHealth  •  AlcAmount  •  J /^~~"\/  psn  T  D  Skinfolds  •  Diet  •  Rest  •  Aerobic  •  Pushups  •  Situps  •  Flex GripQtr  P S I 2  AlcFreq Smoking  ^  O  Figure 2.3: Testable Version of M o d e l I  Adherence  •  ^ ^PEP^  •  Aerobic  D  Pushups  •  Sltups  •  Flexibility  RHealth  • Gripstrength  RSocial  •  Skinfolds  RSelf R Advice  Ufe8tex PerFit PerHealth Barriers Health Age Marital  • • • • • Act  • v _ y _  ActlTME GameFr GameTME ActiFr  Education Income Figure 2.4: Testable Version of M o d e l II  PSI3  Bradburn  Chapter 2. Methods and Procedures  38  a priori. However, general guidelines with respect to decisions about specific procedures can be given. Due to the chronological nature of this study, the procedures applied to each separate test are presented i n conjunction with the results i n chapter 3. This ensures that direct reference to results from a test can be made so that the selection of statistical procedures for the next test can be explained. In order to understand these procedures, the theory behind causal modeling needs to be discussed. Appendix B gives a brief introduction to this theory and general guidelines for the application of specific mathematical models.  In the first part of this appendix, the  general nature of causal modeling and considerations with respect to model selection are discussed, followed by an introduction to the mathematical theory underlying the L I S R E L model, model identification problems, estimation methods and methods for the assessment of fit. Other common models and treatment of categorical and non-normally distributed data are discussed as well.  T h e second part gives general guidelines with  respect to testing the measurement model and structural equation model; furthermore, some of the available methods for respecification are described. In this study measurement models were constructed with the operationalized variables for models I and II. T h e measurement structure was tested with the L I S R E L computer program and modified if necessary.  Manifest variables were eliminated, respecified or  added, based on results from analyses and theoretical considerations. T h e measurement model was modified until a satisfactory solution was achieved. T h e final measurement structure was then implemented into the structural equation model, which included the hypothesized relationships between latent variables. The structural equation model was tested in a similar fashion. Parameter estimates from final solutions were used to assess the fit of the model to the data as well as the strength of hypothesized relationships.  Chapter 2. Methods and Procedures  39  The P R E L I S computer program was used to calculate a matrix including polyserial and polychoric correlations i n order to account for the categorical scale of measurement of many variables. This matrix was subjected to further tests with the L I S R E L program. Elliptical and arbitrary estimation procedures were applied with the E Q S program to account for non-normality of the data. Results from all analyses were compared and interpreted i n light of the theoretical models.  Chapter 3 Results and Discussion  3.1  Model I  After all manifest variables had been operationalized, descriptive analyses were performed using the S P S S computer programs on the U . B . C . mainframe system. Frequencies, several descriptive statistics, distributional characteristics and correlations between variables were calculated. Table 3.4 shows means, number of subjects with valid data, minimum, maximum, kurtosis and skewness for all manifest variables from model I. These descriptive statistics were carefully examined. Because most of the units of measurement for manifest variables were arbitrary, a Pearson product-moment correlation matrix was calculated, which is presented i n table 3.5. Several variables are not normally distributed, indicated by high skewness and kurtoses values, which are shown i n the last two columns of table 3.4. Since normality of the data is a basic assumption for maximum likelihood estimation, distribution-free methods had to be applied when testing the models in order to account for this non-normality. These methods and results from analyses are described i n section 3.1.4. T h e use of a correlation matrix for the analysis of causal models has the advantage that parameter estimates, such as elements of the A or $ matrices, are easily interpretable.  40  Chapter 3. Results and Discussion  41  Table 3.4: Descriptive Statistics for Manifest Variables i n M o d e l I (n=3032)  Variable xl x2 x3 x4 x5 x6 x7 x8 x9 xlO xll xl2 xl3 xl4 xl5 xl6 xl7 xl8 xl9 x20 yi y2 y3 y4 y5 y6 y7 y8 y9  yio yii  Lifestex Reas H F Reas S O Reas S E No Exer No Ener No Disc Know Time Facil Health Limited Skill Cost Skinf AlcFreq AlcAm Smoke Rest Diet Act Sea Year Freq Year T M E L m o n Freq Lmon T M E Adher Aerobic Strength Situps Flex Bradburn  Latent  Scale  ATT ATT ATT ATT ATT ATT ATT ATT BAR BAR BAR BAR BAR BAR MOD MOD MOD MOD MOD MOD IPA IPA IPA IPA IPA IPA FIT FIT FIT FIT FIT  Ord Ord Ord Ord Nom Nom Nom Ord Nom Nom Nom Ord Nom Nom Int Ord Ord Ord Ord Ord Ord Int Int Int Int Ord Int Int Int Int Ord  X 66 157 124 155 0 0 0 0 0 0 0 36 0 0 45 15 0 14 31 40 33 0 0 0 0 106 383 351 442 389 108  1.66 7.48 3.90 4.65 0.12 0.10 0.15 3.66 0.72 0.22 0.07 1.21 0.04 0.13 53.87 3.46 2.14 3.08 1.30 1.54 2.55 18.24 93.39 15.24 216.67 4.72 44.15 108.07 30.44 29.74 8.31  Min  Max  Skew  Kurt  1.00 4.00 2.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 15.90 1.00 0.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 1.00 26.00 47.00 0.00 1.00 1.00  4.00 16.00 8.00 8.00 1.00 1.00 1.00 11.00 1.00 1.00 1.00 3.00 1.00 1.00 146.60 6.00 5.00 5.00 4.00 4.00 3.00 112.25 5475.00 112.25 5475.00 7.00 62.00 161.00 70.00 73.00 19.00  1.04 .67 .57 .29 2.29 2.70 2.01 .45 -.97 1.95 3.41 2.54 4.08 2.25 1.00 .49 .37 -.03 2.05 1.46 -.85 1.59 5.35 1.79 5.31 -.53 .50 -.01 .09 -.25 .10  .45 .11 .06 -.60 3.23 5.30 2.03 -.13 -1.05 3.02 9.64 5.08 18.05 3.09 1.02 -.18 .00 -.18 4.38 1.95 -.27 3.01 34.61 4.08 33.74 -.15 -.64 .39 .60 .17 .16  00  (/» W » o */» * S r« m rr rt- r n * m -• 9 iA B T) ~ Q n — O w c ^ — O O O » * * I O - t r o r i - w m F i i ' i  c »  o o - <C  O O O O O O O O O O O O o ^  —o -  -  . g g o  -  o o o o o o o o o o o . 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O O O O O O O O O O -  o o o o o o o o o  H  o o o a o o o o o o o o o o o o o o o o o o o -  5  2 o  Ul  c  o  43  Chapter 3. Results and Discussion  3.1.1  Measurement Model  The measurement model was constructed as described i n Appendix B and as shown in figure 2.3. Each latent variable is measured by a number of manifest variables and their measurement errors. A l l latent variables are correlated.  It has to be noted that  for the purposes of the measurement model all variables are defined to be exogenous. The original measurement model M M I 1 consisted of 31 observed variables and 5 latent variables, related i n the following manner: • Attitude ( A T T ) - 8 indicators • Barriers ( B A R ) - 6 indicators • Modifiers ( M O D ) - 6 indicators • Involvement ( I P A ) - 6 indicators • Fitness ( F I T ) - 5 indicators This model was set up as a L I S R E L model under SPSS and several versions of the measurement model were analyzed. Table 3.6 provides a list of steps taken i n the test of the measurment model for model I. It lists the nature of each model, the total number of manifest variables, whether the model converged or not, x2> freedom, X /df 2  associated degrees of  ratio, Goodness of F i t Index, Root Mean Square Residual, and C P U  time used i n seconds. Before discussing results from each of these tests, symptoms of invalid solutions should be described. In some cases the computer program does not converge to a proper solution. This can be indicated by several symptoms, which can occur by themselves or in combinations. Sometimes L I S R E L prints error messages such as " T I M E L I M I T E X C E E D E D " , "LIKELIHOOD  F U N C T I O N WAS N O T E V A L U A B L E F O R INITIAL  ESTIMATES"  44  Chapter 3. Results and Discussion  Table 3.6: Steps for the Development of Measurement Model I  Model MMI1 EXI1 EXI2 EXI3 ENI1 ENI2 ENI3 ENI4 MMI2 MMI3 MMI4  Var  Conv  31 20 12 7 12 10 9 8 16 15 15  n n n  x  2  df  GFI  X /df 2  RMR  CPU  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  y n  120  13  9.2  .98  .04  -  -  -  -  -  y y y y n  3642 1655 7388 2009  43 26 19 98  84.7 63.7 388.8 20.5  .76 .87 .79 .89  .13 .09 .14 .07  -  -  -  -  -  y  614  85  7.2  .96  .06  64.0 26.0 6.0 .6 5.2 1.0 .8 .9 3.3 3.2 2.7  or " J O B C A N C E L L E D " , which indicate that the solution is invalid, because the minimization of the fitting function has not been completed. L I S R E L also gives warnings if any matrix is not positive definite, which indicates an improper solution. T h e most common matrices that have this sympton are 0$ and 0 , but $ sometimes becomes non £  positive definite as well. Another indication of an improper solution is an extremely large or negative x  2  value. If the estimation procedure has not located a m i n i m u m of the fit-  ting function, parameter estimates often become unreasonable and impossible values may result. Factor loadings (elements of A ) of 10, 100 or even 1000 indicate a serious problem w i t h the measurement of that latent variable. Sometimes L I S R E L prints a warning message referring to a specific parameter that might not be identified. This usually implies a misspecification of the model and the parameter matrix should be reexamined. Negative elements of 0$ or 0  £  and elements of $ , that are greater than one i n magnitude are  outside the permissable parameter space and are an indication of an improper solution. Sometimes the program will not be able to compute initial estimates for all parameters and they are produced by an unweighted least squares procedure and steepest descent;  Chapter 3. Results and Discussion  45  this indicates an improper model as well. Improper solutions of this kind will occur relatively often when using the L I S R E L program. One has to always be alert of possible symptoms before interpreting a solution. Certain "tricks" have to be known in order to make appropriate modifications to the model. These "tricks" are described throughout this chapter. The following measurement models were tested for model I: • MMI1:  T h e original measurement model was tested and the program d i d not find  a permissable solution, that is, the estimation procedure did not converge.  It  was then decided to test the measurement model seperately for exogenous and endogenous variables before testing the complete model. This procedure is useful because smaller portions of a complex model can be evaluated and modified, and can then be implemented as part of the complete model. Smaller models are simpler and results can be interpreted more easily. • EXI1:  T h e first version of the exogenous measurement model included 8 indica-  tors of A T T , 6 indicators of B A R and 6 indicators of M O D . The program did not converge to a proper solution, indicated by a negative x2 value. T h e 20 manifest variables were reevaluated i n light of their descriptive statistics, and several decisions were made. T h e three items selected from the list of barriers ("do not intend to exercise", "no energy to exercise", "no self-discipline to exercise") had means of .12 , .10 and .15, respectively, which represent the proportion of subjects indicating these barriers. Their dichotomous nature and the fact that these means were rather low imply that they do not contain information that is useful i n explaining or measuring the concept of attitude. A s shown i n table 3.4 all three variables are highly skewed and kurtotic, which violates on of the major assumption of maxim u m likelihood estimation. Since they do not represent measures of attitude that  Chapter 3. Results and Discussion  46  are established i n the literature, these three variables were eliminated from further analyses. T w o indicators of barriers, which were taken from the same list of items mentioned above, had means of .07 and .04 ("health" and "lack of skill").  They  were therefore eliminated as measures of barriers to physical activities. The importance of adequate rest and diet for a feeling of well-being was rated on a scale from 1 to 4. These items had means of only 1.3 and 1.5, respectively. Since they represent an attitude towards a potentially modifying behavior rather than the behavior itself and since most people thought that rest and diet were very important (i.e. the discriminatory value of the variables is low), these variables were eliminated from further analyses.  Skinfolds exhibited no association with the three remain-  ing variables of tobacco and alcohol habits and due to the considerations made i n section 2.2.3 it was also excluded as a modifying variable. • EXI2:  This model of only 12 manifest variables still gave an improper solution,  indicated by a not positive definite 0$ matrix. T h e factor loadings for indicators of barriers varied considerably and some elements of 0^ corresponding to barriers were negative. Since the discriminatory value of these variables is very small, due to their dichotomous nature, the concept of Barriers had to be excluded from further analyses. It is important to note that this decision was not based on theoretical considerations (i.e. the relationship between barriers and I P A ) , but on the conclusion that no valid indicators of barriers to physical activity could be found i n the Canada Fitness Survey data. Examination of indicators of A T T revealed that the factor loading of knowledge was very low compared to the loadings of the other four indicators. Since no significant relationship between knowledge and exercise behavior has been established i n the literature, this variable was eliminated as a measure of attitude.  ei 3. Results and Discussion  EXI3:  47  This model consisted of only two factors and 7 manifest variables and it  yielded a proper solution. A l l factor loadings were reasonably high and the total coefficient of determination of z-variables was above .9. The high G F I (.982) and low R M R (041) indicated that this factor structure fits the data very well. Inspection of modification indices and residuals showed no high values, which means there did not appear to be any locations for possible specification errors. M o d e l E X I 3 was therefore accepted as measurement model for exogenous variables of model I. ENI1:  T h e initial model of endogenous variables consisted of 6 indicators of I P A and  6 indicators of fitness. Skinfolds had been eliminated as an indication of modifiers. Since it has been utilized i n many fitness tests as a measure of anthropometric characteristics, it was respecified to be an indicator of fitness. T h e program did not converge for this model.  A n inspection of the nature of the B r a d b u r n scale  as a measure of psychological fitness revealed that it was virtually unrelated to any other variable; i n particular, it showed no significant relationships with the measures of physical fitness. It was therefore excluded as an indicator of fitness. T h e variable gripstrength did not seem to correlate very highly with other fitness variables. Since it did not appear to be a good measure of the construct of fitness as measured by the other fitness variables, it was excluded as well. ENI2: T h i s model yielded a proper solution, but the fit was very poor, indicated by a G F I of .76 and R M R of .13. A n inspection of the residuals showed that some of the I P A measures had correlations that could not be reproduced by the model very well. In particular the total metabolic expenditure of activities performed i n the last month appeared to create problems. In light of this, and because L M O N T M E was correlated very highly with L M O N F R E Q (r=.99), L M O N T M E was excluded.  Chapter 3. Results and Discussion  48  • ENI3: This modification improved the fit of the model significantly and produced a fit that was not very good, but acceptable (GFI=.87 and R M R = . 0 9 ) . A l l factor loadings were reasonably high. Skinfolds revealed the highest modification index and had fairly high residuals. Based on the assumption that it was conceptually different from the other three measures of fitness and that it has a large hereditary component as well, it was excluded from the model as a measure of physical fitness. • ENI4: T h e solution for model E N I 4 produced a significantly worse fit ( G F I = . 7 9 and R M R = . 1 4 ) as measured by the x -difference test. T h e difference i n x* 2  w a s  A = 7388 — 1655 = 5733 with associated df = 26 — 19 = 7, which is significant. Therefore, the exclusion of skinfolds resulted i n a structure that has a worse fit to the data; it adds important information i n measuring physical fitness. M o d e l E N I 3 was therefore accepted as the measurement model for endogenous variables. • MMI2: This model consists of a combination of the models E X I 3 and E N I 3 . A T T is measured by 4, M O D by 3, I P A by 5 and F I T by 4 manifest variables. T h e estimation of this model converged and yielded an acceptable solution ( G F I = . 8 9 and R M R = . 0 7 ) . Adherence revealed a low factor loading as an indicator of I P A as well as high residuals. It was conceptually different from other measures of I P A i n that it measured past experience or habit rather than the behavior itself. It was therefore eliminated as a measure of I P A . • MMI3: A n invalid solution was the result of testing this model. The problem could be directly located by examining the estimated parameters.  Y E A R F R E Q had a  factor loading just above 1, giving it a negative 8g (i.e. a negative estimate of the measurement error), which produced a non positive definite  matrix. It appeared  as if this variable contributed more variance to the I P A factor than any of the three other variables. T h e frequency of activities performed in the last month and the  Chapter 3. Results and Discussion  49  frequency of activities performed in the last year are conceptually different i n that they represent short-term and long-term involvement, respectively. However, these concepts should have equal importance i n measuring exercise behavior, which is represented by the general concept of I P A . T h e parameters for these two variables were therefore constrained to be equal i n the A  x  • MMI4'-  matrix.  T h e estimation of the parameters specified by this model converged and  produced a good fit (GFL=.96 and R M R = . 0 6 ) . A l l parameter estimates had reasonable magnitude and no large modification indices or residuals occured. This model was therefore accepted as the final measurement model for model I. Parameter values are presented in figure 3.5.  3.1.2  Structural Equation Model  M o d e l M M I 4 was used as underlying structure for the structural equation model. It was constructed as a L I S R E L model as described i n Appendix B. T h e elements of B and T were defined according to the hypothesized relationships i n model I. T h e following paths were defined as free parameters: • from A T T to I P A • from M O D to F I T • from I P A to F I T A T T and M O D are hypothesized to be correlated by definition of the L I S R E L model. It was decided to fix one A per latent variable at 1 i n order to assign a unit of measurement for latent variables. Table 3.7 contains the steps taken in testing the structural equation model. Each model is discussed i n the following section.  950  .057 Lifestex  •  ^.556  .334^.  RSelf  YearFreq •  .48  •  \^973  S  .41  .427N*  •  •  LmonFreq  •  .662^ AlcFreq  AcfScale  .973  RHealth RSocial  •  •  YearTME  Aerobic  ^485 Skinfold 7  AlcAmount  D  Smoking  D  8  2  ( M O D )  "T560 .290  • •  Situps Flexibility  Figure 3.5: Parameter Values for Final Measurement Model I  er 3. Results and Discussion  51  Table 3.7: Steps in the Development of Structural Equation M o d e l I  CMI1:  Model  Var  Conv  CMI1 CMI2 CMI3 CMI4 CMI5  15 15 15 15 15  n  x  2  df  X /df  GFI  2  RMR  CPU  -  -  -  -  -  y y n  626 625  86 87  7.3 7.2  .95 .95  .06 .07  -  -  -  -  -  y  595  86  6.9  .95  .06  2.5 2.4 3.4 3.6 3.4  This model was the "causal" version of M M I 3 . It was originally hypothe-  sized that the constraint put on the paramaters representing frequency of activities in the last month and frequency of activities i n the last year would not be necessary since structural paths were included. However, the solution for model C M I 1 indicated, that this is not the case. T h e estimation did not converge, indicated by a non positive definite 0  £  matrix. This was clearly due to a negative 9 value e  for the variable " Y E A R F R E Q " , just like i n model M M I 3 .  Therefore, the con-  straint of equal factor loading was put back onto the variables " Y E A R F R E Q " and "LMONFREQ". CMI2: T h e test of this model revealed a very good fit. T h e model suited the data well (GFI=.95 and R M R = . 0 6 ) .  A l l factor loadings were reasonably high and 3  and 7 coefficients were acceptable as well. However, the  value for I P A was very  high (32), indicating that the error i n the structural equation for I P A is very high. T h i s situation was also reflected i n a very low total coefficient of determination for structural equations (.02). Therefore the model had to be respecified i n order to solve this problem.  It was decided to fix the scale in an alternate manner.  All  factor loadings A were freed again and the diagonal elements of $ and $ were fixed at one in order to fix the variances of latent variables at one.  er 3. Results and Discussion  52  CMIS: T h e solution for this model was satisfactory (GFI=.95 and R M R = . 0 7 ) . A l l parameter estimates had reasonable values, but the coefficient of determination of structural equations was still very low (.015).  "YEARFREQ"  revealed a factor  loading above one and both " Y E A R F R E Q " and " L M O N F R E Q " had large modification indices. Since they were measured i n the same fashion but were conceptually different variables, it was decided to correlate their measurement errors. This was accomplished by freeing the off-diagonal element i n the matrix 0  £  corresponding  to these two variables. CMI4'- Unfortunately, this model d i d not yield a proper solution, indicated by a non positive definite 0 matrix. T h e problem was still related to the two variables, £  whose measurement errors had been allowed to correlate.  A negative element in  the diagonal of O indicated that one of the factor loadings was probably too high. e  It was decided to constrain the elements of A  y  corresponding to " Y E A R F R E Q "  and " L M O N F R E Q " to be equal, just like in model C M I 2 . CMI5: A valid solution was achieved that produced a good fit. T h e model fit the data well (GFI=.95 and R M R = . 0 6 ) .  A l l parameters had reasonable values  and no large residuals or modification indices were found.  T h e total coefficient  of determination for structural equations was, however, still very low, indicating that the structural parameters should be interpreted with caution. M o d e l C M I 5 was chosen as the best fitting causal model resembling the structure of theoretical model I. Parameter values of the standardized solution of model C M I 5 are presented in figure 3.6.  GFI - .952  to  RMR - .061 Lifestex  ^544  •  ActScale  .826 (ftfj)  RHealth  •  ^ _  RSocial  U  .46&/  RSelf  r-,  •  .742  .203  D .742  ^424  .54 .276  .662,, c  o 3  AlcFreq  ^493  •  O  7  8  2  ( M O D )  T 10  a  Smoking  •  LmonFreq  •  YearTME  •  Aeorblc  •  Skinfold  ^648 •  .012 AlcAmount  YearFreq  t -392  .288  •  Situps Flexibility  •  Figure  3 6: Parameter Values for Final Version of Structural Equation Model I  Chapter 3. Results and Discussion  3.1.3  54  Categorical Data Treatment  Despite receiving a good fit i n model CMI5, the magnitude of structural parameters was still very low and Hmits the interpretability of relationships. This might be due to choosing the inappropriate methodology. One of the problems with the Canada Fitness Survey data is the nature of the variables. As can be seen i n table 3.4 many variables were measured on an ordinal or even nominal scale. In the final version of the structural equation model, eight out of fifteen manifest variables were categorical variables with ordinal scales. Three out of these eight variables had less than six categories. In the model tests described so far these variables were treated as if they had underlying continuous distributions. This assumption might have been violated, which may i n turn have affected the validity of the results obtained. Procedures had to be applied that take the categorical nature of variables into account. Since programs for testing of causal models generally only require a correlation (or covariance) matrix as input with respect to the data, this input matrix had to be modified i n order to account for the categorical nature of some variables. This can be done i n the following manner: • If both variables are categorical, a polychoric correlation coefficient is computed. It is based on the contingency table between the two variables and accounts for the ordinal scaling of both variables. • If one variable is categorical and another variable has a continuous underlying distribution, a polyserial correlation coefficient is computed. It is based on a table of means for the continuous variable for each category of the categorical variable and accounts for the ordinal scaling of one variable. • If both variables have a continuous underlying distribution, a standard Pearson product-moment correlation coefficient is computed.  Chapter 3. Results and Discussion  55  This procedure produces a complete correlation matrix, which accounts for different underlying distributions and can be used as input matrix for the test of causal models. T w o methods were chosen to account for the categorical nature of some of the variables from model I. Firstly, L I S R E L provides a built-in option for the computation of an input matrix as described above. One has to read raw data and set the M V parameter i n the R A card of L I S R E L control commands equal to the minimum number of categories a continuous variable consists of. T h e program will then calculate polychoric and polyserial correlation coefficients for variables that have less than M V categories and test the model with this new input matrix i n the usual fashion. Secondly, the program P R E L I S was designed as a preprocessor of data for L I S R E L and is very useful for the analysis of categorical data. It gives detailed information about each variable, provides all contingency tables and tables of means for categories of ordinal variables, and calculates the appropriate correlation coefficients as stated above. Tests of bivariate normality are given as well. A complete correlation matrix of all variables is then produced, which can be used as input matrix for programs performing analyses of causal models. Several tests of model I were performed using both methods i n order to find out if, (1) the overall fit would improve and/or, (2) the magnitude of parameters would change, when accounting for the categorical nature of variables. T h e program P R E L I S was r u n on an I B M X T with raw data that was transferred from the mainframe. Tables and descriptive information were inspected and the output matrix of product moment, polyserial and polychoric correlations was transferred back to the mainframe.  Initial  analyses were performed with pairwise deletion of cases with missing data; however, this produced a non positive definite input matrix, which could not be used for analysis. Therefore, listwise deletion of cases was utilized i n order to produce a valid input matrix. This correlation matrix was used for all analyses using the P R E L I S input matrix. Table 3.8 lists several steps taken i n testing model I w i t h the polychoric option of L I S R E L and  56  Chapter 3. Results and Discussion  Table 3.8: Steps i n Categorical D a t a Treatment for Model I  Model  Conv  x2  df  MMI5 CMI6 CMI7 CMI8 CMI9 CMI5  y  755  72  10.5  y y y n  -  -  -  y  -  732  595  GFI  X /df 2  RMR  CPU  -  -  86  8.5  .93 .95 .95 .93  .07 .07 .06 .07  -  -  -  -  86  6.9  .95  .05  2.5 5.9 6.2 2.9 84.3 3.4  with P R E L I S input. • MMI5: A measurement model was developed similarily to M M I 4 described above using the input matrix calculated with P R E L I S . T h e structure of the model is identical to that of M M I 4 . T h e fit of the model is acceptable (GFI=.93 and R M R = . 0 7 ) , but is slightly worse than the fit of M M I 4 . A l l parameters are very similar as well. This model was then taken as the basic structure for the structural equation model of model I. •  CMI6:  T h e structural model was constructed i n a manner similar to the con-  struction of C M I 1 . Because the adjustment of the input matrix may violate the assumption of multivariate normality, which is required for maximum likelihood ( M L ) estimation of the model, a different estimation procedure was chosen. Unweighted Least Squares ( U L S ) is an estimation method, that is not as precise as M L , but does not require distributional assumptions about the data. M o d e l C M I 6 was therefore estimated with U L S . T h e analysis produced valid parameter estimates that are very similar to the ones for model C M I 5 , presented i n figure 3.6. A s shown i n table 3.8, U L S does not have an underlying % distribution and can therefore not 2  produce a % value. Other criteria for overall fit are very similar to the values for 2  model C M I 5 (GFI=.95 and R M R = . 0 7 ) . Values for model C M I 5 are listed i n the  57  Chapter 3. Results and Discussion  last row of table 3.8 for comparison. Due to reasons described for model C M I 4 , the measurement error between " Y E A R F R E Q " and " L M O N F R E Q " was respecified as a free parameter for this model as well. •  CMI7: T h e estimation of the model converged and produced a slightly better fit than model C M I 6 (GFI=.95 and R M R = . 0 6 ) .  Because no locations for potential  specification errors could be detected, this model was accepted as the final structural model of model I using P R E L I S input data. Although the factor loadings of the solution were very similar to those of model C M I 5 , the structural coefficients representing the hypothesized causal relationships were slightly higher. •  CMI8: Model C M I 7 was also tested using maximum likelihood estimation. T h e estimation converged and produced a solution very similar to C M I 7 and C M I 5 . The fit is slightly worse (GFI=.93 and R M R = . 0 7 ) , but factor loadings are very similar. Causal path coefficients are lower than i n model C M I 7 , but still slightly higher than i n model C M I 5 .  •  CMI9: It was attempted to run a test with the built-in option of L I S R E L , but a not positive definite input matrix prevented the program from starting the estimation process. This occured despite the default of listwise deletion of cases with missing data. After several more attempts it was decided that all this option did was spend amazing amounts of computer dollars.  3.1.4  Non-Normal Data Treatment  One of the most important underlying assumptions of analyzing complex structures with maximum likelihood estimation is multivariate normality.  Violating this assumption  could affect analyses and therefore produce invalid results. In order to examine whether  Chapter 3. Results and Discussion  58  a violation could have affected the results i n this study, it firstly had to be assessed whether the Canada Fitness Survey data was normally distributed or not. Normality of distribution was assessed on three levels: •  Univariate normality: distributional statistics were examined i n table 3.4, and it was discovered that a number of variables had large kurtosis values.  • Bivariate normality: gooodness-of-fit tests via P R E L I S indicated that many pairs of variables do not satisfy this assumption. • Multivariate normality: Mardia's coefficient of multivariate kurtosis calculated with the E Q S program indicated significant non-normality. Therefore, the assumption of normality of the data is not met on each of the three levels of normality. In order to solve the problem given by this violation, structural equation estimation procedures, which do not require the assumption of multivariate normality have to be applied to the data. T h e program E Q S provides two methods of estimating parameters from non-normal data. • Elliptical distribution theory allows distributions of variables with heavier or lighter tails. Therefore, variables may depart from normal distributions with respect to kurtosis. However, kurtoses are assumed to be equal for all variables. • Arbitrary distribution theory, which uses an asymptotically distribution-free ( A D F ) procedure to estimate parameter values, requires no restrictions on skewness or kurtoses of variables. T h e estimation is, however, computationally very demanding and therefore becomes impractical, if the number of variables exceeds twenty. Arbitrary estimation should also not be used with small samples. Sources for descriptions of these theories and explanations of both methodologies are described i n detail i n the E Q S manual (Bentler, 1985).  59  Chapter 3. Results and Discussion  Table 3.9: Steps in Non-Normal D a t a Treatment of Model I  Model  Conv  CMI10 CMI11 CMI12  y y y  x  2  df  X /df  595 492 539  86 86 86  6.9 5.7 6.3  2  GFI .91 .89 .96  RMR .05 .05 .06  Table 3.9 provides a list of analyses performed with the E Q S program. A P C version of the E Q S program was installed and run on an I B M X T to perform the following model tests. •  CMI10: In order to insure that the results generated by E Q S are directly comparable with L I S R E L results, model C M I 5 was analyzed with the standard maximum likelihood estimation of E Q S . Parameter estimates and goodness of fit criteria were almost identical with those obtained from L I S R E L . Because Bentler reports his own normed fit index the value for G F I is slightly different.  However the fitting  function has an identical value at its minimum, indicated by equal % values. 2  o CMI11: T h e model was then subjected to elliptical generalized least squares estimation followed by elliptical m a x i m u m Hkelihood estimation.  Model C M I 1 0 had  similar parameter values to model C M I 9 . Although the % dropped by over 100, 2  the G F I was slightly lower (GFI=.89 and R M R = . 0 5 ) . •  CMI12: Arbitrary generalized least squares were then applied to the model and again a similar solution was found. T h e x2 value dropped again and the G F I was quite a bit larger, indicating a better fit (GFI=.96 and R M R = . 0 6 ) .  A l l three methods ( M L , E M L , A G L S ) produced very similar solutions.  From the in-  formation given it could not be concluded, whether the maximum likelihood estimation was robust with respect to departures from normality, as indicated in the literature (e.g.  Chapter 3. Results and Discussion  60  Anderson & Gerbing, 1988), whether the elliptical and arbitrary estimation procedures generally produced results that are very similar to results from m a x i m u m likelihood estimation, or whether the solutions just happened to be very similar for the present dataset.  3.1.5  Summary  A large number of analyses were performed i n order to test model I. After the development of measurement models for exogenous and endogenous variables, these were combined into a total measurement model. After several modifications M M I 4 was defined as the final measurement model. It revealed good overall fit and reasonably high factor loadings. This measurement structure was then implemented into the structural equation model. Model C M I 5 represents the final version of the structural equation model. It has a reasonable overall fit and interpretable parameter values. T h e structural path coefficients are very low, which indicates that the hypothesized relationships between constructs are rather weak. Several additional tests of the model were performed. A n overview of all final solutions for the structural equation model of model I is given i n table 3.10. T h e input matrix, treatment of missing data, estimation method, status of the solution, and the goodness of fit index are given. In order to detect whether parameter estimates and/or overall fit assessment criteria are affected by possibly violating underlying assumptions, several other methods accounting for these violations were applied to model I. Several categorical variables were included in the Canada Fitness Survey data set and a continuous underlying distribution was assumed for them i n traditional maximum likelihood estimations of the parameters. T h e P R E L I S program was applied to the dataset i n order to produce a new input matrix. This matrix included polychoric and polyserial correlations, which account for the assumption of continuous distribution i n categorical variables. Results from testing  61  Chapter 3. Results and Discussion  Table 3.10: Summary of Solutions for Structural Equation Model I  Model  Input  Missing  Estim.  Conv  GFI  CMI5 CMI9 CMI7 CMI8 CMI10 CMI11 CMI12  LISREL P P M L I S R E L Poly P R E L I S Poly P R E L I S Poly EQS P P M EQS P P M EQS P P M  Pairwise Listwise Listwise Listwise Listwise Listwise Listwise  ML ML ULS ML ML EML AGLS  y n  .95 .95 .93 .91 .89 .96  y y y y y  model I with this input matrix revealed very similar parameter estimates and overall fit measures.  However, the structural path coefficients were slightly higher, indicating  stronger relationships between latent variables.  M a x i m u m likelihood and unweighted  least squares solutions were very similar for the P R E L I S input. It can be concluded from this study that adjusting the data for categorical variables can be performed by using the P R E L I S program. Even though the overall fit of the model to the data did not seem to be affected, the causal path coefficients appeared to be larger for the P R E L I S input with the Canada Fitness Survey dataset. The assumption of multivariate normality was tested on the C F S data, and found to be violated on the three levels of univariate, bivariate and multivariate normality. T w o alternate estimation procedures available under the E Q S computer program were then applied to the model i n order to test whether they can produce a different solution or an improved fit. B o t h elliptical distribution theory and arbitrary distribution theory estimation methods produced similar solutions with similar overall fit measures. It was concluded that for the given dataset these alternate methods did not produce a different solution or a different fit of the model to the data. The test of a relatively simple model such as model I, can be a lengthy process involving many different steps. A satisfactory solution was achieved for model I. Alternate  Chapter 3. Results and Discussion  62  methods may be advantageous, but produced very similar results to standard procedures in this study.  3.2  Model II  Descriptive statistics were obtained for the manifest variables selected to measure the abstract constructs of model II. Means, number of subjects with missing data, minimum, maximum, skewness and kurtosis for these variables are given i n table 3.11. After careful inspection and several datachecks, a Pearson product-moment correlation matrix was calculated as input for all analyses. This correlation matrix is shown i n table 3.12.  3.2.1  Measurement Model  The measurement model for model II was constructed as described i n A p p e n d i x B and shown i n figure 2.4. T w o latent variables defined i n model II had to be transformed into manifest variables, since only one manifest variable could be found, which measured the abstract concept. Adherence is a direct measure of past experience with physical activity ( P E P ) . T h e Bradburn scale was the only indicator that was available from the C F S data that measured psychological fitness ( P S Y ) . These variables represent a single indicator and therefore no measurement structure exists for them. In the L I S R E L model they are defined as latent variables, but they are not included as part of the measurement model. Therefore the initial measurement model consisted of the following 6 latent variables measured by 24 manifest variables: • Attitude ( A T T ) - 4 indicators • Motivation ( M O T ) - 3 indicators • Barriers ( B A R ) - 2 indicators  Chapter 3. Results and Discussion  63  Table 3.11: Descriptive Statistics for Manifest Variables of M o d e l II  Variable xl x2 x3 x4 x5 x6 x7 x8 x9 xlO xll xl2 xl3 xl4 yi y2 y3 y4 y5 y6 y7 y8 y9 ylO yii yi2  Latent  Scale  Adherenc Reas H F Reas S O Reas S E Reas A D V Lifestex Per F i t Per Hea  PEP ATT ATT ATT ATT MOT MOT MOT  Ord Ord Ord Ord Ord Ord Ord Ord  Barriers Health Age Marital Educat Income A c t Sea Year G a m e Year A c t i T M E Game T M E Acti Aerobic Pushups Situps Flex Strength Skinfold Bradbum  BAR BAR SOC SOC SOC SOC IPA IPA IPA IPA IPA PHY PHY PHY PHY PHY PHY PSY  Ord Ord Int Nom Ord Ord Ord Int Int Int Int Int Int Int Int Int Int Ord  n  miss 106 157 124 155 258 66 42 36  X 4.72 7.48 3.90 4.65 5.81 1.66 1.97 1.21  Min  Max  Skew  Kurt  1.00 4.00 2.00 2.00 2.00 1.00 1.00 1.00  7.00 16.00 8.00 8.00 8.00 4.00 3.00 3.00  -.53 .67 .57 .29 -.46 1.04 .01 2.54  -1.45 .11 .06 -.60 -1.08 .45 -.25 5.08  0 36 0 11 51 438 33 0 0 0 0 383 415 442 389 351 45 108  1.73 1.21 29.28 1.38 4.10 4.52 2.55 3.55 15.03 31.07 62.70 44.15 21.70 30.44 29.74 108.07 53.87 8.31  0.00 1.00 20.00 1.00 1.00 1.00 1.00 0.00 0.00 0.00 0.00 26.00 0 0.00 1.00 47.00 15.90 1.00  4.00 3.00 40.00 2.00 7.00 7.00 3.00 69.67 89.58 892.00 1267.88 62.00 110.00 70.00 73.00 161.00 146.60 19.00  .41 2.54 .13 .50 .27 .03 -.85 3.08 1.50... 4.53 4.06 .50 1.01 .09 -.25 -.01 1.00 .10  -1.08 5.08 -1.14 -1.75 -1.33 -.63 -.27 15.76 2.10 30.72 24.51 -.64 2.67 .60 .17 .39 1.02 .16  CORRELATION  RHF RSOC RSELF RADV PEflHEALT L I F E 7 ', PERF1T BARRIERS HEAL TM MARITAL EOUCAT INCOME ACE YEARCAME YEAflAC T, I TUEGAME TMEACT1 AC TIVSCA SKINFOLD AEROBIC GRIPSTR PUSHUPS FLEXION S I TUPS  EOUCAT INCOME AGE YEARGAME YEARACTI TMEGAME TMEACT I ACTIVSCA SKINFOLO AEROBIC GRIPSTR PUSHUPS F L E X ION SI TUPS  CRIPSTR PUSHUPS FLEXION S I T UPS  RUT  MATRIX  000 0i. 1 9 5  0. 4 1 3 0 . 379 0 065 0 45 1 - 0 . 075 •0 .018 0 .00 7 -0 . 0 1 3 •0 •0 . 0 1 ? •0 . 0 4 6 - 0 .077 - 0 , 177 • 0 . 068 • 0 . 140 - 0 . 114 •0 043 0 .000 0 024 -0. 07? - 0 037 • 0 054  on  EOUCAT 1 .0 0 0 0 23 1 0 024 0 122 0 ..i* 1 0 094 0 .084 0 . 148 • 0 001 0 .001 -0 .07? 0 .088 0 009 0 169  GRIPSTR . 1.000 0.140 0.123 0.094  DETERMINANT  TO BE ANALYZEO  RSOC  RSELF.  1 000 0 . 421 0 . 154 0 . 045 0 236 - 0 . .046 •0 . 0 1 2 0 .028 - 0 .043 0 .048 0 .037 0 . 134 •0 . 176 0 033 • 0 163 • 0 . 006 - 0 . 103 0 048 - 0 . 121 • 0 .057 - 0 . .036 • 0 . 040 • 0 . 090  INCOME .  1. 0 0 0 0 . 262 0 . 055 0 . 260 • 0 113 - 0 . 006 0 018 • 0 . 059 0 073 0 052 0 129 • 0 . 145 •0 045 - 0 131 - 0 . 070 • 0 . 1 16 0 . 063 - 0 101 • 0 . 083 • 0 . 105 • 0 . 073 - 0 . 146  AGE  1 000 0 258 0 .047 - 0 .027 0 .024 - 0 U20 0 .08 1 0 . 1 15 -0 . 1 1 3 0 .092 -0 .015 - 0 028 0 006  PUSHUPS..  i . 000 - 0 207 - 0 . 114 - 0 . 188 • 0 . 157 - 0 . 102 0 . 171 • 0 353 • 0 . 019 - 0 . . 308 - 0 128 • 0 433  FLEXION  1.000 0.254 0.505  = 0.265731E-02  1.000 0.21?  RAQY  PfRHEALI  LIFE;  1. 0 0 0 -0 040 0 138 0 . 069 - 0 .04 7 - 0 .06 7 0 . 123 0 . 203 0 .072 • 0 .117 0 079 0 .058 0 .06* 0 .027 0 091 - 0 . .074 0 .081 0 .018 0 102 0 . 044 0 . , 158  1 000 0 121 - 0 400 0..074 0 128 0. 029 • 0 034 • 0 .066 • 0 .057 - 0 .117 - 0 . 122 - 0 114 • 0 . . i 3r> 085 0 143 • 0 . 153 - 0 . 058 - 0 . 191 - 0 . 098 • 0 . 123  I .0 0 0 - 0 183 • 0 . 006 • 0 . 00 7 - 0 . 078 - 0 . 092 - 0 . 008 0 . 102 • 0 . 237 - 0 . 188 • 0 . 20 3 • 0 . 154 • 0 . 187 0 088 - 0 . 128 0 . 012 • 0 . 176 - 0 065 - 0 . 196  TEARGAME  YEARACU  1MEGAME_  1 000 0 . 148 0.871 0.146 T.246 -0.074 0.180 0.044 0.149 0.071 0.258  1.000 0.114 0.870 0 416 -0.10T 0.137 -0046 0.202 0.064 0 215  I 000 0.139 0.205 -0.087 0.171 0.048 0.123 0.052 0 219  SITUPS  1.000  •o.  PERfll.  1 •0 •0 0 0 0 0 0 0 0 0 0 -0 0 0 0 0 0  .0 0 0 083 075 054 056 064 002 1 38 174 . 129 1 78 157 258 250 056 298 165 262  TMEACT I  1 000 0 266 . C 116 0.164 0 028 0.192 0.080 0.215  BAHBILBS  1 .000 "049 -0.1)34 0 007 •0 001 0.004 0.015 •0.008 0.008 •0 033 0.059 0.072 -0.065 0.014 •0 086 •0.038 •0.055  ACTIYSCA  HEAL IM  *  000  0 •0 -0 0 •0 0 •0 0 •0 u •0 •0 •0 0 •0  018 063 061 031 024 .028 001 008 018 031 020 .040 000 023  Cl*  SKINFOLD  MARITAL..  1.000 0.059 •0 232 •0.493 0 119 0.206 0 . 105 0.191 0.093 -0.165 0.191 •0.074 0.231 0.044 0.287  AEROBIC  1 000  o. 074  0 103 0 .052 0 162 0 023 0 222  1 •0 0 •0 •0 -0  000 431 080 354 199 323  1 .0 0 0 - 0 127 0 . 32 l 0 129 0 33?  Chapter 3. Results and Discussion  65  • Social Status ( S O C ) - 4 indicators • Involvement ( I P A ) - 5 indicators • Physical Fitness ( P H Y ) - 6 indicators Only two endogenous latent variables were defined i n model II. Since they both had fairly distinct indicators, separate tests of the exogenous and endogenous variables were not considered necessary. T h e complete measurement model was constructed as a L I S R E L model under SPSS and several modified models were tested i n order to develop its final form.  Table 3.13 contains a fist of all analyses performed.  It lists the nature of each  model, the total number of manifest variables, whether the model converged or not, % , 2  associated degrees of freedom, x 2/df ratio, Goodness of F i t Index (GFI), and Root Mean Square Residual ( R M R ) . Each step is described i n the following section: Table 3.13: Steps i n Development of Measurement Model II  • MMII1:  Model  Var  Conv  MMII1 MMII2 MMII3 MMII4 MMII5  24 20 18 17 17  y y y y y  x  2  6057 4244 1191 869 676  df 237 155 120 104 104  X 2/df 25.5 27.4 9.9 8.4 6.5  GFI .85 .88 .94 .96 .97  RMR .09 .08 .05 .04 .04  T h e test of the original measurement model did, surprisingly, produce a  valid solution. Some parameters were very low, however. T h e overall fit was not very good (GFI=.85 and R M R = . 0 9 ) . A closer look at parameter estimates revealed several potential weaknesses in the factor structure. T h e Specialist's Advice factor of the attitude scale had a low factor loading and very large modification indices (all about 100). Examination of the residuals provided further support for the  Chapter 3. Results and Discussion  66  conclusion that this variable is not a very useful indicator of attitudes. It appeared to measure every other latent variable, but could not be conceptually related to any of them. Therefore it was decided to exclude Specialist's Advice as a measure of attitudes. T h e factor loading for education was only A = — .01 and a look at the raw residuals confirmed the conclusion that education did not measure the same concept of social status that the other three variables measured.  Four residuals  were larger than .1, and two residuals were larger than .2. Education could not be conceptually related to any other latent construct. The extreme complexity of relationships amongst demographic variables has been discussed i n section 2.3.6. Based on these considerations, education was excluded as an indicator of social status.  Originally, involvement measures for games and activities (as described  in section 2.2) were included as conceptually different measures of I P A . B o t h the frequency and the total metabolic expenditure measure for games revealed relatively low factor loadings compared to the corresponding measures for activities. However, at this stage of the analysis all indicators of I P A were retained.  T h e physical  fitness factor contained two very low factor loadings for gripstrength and flexibility. Examination of the correlation matrix revealed that both measures had very low correlations with other measures of physical fitness.  They measure very specific  physical fitness aspects, namely muscular strength and flexibility; these aspects are probably more dependent on specific training rather than on I P A per se. Therefore, they were eliminated as indicators of physical fitness. T h e variable importance of exercise had the largest modification index ( M I = 372). Inspection of the matrix of residuals confirmed the implication of this index, that it really measures attitude and not motivation. Because it measures how important regular physical activity is for a general feeling of well-being, it was hypothesized to be an indicator of attitude rather then motivation. These considerations were implemented into the  er 3. Results and Discussion  67  next model.  MMII2:  The solution for this model produced a drop i n % of almost 2000, which 2  indicated a significant improvement.  However, the fit was still unsatisfactory  (GFI=.88 and R M R = . 0 8 ) . The lowest factor loadings, highest modification indices and largest residuals occured for the two measures of I P A relating to activities. It appeared as if L I S R E L wanted to treat the I P A factor as two separate factors. T h e correlation between A C T I and G A M E measures is very low, because subjects who play many games do not run as much and vice versa, as mentioned earlier. After another inspection of the analyses of different I P A scores, which are discussed i n section 2.2.7, it was decided to only include total measures of all major activities combined as measures of I P A .  MMII3:  T h e substitution of I P A measures improved the fit of the measurement  model tremendously. The % value dropped by over 3000, and the overall fit was now 2  very good (GFI=.94 and R M R = . 0 5 ) .  A l l parameters had reasonable magnitude,  with only four factor loadings being under .5. Examination of residuals revealed that the attitude measures had correlations that could not be precisely reproduced by the model. Modification indices for importance of exercise were fairly large and its exclusion was therefore decided. It did not measure the same concept as the attitude scale i n the questionnaire.  MMII4ference in x  T h e estimation of model M M I 4 produced a superior solution. 2  w  a  s  T h e dif-  A = 1620 — 869 = 751 with associated degrees of freedom  df — 120 — 104 = 16 which was a highly significant improvement of fit. The overall fit was very good (GFI=.96 and R M R = . 0 4 ) . Except for measures of barriers and income, all factor loadings were above .4. T h e total coefficient of determination  68  Chapter 3. Results and Discussion  of ai-variables was .999, indicating that the data fits the hypothesized factor structure well. N o extremely large modification indices or residuals existed. Skinfolds represented a measure of anthropometric characteristics, and even though weight loss and reduced percent body fat have been shown to be directly associated with involvement i n physical activity, somatotype is dependent on a hereditary component as well. It is therefore not a direct measure of physical fitness like the other measures (aerobic power, situps, pushups). Originally defined measures for physical fitness were reconsidered and flexibility was found to have reasonably high correlations with these three measures. Therefore skinfolds was replaced by flexibility as a measure of physical fitness. Flexibility is a specific component of physical fitness, which has been shown to be directly associated with increased exercise. • MMII5: T h e estimation for this model converged and produced a very good solution. T h e x2 value dropped almost by 200, which indicated that the fit improved. T h e overall fit of the model was good (GFI=.97 and R M R = . 0 4 ) .  T h e parame-  ter values were very similar to the ones produced by M M I I 4 , and indicated that the data fits this hypothesized factor structure very well. A l l modification indices were reasonably low, and no large residuals emerged. N o location for a potential specification error could be found, and therefore M M I I 5 was accepted as the final measurement model for model II. Parameter values for model M M I I 5 are shown i n figure 3.7.  3.2.2  Structural Equation Model  T h e final version of the measurement model was used as the underlying measurement structure for the structural equation model.  T h e structural equation model was con-  structed similarily to model I. In order to assign the unit of measurement for latent  GF1 • .965  RHealth  to  RMR - .040  RSocial RSelf  .910  .619  e  PerFit PerHealth  Barriers c  .0 V)  c  3  .494  _  _  •  Aerobic  D  Pushups  •  Situps  •  Flexibility  .722  .770  Health  • •• Act  Age  YearTME Year F r e q  Marital Income .893 Figure  3.7: Parameter Values for F i n a l Version of Measurement Model II  Chapter 3. Results and Discussion  70  variables the factor loading (A) of the first manifest variable for each latent variable was fixed at one. T w o single manifest variables, adherence and Bradburn scale, were defined as latent variables. Their factor loadings (A) were fixed at one as well and their measurement error (6$ and 8 , respectively) was fixed at zero. This procedure ensured e  identification of the model. Even though the two variables are defined as latent variables i n the model, they are only measured by themselves and therefore their scale should be fixed. Elements of the T and B matrices were defined as free parameters according to the hypothesized relationships between latent variables defined i n model II (see figure 2.4). The following directed causal relationships were included i n the model: • from P E P to I P A • from P E P to P H Y • from A T T to I P A • from M O T to I P A • from B A R to I P A • from S O C to I P A • from I P A to P H Y • from I P A to P S Y • from P H Y to P S Y P E P , A T T , M O T , B A R and S O C were hypothesized to be mutually correlated by definition of the L I S R E L model. Only one version of the structural equation model was tested:  Chapter 3. Results and Discussion  •  71  CMII1: T h e original version of the structural equation model of model II was analyzed as a L I S R E L model and the estimation converged. A satisfactory solution was achieved. T h e overall fit of the model was good (GFI=.93 and R M R = . 0 8 ) . The standardized solution revealed factor loadings that were very similar to the parameters from the final measurement model. A l l structural parameters had reasonable values and were interpretable.  T h e matrix $ contained no unreasonable  values. T h e correlation between barriers and motivation was high (r=.61). Model C M I I 1 was therefore accepted as the final version of the structural equation model for model II. A l l parameters from the standardized solution of the structural equation model are shown i n figure 3.8. T h e largest modification indices occured for structural path coefficients i n the matrices B and T. T h e modification index for the path from physical fitness to I P A , for example, is 776, which is fairly large and would imply a m i n i m u m reduction i n % of almost one third. In terms of the model 2  the high value of this index means, that relaxing this paramater would result i n an improved fit. Therefore, if a causal relationship between physical fitness and involvement in physical activity had been hypothesized in conjunction with the already denned relationships, the hypothetical model would have probably suited the data better. However, this directional path would imply a reciprocal relationship between I P A and physical fitness, which contradicts the defined hypothetical model. This structural parameter can therefore not be relaxed. As mentioned i n A p p e n d i x B, relaxing a structural paramater after a model has been defined defies the purpose of causal modeling and should only be done i n extreme cases. Causal modeling techniques test models that are based on theory and have been defined a priori. Even if a new path, which would improve the fit of a model, can be interpreted properly, the model should therefore generally not be respecified with this new parameter.  apter 3.  Results and Discussion  72  "0 3 O O  3  DO  — 09  > (»  CD  2.  3"  2  I 9 0  ~0 ft  13 73 CO CO o ft o —  37 I ft » 3"  >  Q.  (V 3 O ft  73  Chapter 3. Results and Discussion  One can, however, attempt to explain the occurence of high modification indices. In the case described above such an explanation can be given. People who are physically fit tend to have the urge to maintain their fitness, because they feel good about their physical state. Physically fit individuals are also able to perform activities that an unfit individual cannot perform, such as high intensity activities.  In fact, reciprocal effects  can probably be explained for exogenous latent variables as well. Being physically fit and feeling better mentally due to involvement i n physical activity could change one's attitude towards physical activity and one's motivation to participate i n them. Other high modification indices occurred for paths between M O T and P H Y , B A R and P H Y , S O C and P H Y . Increased motivation to participate i n an activity could i m prove general well-being which affects physical fitness. Barriers towards participation i n physical activity could prevent an individual from participating i n other activities as well, which could have a direct effect on health and therefore physical fitness. Individuals with high social status generally live in a healthier environment and lead a healthier lifestyle, which affects physical fitness. These statements represent tentative thoughts rather than specific conclusions.  3.2.3  Summary  M o d e l II was theoretically developed based on findings reported i n the literature review. A measurement model was constructed as a L I S R E L model and after several tests a model with a very good fit was achieved ( M M I I 5 ) . This model consisted of 6 latent and 17 manifest variables. T h e measurement structure was then implemented into the structural equation model.  T w o single indicator variables were defined and included as latent  variables as well. T h e structural equation model consisted of 8 latent and 19 manifest variables and 9 hypothesized causal paths. It was tested and a satisfactory solution was produced by the estimation process.  T h e overall fit of model C M I I 1 was acceptable.  74  Chapter 3. Results and Discussion  Parameter values for manifest variables were of reasonable magnitude. path coefficients were reasonably large and interpretable.  T h e structural  Therefore, the hypothetical  model of I P A , model II, was found to fit the Canada Fitness Survey data well.  3.3  Predictors and Consequences of IPA  T w o models of involvement i n physical activity and its predictors and consequences have been successfully tested on a subsample of (n=3055) 20 to 40-year old males from the 1981 Canada Fitness Survey.  Measurement models indicated strong factor structures.  The tests of structural equation models produced solutions that revealed good fits of the models to the data. T h e parameter estimates from these models can now be used to interpret the results i n terms of the theoretical models. Findings are interpreted for model I and II i n the next sections, followed by a comparison of results.  3.3.1  Model I  M o d e l I represents the conceptual model of fitness denned by the Canada Fitness Survey. It was not developed as a causal model and it was not based on solid theoretical grounds. Due to the lack of established theory it was decided a priori to test model I using a modelbuilding approach.  This approach is different from the truly confirmatory  approach  often required i n testing causal models i n that it gives the researcher more freedom to respecify the model i n order to produce a model with an acceptable fit to the data. During this building process of model I, the concept of barriers had to be eliminated because no valid measures could be found i n the dataset. M a n y tests did not converge and "respecification tricks" had to be used as described above. T h e final solution for the structural equation model C M I 5 has a good fit, indicated by a high Goodness of F i t Index (.95) and a low Root Mean Square Residual (.06). Since no locations for potential  Chapter 3. Results and Discussion  75  improvement of the fit could be found, this model fits the data best within the context of the specified theoretical model. T h e correlation matrix S reproduced by the model with maximum likelihood estimation is similar to the sample correlation matrix S. However, the estimation produced low structural path coefficients and a very small coefficient of determination for structural equations. Because of these results and the more exploratory approach to the analyses, the parameters are interpreted with respect to the hypothetical model I only. References to existing literature cannot be made. Parameter values from the final solution for model CMI5 are shown i n figure 3.6. Several conclusions were made with respect to measurement of the latent variables. Note that a negative factor loading is simply due to reverse scaling and can therefore be ignored for interpretations. • A T T : Attitudes were adequately represented by the three scales of reasons for being physically active and by the measure of importance of exercise for one's lifestyle. Health and fitness reasons for involvement seemed to be the strongest measure of attitude. • M O D : Alcohol and tobacco habits formed a factor of modifying variables. T h e number of drinks consumed per drinking occasion, representing the intensity of the drinking habit, was the strongest measure of this factor. • I P A : Involvement i n physical activity was adequately measured by the activity scale, defined by the Canada Fitness Survey, two measures of total frequency of all activities and a measure of total metabolic expenditure. T h e measures of frequency assessed long-term (in the last year) and short-term (in the last month) involvement and were constrained to be of equal importance i n measuring I P A . They are the strongest measures of I P A , indicated by high factor loadings.  76  Chapter 3. Results and Discussion  • F I T : Fitness was adequately measured by predicted aerobic power, the sum of five skinfolds, situps and flexibility.  Flexibility h a d a rather low factor loading  (.29), indicating that it is not a strong measure of fitness as measured by the other three variables. Aerobic power and skinfolds contributed equally as the strongest measures of F I T . The structural path coefficients from the standardized solution of the final version of the structural equation model indicate the strength of relationships between latent variables. Model C M I 5 produced very low path coefficients, indicating that the hypothesized relationships are probably not very strong. The 1981 Canada Fitness Survey was a crossnational survey that produced a large sample (n=3055), and therefore this sample can be considered representative of the population of 20 to 40-year old Canadian males. Generalization can therefore be made with respect to this population. The strongest path coefficient occurred from I P A to F I T (8. = .28). This confirms the strong evidence i n the literature, which suggests that exercise can improve physical fitness. Although the relationship is not very strong i n this model, the significant parameter suggests, that a Canadian 20 to 40-year old male, who participates i n physical activities is more physically fit than an individual from the same population, who does not exercise very much. The path coefficient from A T T to I P A was 7 = .20. According to this model, individuals who have a positive attitude towards being physically active do i n fact participate in physical activities to a greater extent than those with less positive attitudes. The path coefficient from M O D to F I T was insignificant ( 7 = .01). It can be concluded that drinking and smoking habits do not affect physical fitness. Comparing the paths M O D to F I T and I P A to F I T it can furthermore be concluded that it is probably more important to become more physically active than to change drinking or smoking  77  Chapter 3. Results and Discussion  habits i n order to improve physical fitness. Finally, attitudes towards participation i n physical activities and smoking as well as drinking habits are virtually uncorrelated ((j)  =  —-01). Since there is no theoretical basis  for a significant correlation between these two concepts, this finding was expected. Alternate methods for analyzing the Canada Fitness Survey data were applied to model I i n order to account for categorical data and non-normally distributed data. Categorical and non-normal data was present i n the C F S dataset and some basic underlying assumptions were therefore violated, which might have produced invalid results. Model estimations with a P R E L I S input matrix, accounting for categorical data, were performed with unweighted least squares and maximum likelihood estimation methods. Elliptical and arbitrary estimation methods available under E Q S were utilized to test model C M I 5 , accounting for violations of the assumption of multivariate normality. T h e only analysis that produced significantly different results from standard maximum likelihood estimation was the unweighted least squares estimation of model C M I 5 . Although factor loadings were very similar to the ones presented i n figure 3.6, structural path coefficients were all larger. The estimated coefficients were 8 = .38 for the path from I P A to F I T , 7 = - . 3 0 for the path from A T T to I P A , and 7 = .04 for the path from M O D to F I T . These results suggest, that accounting for categorical data may produce estimations which suggest stronger relationships than i n the standard solution. However, no general statements could be made about the applicability of alternate methods and therefore the standard maximum likelihood solution of model C M I 5 was accepted as the final version of model I. In summary, the above conclusions have to be regarded with caution for two reasons. Firstly, model I was not developed on a strong theoretical basis and therefore the final version of the model was developed i n a mo del-building process. A s explained i n A p p e n d i x B, many valid structures can be found for the same dataset, and therefore a  78  Chapter 3. Results and Discussion  better fitting model, which is easier to interpret, could exist.  Secondly, the structural  parameters were very low, indicating that the discussed relationships are not very strong. It is important to note that there are two distinct situations with respect to model solutions, which require different interpretations.  In the case of an acceptable, but not  very good fit, it is concluded that the model does not fit the data very well, based on criteria for overall fit. N o strong statements about the hypothesized relationships can be made based on the structural path coefficients, regardless of their magnitude, since they were not estimated very accurately. In the case of a good fit of the model, it is concluded that the model does fit the data. Conclusions can then be drawn from the magnitude of the causal path coefficients. If a causal path coefficient is high, support has been gained for the hypothesized relationship. If a causal path coefficient is low, no strong statements can be made about the hypothesized relationships, similarily to the first case. M o d e l I is an example of the last situation: the model fits the data well, but low causal path coefficients prevent firm conclusions about hypothesized relationships. In order to eliminate the limitations given by the solution of model I, model II was developed and tested.  3.3.2  Model II  Based on a review of the literature pertaining to predictors and consequences of involvement i n physical activity, model II was developed as a model of I P A , its causes and predictors. This model was based on theoretical grounds; concepts and relationships can be justified with existing evidence. Because this model had been developed from theoretical considerations, a more confirmatory approach was taken with respect to testing the model. This implied more restrictive analyses i n the sense that only minor respecifications were performed and not as many tests were performed as for model I. A l l respecifications were justifiable with theoretical arguments.  A measurement model of latent variables,  79  Chapter 3. Results and Discussion  except for two single indicators, was tested and after a few respecifications a measurement structure with a very good fit was produced. This measurement model was then implemented into the structural equation model. It was tested and accepted as the final structural equation model for model II. This illustrates the confirmatory approach taken for the test of model II. It is recognized that alternate models might have produced better fits to the data. However, the intent of the study was to test the relationships hypothesized i n model II, rather than finding the strongest possible relationships between the defined latent variables. The overall fit of model C M I I 1 was good, indicated by a high Goodness of F i t Index (.93) and low Root M e a n Square Residual (.08). No locations for potential fit improvements, which would not alter the basic theoretical structure of the model, could be detected. A s discussed above, relaxing additional structural parameters could have possibly improved the fit of the model, but the confirmatory nature of the model eliminated this option. It can be concluded, that model C M I I 1 fits the data well. Parameter values for the standardized solution of model C M I I 1 are shown i n figure 3.8. The following conclusion could be drawn with respect to the measurement of latent variables. • A T T : Attitudes towards participating i n physical activities were adequately measured by the three scales representing Health and Fitness, Social and Personal Development reasons for involvement.  T h e Personal Development scale was the  strongest measure of attitudes. • M O T : Motivation was well represented by a measure of perceived health and a measure of perceived fitness. • B A R : Barriers were measured by a sum of barriers to physical activity and by a measure of limitations due to illness or injury. T h e factor loadings were very low,  Chapter 3. Results and Discussion  80  indicating that these variables did not form a strong distinct factor. • S O C : Social status was measured adequately by age, marital status and income. Age was the strongest measure. • I P A : After elimination of scores representing "games" and "activities", as described above, three variables were retained to form a strong measure of I P A . T h e activity scale derived by the Canada Fitness Survey, and measures of frequency and total metabolic expenditure for 24 major activities all revealed factor loadings over .5. Total metabolic expenditure, which is an indication of the overall effort invested by the individual, appeared to be the strongest measure of I P A . • P H Y : Predicted aerobic power, pushups, flexibility and situps represented strong measures of physical fitness. Flexibility had the lowest loading, while situps were the strongest indicator of physical fitness. The path coefficients estimated by the model, which represent the hypothesized causal relationships i n model II, are of reasonable magnitude. Past experience with exercise, as measured by adherence to exercise, is strongly related to physical fitness. T h e path coefficient from P E P to P H Y is 7 = . 3 3 . M a n y benefits from physical activity have a long term effect on physical fitness. The onset and duration of improvements i n physical fitness is dependent on the type of physical activity performed. Individuals who have been involved i n physical activities i n the past are more likely to be physically fit now, as indicated i n the physical activity literature (e.g., Dishman, 1982; G o d i n et al., 1987; Mullen, Hersey & Iversen, 1987). This conclusion is supported by the model. Past experience lias small influence on actual exercise behavior, indicated by a low 7 = .15 from P E P to I P A . Therefore, people with experience i n exercise do not necessarily  Chapter 3. Results and Discussion  81  become more involved i n physical activities than people with no experience. Conversely, lack of experience does not appear to limit newcomers very much to become active. This finding does not correspond to findings by G o d i n et al. (1987) and Hammitt (1984). These authors found relatively strong relationships between habit and behavioral intention and physical activity behavior. However, these studies did not include consequences of the behavior i n their model. The rather weak relationship between past experience and I P A found i n model II might be due to the strong relationship between past experience and one consequence of I P A , physical fitness. According to the model, attitude has no influence on exercise behavior.  The path  coefficent from A T T to I P A is insignificant ( 7 = .00). One's attitude towards being physically active does not predict exercise behavior. This finding is i n direct contrast to major behavioral models. However, as described i n Appendix A , the attitude-behavior relationship has been the focus of controversy for many behavioral researchers.  With  respect to exercise behavior, evidence has been produced that such a relationship exists, but it is not overwhelming. As indicated by Bentler (1981), G o d i n and Shepard (1986) and Sonstroem and Kampper (1980), the measured attitudes should relate directly to the behavior. The measures used to measure attitudes towards physical activity i n this study might have limited the attitudinal model and affected the relationship with I P A . Results from this model suggest, that other psychological constructs predict exercise behavior much better than attitude towards the behavior. Therefore, a Canadian male could have a positive attitude towards regular exercise, but be completely sedentary, and vice versa. If an individual has a positive attitude towards physical activity, he is not more likely to become involved i n physical activity than an individual who has a negative attitude towards physical activity. This is very important information for planning of activity programs. Based on findings from this study, attempting to change an individual's attitude towards physical activity through, for example, educational programs, is of no direct use,  Chapter 3. Results and Discussion  82  because it will not necessarily change actual exercise behavior. Motivation has the strongest influence on involvement i n physical activity. The path from M O T to I P A had the highest coefficient i n the model ( 7 = .42). According to the model, highly motivated individuals will participate i n physical activities more than individuals with low motivation. This has been shown i n the literature for both intrinsic and extrinsic motivation. Serfass and Gerberich (1984), for example, have shown that motivation can predict behavior. Slenker et al. (1984) found general health motivation to be a significant predictor of I P A . Although the intention to exercise may depend more on other factors (this issue was not tested i n the model), actual involvement i n physical activity can best be predicted from motivational characteristics. Designers of promotional strategies' for physical activity should implement this finding by focussing their methods on the motivation of individuals. Barriers prevent individuals from becoming involved i n physical activity. T h e second largest loading occured for the path from B A R to I P A ( 7 = .37). This is probably the most obvious finding. If someone does not have adequate facilities i n the vicinity or is limited by illness, he/she will less likely exercise than someone who is healthy and lives next to a pool, for example.  This finding has been established i n the literature (e.g.,  Andrew et al., 1981; Desharnais et al., 1987; Noland et al., 1981). Health can indirectly be controlled by directly motivating individuals, who are limited by illness, to become more physically active. This could i n turn improve their health, which would decrease these hmitations. Social Status has a significant effect on involvement i n physical activity.  The path  coefficient between S O C and I P A is lower but still of reasonable magnitude ( 7 = .25). As has been repeatedly shown i n the literature (e.g., Dishman et al., 1985; Gale et al., 1984; Gottlieb &; Baker, 1986; Oldridge, 1984), social status as indicated by age, marital status and income is an important factor with respect to exercise behavior.  Married,  83  Chapter 3. Results and Discussion  younger men with a higher income exercise more. Possible reasons for this relationship could be that people with higher social status have more free time, greater accessibility to facilities, and more money available; there also exists a basic difference i n mentalities between social classes. Increased involvement in physical activity improves physical fitness as indicated by the path coefficient from I P A to P H Y (8 — .22). Even though this coefficient is rather low, it can still be concluded that physically active people are generally more fit due to this increased activity. This confirms the physical benefits of physical activity which are reported i n the review by Leon and Fox (1981). The strongest path to P H Y , however, is from P E P ( 7 = .33). Therefore physical fitness appears to be more a result of long-term involvement than present short-term exercise behavior.  This emphasizes the need to focus on adherence as a major factor  with respect to involvement i n physical activity.  Sedentary individuals not only have  to be motivated to initiate the behavior, they have to get the urge and will to continue exercising. If physical activity becomes part of their lifestyle, physical fitness will likely improve. Psychological fitness is affected neither by I P A nor by physical fitness. B o t h path coefficients are insignificant (8 = —.02 from I P A to P S Y and 8 = .03 from P H Y to P S Y ) . This finding has to be regarded with caution. As explained earlier, the Bradburn scale is not considered a very good measure of psychological fitness. Since it is the only indicator of P S Y , the insignificant effects of I P A and physical fitness on psychological fitness might be due to poor measurement rather than to underlying processes. Interpretations of structural parameters are strong due to three factors.  First, the  model was developed on strong theoretical grounds, which implied a more restrictive analysis and allows interpretation of parameters based on the theory underlying the model.  Second, the overall fit of the model was good and no locations for potential  Chapter 3. Results and Discussion  84  specification errors could be detected. Therefore the solution can be regarded as a valid representation of the data. T h i r d , the magnitude of structural parameters was acceptable. Therefore, conclusions about hypothesized relationships can be drawn based on these coefficients. In summary, interesting information was gained from the parameter estimates for model C M I I l . T h e following conclusions can be made for 20 to 40-year old Canadian males. Motivation, barriers and social status appear to be strong predictors of exercise behavior.  Attitude seems unrelated to I P A and past experience with physical activity  had a small influence on present involvement.  Past experience d i d , however, predict  physical fitness. People who exercise more have improved physical fitness. Psychological fitness, as measured by the Bradburn scale, is not affected by I P A or physical fitness. Since the model is based on a large cross-national sample, knowledge about these relationships can be directly applied to the design of recreation programs.  3.3.3  Comparison of Models  T w o models of I P A have been tested using causal modeling techniques.  Model I was  defined as a conceptual model, but was not developed i n terms of a causal model. M o d e l II, however was carefully developed based on existing evidence. This apparent difference i n model construction required different approaches with respect to causal modeling procedures. Whereas model I was subjected to a lengthy process of model building, model II was tested under more restrictive guidelines, which illustrated the confirmatory nature of causal modeling. M a n y of the tests performed i n building model I did not produce a proper solution inside the permissable parameter space, and several "tricks" h a d to be used to achieve convergence of the estimation procedure. Only minor respecifications had to be done to achieve a good overall fit between model and data for model II. Its structural equation model was accepted as the final model after the first test.  Chapter 3. Results and Discussion  85  The final solutions for models I and II had similar overall fits ( G F I = . 9 5 and G F I = . 9 3 , respectively). M o d e l I has a much simpler structure, consisting of only four latent variables and three hypothesized causal relationships. Model II is a more complex model of eight latent variables and nine hypothesized causal relationships.  Whereas path coeffi-  cients were rather low i n model I, model II contained several coefficients of reasonable magnitude. Only two paths from the two models could be compared. T h e path from A T T to I P A had structural coefficients of 7 = .20 and 7 = .00 for models I and II, respectively. T h e significant parameter i n model I might be due to the fact, that no other latent variables were hypothesized to cause I P A . Paths from I P A to P H Y had similar coefficients (3 = .28 and 3 — .22 for model I and II, respectively), indicating that this relationship was confirmed in both models. In general, stronger statements about the strength of relationships could be made from model II, based on the nature of the model. Interpretations made on the basis of parameter estimates given i n model II are therefore accepted as conclusions w i t h respect to predictors and consequences of involvement i n physical activity.  These  conclusions are given i n the previous section (3.3.2).  3.4  Recommended Causal Modeling Procedures  Causal modeling appears to be a very powerful statistical technique for testing hypothetical models w i t h observational data. W h e n examining behavioral processes, for example, the analysis of comprehensive models provides a better understanding of underlying relationships than studies of single variables with univariate techniques. Even though causal modeling seems to offer a lot of potential with respect to data analysis, there is an ongoing controversy about the appropriateness of this method for the analysis of survey data. Its application to the test of models with defined causal structure seems to be very  Chapter 3. Results and Discussion  86  useful. Based on a review of the literature on causal modeling and based on experience with the application of several computer programs ( L I S R E L , C O S A N , E Q S , E Z P A T H ) to observational data, it is the view of the author, that causal modeling can be used as a legitimate and powerful statistical technique for the analysis of complex data structures, if, and only if, general guidelines are followed. Some general guidelines are suggested i n this section. From the variety of different procedures and analyses reported i n this chapter one can see how flexible causal modeling is. Given a specific dataset and a predefined hypothetical model, there are an indefinite number of different ways to test the model, which are likely to produce different solutions. Sometimes solutions can be very similar, but other times different tests can produce very different solutions. Guidelines for procedures are needed i n order to prevent the latter case. Even if the researcher understands the mathematical theory behind causal modeling, he or she still has to be creative and define the model i n such a way that all parameters are identified and a solution within the permissable parameter space is achieved. This distinguishes causal modeling from most other statistical techniques, which generally require strict application of mathematical principles. The flexibility of causal modeling techniques therefore implies several advantages and disadvantages. Simple and complex models with or without predicted relationships and with any number or form of variables can be tested. Different applications, such as confirmatory factor analysis, used for the test of the measurement model, or causal analysis, used for the test of the structural equation model, can be made. The researcher has the freedom to manipulate a model i n any possible way. This is an advantage for more exploratory purposes, but can be of great danger for purely confirmatory tests of models. The main disadvantage of this  flexibility  is that completely different structures with similar fits can be found for the same dataset. Two researchers might therefore come up with very different conclusions based on the  87  Chapter 3. Results and Discussion  same data. Unfortunately, this problem is amplified by the sensitivity of most computer programs. In practice, small changes often have large effects. Standards for procedures with respect to the application of computer programs for the test of causal models have not been established, simply because they are almost impossible to be established. A l l manuals for available computer programs present simple examples of models, that fit the data almost perfectly.  Unfortunately, most datasets do not resemble that  "neatness" characteristic. In practice, many model tests do not achieve convergence of estimation, which produces an invalid solution. T h e fact that the estimation procedure for the parameters cannot find a m i n i m u m for the fitting function can be due to large sampling error or model misspecification. Misspecification of a model can occur on two levels: • Hypothetical:  the theoretical assumptions are false or do not hold for the sam-  ple; the hypothesized factor structure and/or causal relationships have been inadequately defined. • Technical: the model is not identified, because parameters have been defined inappropriately i n terms of the mathematical model. The maximum likelihood estimation procedure has a tendency to become unstable if more than fifty or sixty parameters are to be estimated. For very complex models nonconvergence of the fitting function is therefore usually a purely mathematical problem. Another matter that complicates the decision process with respect to appropriate causal modeling procedures is the different nature of models.  Models that represent  untested ideas rather than elements based on theory require a more exploratory approach for their analysis.  Models profoundly based on theoretical grounds should be  tested i n the true confirmatory sense. In the first case, the researcher wants to almost detect relationships between variables. In the second case, the researcher is interested  88  Chapter 3. Results and Discussion  in confirming the defined model, rather than searching for alternate and better models. However, we can never confirm a model with causal modeling, we can only gain support for not disconfirming it, as mentioned i n A p p e n d i x B. Exploratory and confirmatory analysis should be viewed as a continuum rather than a dichotomy. There are studies, which require a mixture of both types of analysis. This mixture depends completely on the nature of the model and the strength of the underlying theory. This issue has been a focus of discussion for researchers i n the area of causal modeling. It is the view of the author, that while undirected searching for structure does not have any specific purpose (other than perhaps a fun game), certain exploratory elements of analysis can be useful for testing certain models with causal modeling. In the case of a clearly defined model based on existing evidence, however, a true confirmatory approach should be taken to causal modeling. T w o basic assumptions for the use of structural equation modeling have to be considered for the test of a model and the interpretation of a given solution. • Causality cannot be inferred. • M a x i m u m Likelihood estimation requires multivariate normal distribution of the data.  3.4.1  General Guidelines  Some general guidelines for the test of causal models have been developed.  Following  them can reduce some of the variability with respect to applications and can help the researcher achieve a valid solution with an acceptable fit to the data. T h e guidelines are shown i n a flowchart i n figure 3.9. Although they are based on and discussed with reference to the L I S R E L methodology, they can easily be applied to other methodologies as well. A l l procedures are discussed with relation to a correlation input matrix.  Chapter 3.  Results and Discussion  Define tneoretloal model  Operational!** variable*  E  All latent var. measured o.k. ?  1  no  yes  Eliminate latent variables with Inappropriate measures  I • 1  I I  Teat Measurement Model l  l •I•1  Did estimation oonverfte ?  Modify model by applying 'tricks*  no  feepsolfloallon poaa. •nd promising 7  Retain Measurement Model 1  Reepeoifioatlon  Test Measurement Model I  >  "o \ Consider redevelopment of model  Fit acceptable ?  M8q  (l-D - C M 8 q (i);  significant ?  )•«fespeoifioatton poss and promising ? /  no Structural Model  T  Retain Measursmsnt Model I  /•*  Chapter 3. Results and Discussion  90  After being inspired by a brilliant idea, the researcher has to define the research problem. Causal models are generally tested to gain an understanding of behaviors or other processes.  Through the examination of relationships among several independent  and dependent variables, the first step is the definition of a hypothetical model.  This  is usually a fairly time-consuming task, but if the model is defined very carefully, the chances of achieving a model with a good fit to the data and with meaningful parameters are much greater.  Therefore investing more time at this initial stage may benefit the  outcome of the study very much. The model typically consists of several latent variables, which are abstract contructs that cannot be measured directly, and hypothesized causal relationships between these variables.  Directed relationships can only be defined from  independent to dependent variables or among dependent variables. A review of the literature relating to the defined constructs and the hypothesized relationships is absolutely necessary i n order to define a valid model. Each predicted causal relationship should be supported by existing evidence i n the literature. Also, a model should have an appropiate level of complexity. Neither a very complex model with relationships between all latent variables, nor a very simple model with only a few constructs and relationships is likely to produce results that can be interpreted and are useful. A s mentioned i n A p p e n d i x B, a happy medium has to be found. The next step is the operationalization of variables. It involves assigning manifest or observed variables to latent variables. Latent variables are hypothesized to be measured or indicated by these manifest variables. The observed variables have to be selected from the variables available i n the data. Manifest variables should have established validity and reliability to ensure that they represent a valid measure of the construct and that this measure is consistent. If no measurement properties exist, the context of the observed variable should clearly indicate that it measures what it intends to measure. Each latent variable should have a sufficient number of indicators.  If only one measure exists, the  Chapter 3. Results and Discussion  91  latent construct becomes a measured variable, but is still defined as a latent construct in terms of the mathematical model. T w o indicators often cause serious estimation problems by causing Heywood cases (discussed i n the following section).  One or two indicators  per latent variable should be avoided if possible; three or more indicators are preferred. Even though there is no upper limit to the number of measures per latent variable, too many indicators complicate the analysis tremendously. After several indicators have been denned, each additional manifest variable adds less and less variance and therefore less information with respect to the unmeasured variable.  Usually three to six indicators  are sufficient to measure a latent variable adequately. After the manifest variables have been selected, it should be assessed if all latent variables are measured appropriately. If no valid measures can be found for a latent construct, it should be eliminated from the model at this point. Following the flowchart i n figure 3.9, the index i is now set to one. The measurement model should then be constructed as exemplified i n Appendix B. A n example of the appropriate L I S R E L control commands is given i n Appendix D. T h e model should then be tested with a confirmatory factor analysis using maximum likelihood estimation. If the parameter estimation did not converge, the model has to be modified by using techniques, which are described i n the section 3.4.2. Non-convergence is indicated by solutions outside the permissable parameter space (e.g., negative variances) or by L I S R E L warning messages.  The counter i is increased by one and the modified model is then  tested. This procdure has to be repeated until a proper solution has been achieved. Once a model has produced a solution with valid parameters, parameter values, residuals and modification indices should be inspected in order to make a decision, whether respecification is possible and useful.  Some general crude criteria can be given, even  though they depend on the nature of the model.  Chapter 3.  Results and Discussion  • Parameters:  92  Factor loadings (A) can be interpreted similarily to loadings from  exploratory factor analyses.  In general, factor loadings above .5 are good, but  lower loadings can occasionally be accepted.  If several manifest variables have  high loadings and one or two indicators of the same construct have relatively low loadings, the latter variables should be more closely examined.  Elements of 0$  have to be positive. Correlations between factors should not be too high (elements of $ ) . . • Residuals: They should generally be below .1. Again, this criterion depends on the average size of correlations. If a variable has several high residuals, it does not fit the model very well, and its role as part of the model should be reevaluated. • Modification Indices: Although these indices should be regarded with caution, they can usually detect possible locations of specification errors. The highest index generally indicates a constrained parameter that should be relaxed. If one variable has several high modification indices, its inclusion i n the model should be reevaluated. These criteria should always be examined in conjunction with each other. Modifications should be made step by step, that is one per respecification.  A n y modification to the  original model can only be made if it is justifiable on theoretical grounds. If a location has been detected that could potentially contain a specification error, which can be explained in terms of the theoretical model, the model should be respecified and tested. The sequential % difference test should be used to assess whether an improved fit to 2  the data has been achieved or not. If the difference i n % with the associated difference 2  in degrees of freedom is significant, the new model shall be accepted as a model that fits the data better.  The possibility of respecification then has to be examined again  as explained above. This process has to be repeated until respecification does not seem  93  Chapter 3. Results and Discussion  promising and useful. If the difference i n % between the present and the previous model 2  is significant, the present model shall be retained. If it is not, the previous model shall be retained. The final step i n the test of the measurement model is the assessment of overall fit. Criteria for this assessment have been discussed in Appendix B. Some general crude guidelines with respect to the magnitude of these criteria can be given, even though they highly depend on the nature of the model. • T h e Goodness of F i t Index ( G F I ) should be above .9 for a good fit and above .95 for a very good fit. e T h e Root Mean Square Residual ( R M R ) should be below .1 for an acceptable fit and below .05 for a good fit. • Coefficients of determination for x- and y-variables and for structural equations should be above .9 (the two latter coefficients are used in structural equation models only). If the fit is not acceptable based on these criteria, redevelopment of the model or outright rejection of the model should be considered and no further analyses conducted. If it is acceptable, the structure from the final version of the measurement model can be implemented into the structural equation model. Methods for the construction of the structural equation model have been described in A p p e n d i x B. B o t h methods of fixing the scale of latent variables were applied i n tests of models of I P A described above. Neither method appears to offer a particular advantage. The test of the structural model is very similar to the test of the measurement model. In the flowchart one should start the analysis of the structural model back at step 5 (indicated by an asterisk). There are, however, several differences i n the test of  Chapter 3. Results and Discussion  94  the structural model that have to be recognized. Since the measurement structure has already been tested within the measurement model, modifications with repect to the relationships between manifest and latent variables (specified i n A matrices) should only be made if absolutely necessary. Strutural parameters should only be added or eliminated in very extreme cases. T h e test of the structural equation model should generally have a converged estimation and an acceptable solution after the first test. If a converged solution with an acceptable fit has been found for the structural equation model, all parameters can be interpreted i n light of the theoretical model.  Missing Data Treatment M o d e l M M I I 5 was retested several times i n order to examine the effect of missing data treatment.  In general, listwise deletion of cases can be used to avoid any problems.  Cases with missing data on any of the observed variables are eliminated from the sample and the input matrix is calculated based on the remaining subjects. If pairwise deletion of cases is used, subjects with missing data are only ignored for the calculation of the covariance or correlation between the variable, for which data is missing, and another variable.  Unfortunately, this can produce a non positive definite input matrix, which  cannot be analyzed by L I S R E L . However, especially i n a model with a large number of variables or i n small samples, it is often desirable to use data from as many subjects as possible. In this case, pairwise deletion of cases can be used, provided it produces a positive definite input matrix. The results from several tests of model M M I I 5 are listed in table 3.14. A s can be seen i n this table, listwise deletion caused the deletion of over 1200 subjects. T h e model produced a slightly better fit using listwise deletion of cases (GFI=.967 as opposed to GFI=.965 for pairwise deletion). Solutions for covariance and correlation input matrices were identical, as was expected. L I S R E L cannot produce a covariance matrix with pairwise deletion of cases; it was produced using a descriptive  95  Chapter 3. Results and Discussion  Table 3.14: Alternate Tests of Measurement Model II ( M M I I 5 )  Input  Missing  Pearson Pearson Covariance Covariance Polychoric  Pairwise Listwise Pairwise Listwise Pairwise  n 3032 1807 3032 1807 3032  x  2  676 517 676 517 1263  df 104 104 104 104 104  X /df 2  6.5 5.0 6.5 5.0 12.1  GFI .965 .967 .965 .967 .953  RMR .040 .039 12.5 21.1 .044  program under S P S S .  3.4.2  A List of " T r i c k s "  Several procedures have been successfully used i n applications of causal models for producing a better fit. Most of these procedures have been applied i n order to produce proper solutions for models with non-converged estimations. Knowledge about their usefulness is based on experience with many tests of different models.  H e y w o o d Cases If a Heywood case exists i n a model, an invalid solution is produced. T h e typical case for a Heywood case is a latent variable with two indicators where only the sum of the two factor loadings A i -f A2 is identified. A n y combination of A i and A2 that produces this sum satisfies the restrictions implied by the equations i n the model. Therefore the model is not identified. T h e most common and easily detectable sympton for a Heywood case is one factor loading above one i n conjunction with a negative 6s (this is invalid). The easiest solution is to find a third manifest variable as a measure of the latent variable.  However, this is often not very practical.  There are two ways to at least  attempt producing a proper solution. T h e factor loadings can be constrained to be equal ( A i = A ) . If this does not work, the parameter that produced the higher A should be 2  Chapter 3. Results and Discussion  96  fixed at one.  Elimination of Manifest Variables If an observed variable has factor loadings, that are different from other indicators of the same latent variable, or if it has several high modification indices and high residuals, its exclusion based on these criteria should be considered. If elimination can be justified within the context of the theoretical model, the model should be respecified and tested without this manifest variable. Often this one variable creates all the problems encountered by the estimation procedure i n attempting to find a global m i n i m u m for the fitting function.  Correlated Measurement Errors In the standard construction of the measurement and structural equation models, error variances for manifest variables are uncorrected (i.e. Q$ and 0  e  are diagonal matrices).  In some cases, correlating the measurement errors of observed variables makes sense from a theoretical point of view and can improve the model fit. If two measures of a concept were measured with the same instrument, for example, their errors of measurement should be correlated, because they are possibly due to the inaccuracy of the same instrument. In order to correlate these errors, one has to relax the corresponding off-diagonal element of Qs or 0  £  and estimate it as a free parameter i n the test of the respecified model. This  generally produces an improved fit.  Chapter 4 Summary and Conclusions  Involvement i n physical activity is a complex behavioral process, which has become an integral lifestyle component for many Canadians. T w o comprhensive models of I P A and relating factors were tested i n order to gain a better understanding of this process. They consist of unmeasured abstract concepts, which can be measured by several observed variables, and hypothesized directional relationships between these concepts.  Model I  was taken directly from the 1981 Canada Fitness Survey data tape manual. M o d e l II was developed on the basis of a review of the literature (see A p p e n d i x A ) . T h e 1981 Canada Fitness Survey contained many variables relating to I P A and was administered to a very large sample.  Both models were tested with data from a subsample of this  extensive dataset, namely- 20- to 40-year old Canadian males. A very powerful statistical methodology, causal modeling, was selected as the most appropriate tool to test the hypothetical models of I P A and to evaluate the strength of the hypothesized relationships.  B o t h models were transformed into L I S R E L mathematical  models and many tests had to be carried out before satisfactory solutions were reached. A good fit of the model to the data was found for both models.  However, the test of  model I consisted of many non-converging estimations and many modifications. T h e test of model II presented far less problems. A good indication for this is the fact, that the original version of structural equation model II was accepted as the final version after its test. It is concluded, that the main reason for this discrepancy is the difference i n model  97  Chapter 4. Summary and Conclusions  development.  98  A sound theoretical model, based on existing evidence, appears to be  essential for successful applications of causal modeling techniques. Applications become much simpler and are more likely to produce valid and useful results. The following conclusions with respect to predictors and consequences of I P A are therefore based on results from the more theoretically sound model, namely model II.  4.1  Physical Activity Behavior • Past experience with physical activity improves physical fitness, indicating the i m portance of long-term involvement i n physical activity. • Motivation has the strongest influence on physical activity behavior. • Barriers tend to prevent Canadians from becoming involved i n physical activities, o Social status is an important factor influencing I P A . • Attitudes and past experience appear to have little effect on participation i n physical activity. • For the general population of 20- to 40-year old males I P A seems to improve physical fitness. • I P A has, however, no effect on psychological well-being, as measured by the Bradburn scale. Based on these conclusions the following recommendations can be made to designers  of recreational physical activity programs. Motivation of the individual appears to be a very important factor that has to be recognized by program planners.  Barriers such as inaccessibility and cost of facilities  Chapter 4. Summary and Conclusions  99  should be eliminated for all sections of society, i n particular i n rural areas and regions with lower economic status.  Social status determines exercise behavior to a certain  extent, and efforts have to be made to target Canadians from lower social classes with recreational physical activity programs. T h e finding that physical fitness tends to improve with increased involvement i n physical activity can be used to promote the benefits of I P A to the public.  4.2  Causal Modeling  The large number of tests and problems with reaching a satisfactory solution indicated the complexity of applying computer programs such as L I S R E L . T h e interpretation of parameters is often very difficult.  It appears as if a certain degree of experience is  required i n order to use L I S R E L and similar models. In general, it is concluded that causal modeling represents a very powerful multivariate approach to testing hypothetical models with observational data. Applications, however, are still very complex and present many problems, which are often difficult to resolve. More user-friendly programs such as E Z - P a t h are necessary to allow access to this statistical technique for the social science researcher. Procedures for the treatment of categorical and non-normally distributed data were applied; results were very similar to standard maximum likelihood estimation under LISREL. Even though the novelty and flexible nature of causal modeling do not allow the definition of clear procedures for its application, general guidelines could be developed i n this study.  A flowchart of general procedures is presented i n figure 3.9. It is rec-  ommended that these procedures are followed i n conjunction with the described general strategies and specific "tricks" when applying structural equation modeling.  Problems  Chapter 4. Summary and Conclusions  100  with analyses can thus be avoided and parameter estimates are likely to have greater validity.  4.3  Recommendations for Future Research  Firstly, it is recommended that sport scientists acknowledge the usefulness of causal modeling and utilize it as a statistical tool for the evaluation of a hypothetical model. Such theoretical models often occur i n sub-disciplines such as sport psychology or sport sociology. Secondly, more research is needed on predictors of I P A as well as on the effect of physical activity on psychological well-being. Thirdly, a very interesting data base will become accesible i n early 1990. A revised version of the Canada Fitness Survey was administered i n 1988 and data has been collected from over 5000 subjects.  These subjects are from the original sample used in  1981. Therefore, the Canada Fitness Survey represents a very comprehensive longitudinal dataset, which should be subjected to analyses i n order to assess longitudinal trends. In particular, the model of I P A that was developed i n this study (model II) could be tested w i t h the new data. Causal modeling allows both datasets to be entered into a longitudinal analysis. These tests could show, if and how physical activity behavior has changed i n Canada between 1981 and 1988. If it has changed, new recreation programs should be designed. If it has not changed, recreation programs are not effective enough and should be redesigned. T h e area of recreation and physical activity offers a challenge to everyone and every day; this allows the field of sport science to make constructive contributions to human life.  Appendix A Literature Review - Predictors and Consequences of Physical Activity  Physical activity is the central focus of this study. Casperson, Powell and Christenson (1985) give some useful definitions relating to this concept. "Physical activity is movement produced by skeletal muscles that results i n energy expenditure. Exercise is a subset of physical activity that is planned, structured, repetitive, and has the improvement or maintenance of physical fitness as an objective. Physical fitness is a set of attributes, some of which are health-related, that people have or achieve" (p.127). Since almost all studies that relate to physical activity examine leisure-time physical activity or exercise rather than physical activity at work, the above definitions are adopted here within the context of leisure-time activities. Numerous sport scientists have examined the effects of exercise upon the human system; associations between physical activity, physical fitness and psychological wellbeing have been well-established. In general, the purported benefits of physical activity are widely accepted by the public, and have been strongly promoted i n recent years by sport scientists as well as members of the medical community. Attempts to explain underlying mechanisms that lead to these consequences are frequently reported i n the literature.  101  Appendix A. Literature Review - Physical  Activity  102  Despite the strong evidence regarding the benefits of regular physical activity, it appears that the majority of North American adults do not engage i n regular physical activity. L u p t o n , Ostrove and Bozzo (1984) compared results from twelve North American surveys and found the proportion of people who exercise on a regular basis to vary between 36% and 59%, depending on whether regular exercise is defined as planned exercise several times a week or as regular activity at any time during the year. Brooks (1987) evaluated a number of surveys containing physical activity information and concluded that although 53% participated at least once i n one or more activities i n 1984, only 18% were active for more than 60 days per year.  Fitness Ontario (1984) reports a rate of  45% in the spring and 35% in the fall for people who are active three times a week or more. T h e C a n a d a Fitness Survey (1983) classified 56% of Canadians over the age of 10 to be physically active, but as Shepard (1988) indicates, less than 20% were involved i n vigorous activity. F r o m these and other sources reporting physical activity involvement patterns it is safe to conclude that i n general, less than half of the North American population engages i n regular physical activity, with participation rates being slightly higher in C a n a d a than i n the United States. Therefore the majority of people do not receive the health benefits from physical activity which have been advocated and promoted by sport scientists.  Unfortunately, those who can benefit the most from physical activity  seem to be least likely to initiate or adhere to exercise. W h i l e the benefits and risks of physical activity should be subject to further investigation, it is also important to examine why people engage i n physical activity, that is, to ascertain the determinants and predictors of physical activity. Powell and Pfaffenbarger (1985) conclude, that "knowledge of the patterns of physical activity within our society and the determinants of those patterns is l i m i t e d " (p.118). In order to receive any of the benefits associated with physical activity, people have to be motivated to exercise i n the first place, and, once an activity program has been initiated, they must be sufficiently  Appendix A. Literature Review - Physical Activity  rewarded to continue.  103  A n average dropout rate from supervised exercise programs of  about 50% after the first six months, which has been reported repeatedly i n the literature (e.g. Dishman, Sallis & Orenstein, 1985; Gale, Eckhoff, Mogel & Rodinck, 1984; Sonstroem, 1982), indicates that such motivation or reward is often lacking. Sonstroem (1982) describes the study of exercise involvement as the most important issue facing exercise scientists at the present time, and Dishman et al. (1985) state that "one barrier to developing effective methods to encourage physical activity among all segments of the population is the lack of knowledge of determinants of regular physical activity" (p. 159). The first section of this review focuses on determinants and predictors of physical activity, while findings related to outcomes and consequences are presented i n the second section.  A.l  Determinants of Physical Activity  There has been considerable study of the factors associated with regular physical activity and Dishman et al. (1985) have provided an extensive review of this research.  Before  discussing any of the findings two important distinctions with respect to study design have to be made. One relates to the point i n time at which exercise behavior is observed (time) and the other relates to the type of physical activity that is examined as an indicator of exercise behavior (type). • Time 1. One way to examine determinants of physical activity is to identify variables associated with behavior initiation, which implies voluntary control. 2. The other more common form is to examine exercise adherence, given a fixed starting point of behavior initiation.  Appendix A. Literature Review - Physical Activity  104  • Type 1. Subjects from supervised exercise programs form the sample for most studies of physical activity determinants, mainly because of the advantages of temporal control and convenient accessibility of the sample. 2. The other option is to examine patterns of spontaneous leisure time physical activity. One of the major shortcomings of most studies looking specifically at adherence within exercise classes is the fact that the possibility of continuation of involvement in spontaneous activities after dropping out of the exercise class is completely disregarded. In addition to the diversity of designs arising from these distinctions there are a number of other problems associated with studies of determinants of I P A . First, the assessment and quantification of physical activity involvement patterns represents a very complicated and difficult problem i n itself; it is discussed i n section 2.2. Second, the theoretical basis for gaining an understanding of exercise behavior is often insufficient or non-existant. Although quite a few factors have been associated with I P A on a descriptive level, the process by which exercise behavior is developed is not very well understood, even though "this information is crucial to the planning of more efficient physical activity promotion programs" (Godin, Valois, Shepard, & Desharnais, 1987, p. 146). In order to change behavior it is necessary to gain an understanding of the factors that influence it as well as the nature and strength of relationships between physical activity involvement and these factors. Potential psychological and environmental barriers can be identified and the knowledge or skills necessary for the initiation and/or continuation of activity can be provided. G o d i n et al. (1987) have identified three major factors that prevent us from gaining this important information: (a) Most researchers have not developed or applied a theoretical model of exercise behavior, (b) they have  Appendix A. Literature Review - Physical Activity  105  usually based their findings on retrospective comparisons, and (c) multivariate statistical techniques, which are more appropriate for analyzing processes, should have been used rather than univariate methods. The third problem with studies of determinants of I P A is that relationships between determinants and I P A appear to be inconsistent. Most factors vary across populations, environmental settings and time. For example, males seem to have a different motivation to exercise than females, rural and urban environments affect people's intention to exercise i n different ways and involvement patterns change substantially with seasons. This inconsistency of findings might be mainly due to the fact that specific and small samples rather than community samples have been examined. The fact that I P A represents a very complex concept with significant interactions between determining factors explains the difficulty that researchers have had with finding a clear and consistent explanation of the determinants of I P A . Exercise behavior has to be viewed and examined as a behavioral process influenced by many variables, as indicated by several studies (Bentler, 1981; Dishman et al., 1985; Gale et al., 1984; G o d i n et al., 1987; Sonstroem, 1982). Despite all problems mentioned above, the factors identified i n Dishman's review are very helpful i n understanding some of these processes leading to I P A . Factors that have been shown to have a significant relationship with I P A in more than 50% of the reviewed studies examining these factors are: • Personal characteristics: past participation, occupation, smoking, overweight, risk of coronary heart disease, attitudes and knowledge, education, perceived health, mood disturbance, self-motivation, cost and benefits, age. o Environmental characteristics:  Appendix A. Literature Review - Physical Activity  106  social support, available time, accessibility of facilities, disruptions i n routine. • Activity characteristics: perceived exertion. In this review a number of studies that have shown single factors to be associated with I P A and studies presenting exercise behavior models are identified. T h e reviewed research has defined either intention to exercise or actual involvement i n physical activity as the dependent variable and examined its relationship with selected potential predictors. Behavioral intention has been shown to be a very strong predictor of behavior by behavioral psychologists (e.g. Fishbein & Ajzen, 1975) and several sport scientists (Dishman, 1986; Godin et al., 1987; Hammitt, 1984; Riddle, 1980). Therefore, variables associated with intention to exercise are very likely to have a strong relationship with I P A as well. In the following section, selected findings relating to personal and environmental characteristics of people who become involved i n physical activity are summarized and some behavioral models are discussed.  A. 1.1  Past Experience  The influence of past experience or habit on behavioral intention as well as behavior itself has been recognized and included i n abstract models by behavioral psychologists (e.g. Bentler & Speckart, 1979). Early studies (Harris, 1970; Sofranko & Nolan, 1972; Yoesting & Burkhead, 1973) have shown that past experience has an important influence upon leisure behavior. G o d i n et al. (1987) and Valois, Shepard and G o d i n (1986) found that habit is a strong predictor of intentions to exercise, proximal behavior (after three weeks) and distal behavior (after two months). A very similar model was tested by Hammitt (1984) and she concluded that past experience i n sports and/or physical activity was a significant predictor of intentions and the strongest predictor of participation level. More than 50% of the variance i n exercise behavior was accounted for by past experience  Appendix A. Literature Review - Physical Activity  107  (measured eight to nine months previous) i n three models of exercise behavior tested by Mullen, Hersey and Iversen (1987). Past participation in exercise programs as well as routine walking and active leisure have been shown to be the most reliable predictors of adherence to an exercise program for participants i n a cardiac rehabilitation program (Oldridge, 1982) and in healthy populations (Dishman, 1982; Gale et al., 1984). T h e important role of past exercise participation i n the social motivation to become or remain involved i n physical activities is emphasized by Heinemann (1978). The degree of involvement i n leisure behavior i n the past has been shown to have a strong relationship with various types of exercise behavior, which is consistent with findings i n the field of psychology.  In particular, past experience i n physical activity  appears to have a strong influence on present involvement i n physical activity.  A.1.2  Attitude  As Bentler and Speckart (1981) note, the relationship between behavior and attitude has been one of the fundamental problems for social psychologists.  Four different views of  this relationship with respect to causality have been taken by researchers i n this field: (a) attitude causes behavior, (b) behavior causes attitude, (c) attitude and behavior have mutual causal impact, and (d) attitude and behavior are only slightly or not at all related. This inconsistency has been shown to be due to factors influencing the attitudebehavior relationship as well as the use of invalid measures and incorrect designs (Bentler & Speckart, 1981). T h e notion of attitudes causing behavior appears to be well accepted and researchers are now studying when and what types of attitude lead to behavior. Bentler and Speckart showed significant causal path parameters i n a simple attitudebehavior model of exercise; however, the direct causal relation between attitude and exercise behavior was attenuated when additional concepts, variables and paths were added.  Appendix A. Literature Review - Physical Activity  108  Attitudes are also a central component for predicting behavior in the Theory of Reasoned Action which was developed by Fishbein and Ajzen (1975). According to their theory an attitude consists of cognition and state of affect. It is crucial that attitudes and behavior possess a high degree of correspondence, that is attitudes should be stated specifically and be congruent in terms of action, target, context, and time. Therefore, in examining the attitude-IPA relationship, attitudes toward performing the behavior should be assessed. T h e general Attitude Toward Physical Activity ( A T P A ) inventory developed by Kenyon in 1968 has been widely used to measure attitudes (e.g. Biddle & Bailey, 1985; Dishman, Ickes & Morgan 1980; Dishman, 1982); the Schutz and Smoll (1985) revised instrument ( C A T P A ) has been applied extensively with children and young adults (e.g.  Smoll,  Schutz & Kenny, 1976; McCready & Long, 1985). G o d i n and Shepard (1986) as well as Sonstroem and Kampper (1980) note that prediction of behavior has been limited by the attitudinal model used and that attitudes should be more congruent with desired and specific behaviors. G o d i n and Shepard (1986) and Sonstroem and K a m p p e r (1980) have shown that the Attitude Toward A c t (Aact) and Physical Estimation and Attraction Scale ( P E A S ) , respectively, are better predictors of exercise behavior than the A T P A inventory.  Sonstroem (1982) argues that the two important central processes are esti-  mation, that is self-perception of ability to exercise, and attraction, that is interest i n vigorous physical activity. Dishman (1982, 1986) argues that although relationships between attitudes and intentions to exercise and between intentions and actual exercise behavior may exist, there appears to be no relationship between attitudes and behavior. This finding is i n contrast with several studies that have shown a direct relationship between attitude and maintenance of vigorous activity (Sallis et al., 1988), as well as between attitude and regular exercise participation (Hammitt, 1984; Lupton et al., 1984; McCready, 1984; Noland,  Appendix A. Literature Review - Physical Activity  109  Feldmann & Burt, 1981; Wankel, 1980). A very strong relationship between attitudes and intentions to exercise has been found as well (Godin et al., 1987; Hammitt, 1984; Pender & Pender, 1986; Riddle, 1980). It has been shown that a major reason for initiating involvement in exercise programs is improvement of health, which is indicated by a positive attitude towards the value of exercise as a health-enhancing behavior (e.g. Abele & Brehm, 1985; Serfass & Gerberich, 1984). Wankel (1985) argues that although the initiation of a physical activity program is mainly determined by attitudes towards health-related benefits of exercise and threat of disease, such as fear of a heart attack, the continuation of such a program depends primarily on daily routine or habit and the degree of enjoyment. In general the existing evidence points towards a direct causal relationship between attitudes and I P A , providing that the attitudes measured have involvement per se as the attitude object.  A. 1.3  Motivation  Motivation can influence the direction and intensity of behavior (Serfass &; Gerberich, 1984). A n important distinction has to be made in order to understand this influence. Extrinsic motivation such as rewards, prizes and trophies can have either informational value in the form of cognitive feedback, or control value, resulting i n an urge for higher performance. Contracting and goal-setting have been successfully used as extrinsic motivators in exercise settings (Sonstroem, 1982). Intrinsic motivation refers to enjoyment of the activity itself, and this appears to be the most logical reason for somebody to exercise.  Self-motivation, that is "the tendency to persevere i n the absence of extrin-  sic motivation" (Serfass &: Gerberich, 1984, p.88), has been examined within models of exercise behavior.  Dishman and Ickes (1981) developed the Self-Motivation Inventory  A p p e n d i x A . Literature Review - Physical Activity  110  (SMI) to measure intrinsic motivation and this measure was included in a psychobiological model of exercise behavior (Dishman, 1981; Dishman et al., 1985).  In a test  of this model Dishman and Gettmann (1980) were able to accurately identify adherers to exercise versus dropouts with 80% accuracy when biological variables such as body weight were included. Andrew et al. (1981) reported that exercise was of little value to dropouts, indicating low self-motivation. However, Gale et al. (1984) found the Dishman Self-Motivation Inventory to be of little predictive value with respect to adherence. Slenker et al. (1984) examined motivation as one component of readiness to undertake a recommended compliance behavior within a modified Health Belief Model; results suggest that general health motivation is a significant discriminator between joggers and non-exercisers.  W i t h i n the Health Belief M o d e l perception of one's own health status  was found to be an important motivational component for I P A by Serfass and Gerberich (1984). Dishman et al. (1985) concluded that people who perceived their health as being poor are less likely to initiate or adhere to an exercise program.  Similarily, perceived  health and perceived physical ability have been shown to be determinants of one's physical activity level (McPherson, 1980). O n the other hand, Davis, Jackson, Kronenfeld and Blair (1987) found that employees with higher perceived job stress and anxiety were more likely to participate in corporate activity programs. In a test of a combined protection motivation and self-efficacy theory by Stanley and M a d d u x (1986), response efficacy, that is expected outcomes of participation, and self-efficacy expectancy, that is perceived ability to perform a behavior, were significantly related to intentions to be physically active. According to Heinemann (1978), perceived abilities and skills and the motivational structure form an achievement orientation, which i n turn leads to increased involvement in physical activity. General motivation to exercise has been related directly to I P A by a number of researchers (McPherson, 1980; Oldridge, 1984; Seppanen, 1978; Wankel, 1980).  Appendix A. Literature Review - Physical Activity  111  Biddle and Bailey (1985) found men to be highly motivated to exercise by competitive factors, including self-competition. Evidence from the literature discussed above suggests that both intrinsic and extrinsic motivation seem to be important determinants of I P A . It appears as if a highly motivated individual is more likely to exercise than an individual with no motivation to be involved in physical activity.  A.1.4  Knowledge  It appears reasonable to expect people who have a greater knowledge about exercise and its health benefits to be more physically active than people with little or no knowledge. Sallis et al. (1986) concluded that adoption of moderate activity can be predicted from general health knowledge and maintenance of moderate activity can be predicted by specific exercise knowledge.  However, they found no significant relationship between  health or exercise knowledge and vigorous exercise.  Knowledge about a disease that  poses a threat has been shown to relate to intentions to exercise within the Health Belief M o d e l (Serfass k Gerberich, 1984). Other studies have found that knowledge has no significant influence on intentions to exercise or on activity level (e.g. Noland et al., 1981). Dishman et al.(1985) report controversial findings with respect to knowledge predicting I P A ; while some studies show that knowledge about exercise can be important for the initiation of and adherence to supervised exercise programs, other studies conclude that knowledge is not an important factor. In general, there is very little evidence i n the literature supporting the influence of knowledge on exercise participation and health; exercise knowledge can therefore not necessarily be considered a determining factor of I P A .  Appendix A. Literature Review - Physical Activity  A.1.5  112  Social Support  The influence of behaviors and attitudes of significant others on behavior appears to be strong. The family as the smallest social unit, for example, offers support for individuals and directs their behavior, such as I P A . In their review, Serfass and Gerberich (1984) reported several studies i n which spouses of inactive individuals have been shown to be indifferent or have negative attitudes towards physical activity and/or to be inactive themselves.  Family opposition has been  identified as a reason for dropout from an exercise program by some of these studies. Spouse and family support influence exercise behavior and appear to be directly related to compliance with exercise programs (Andrews et al., 1981; Dishman, 1982) and cardiac rehabilition programs (Oldridge, 1984). Gottlieb and Baker (1986) found the activity level of the father and male friends to be significantly related with the degree of involvement i n physical activity. O n the other hand, Noland et al. (1981) conclude that exercise locus of powerful others cannot predict exercise behavior. Snyder (1978) notes that peer prestige is the major reason for athletic participation in youth. Attitudes and involvement patterns of significant others can also influence one's attitude towards physical activity (Bassey, 1981). Subjective norms form a key element of the Behavioral Intentional Model proposed by Fishbein and Ajzen (1975). They consist of two components: 1. Normative beliefs refer to perceived social pressure to engage i n the behavior, that is, how likely it is that significant others think that an individual should be involved in the behavior; 2. Motivation to comply refers to the motivation to comply with these norms or expectations of significant others.  Appendix A. Literature Review - Physical Activity  113  Sonstroem (1982) has suggested the application of such a model including subjective norm to the study of exercise behavior. A strong relationship of subjective norm as well as its components with physical activity level has been shown for a group of joggers and nonexercisers (Riddle, 1980). T h e influence of subjective norm on behavioral intentions has also been demonstrated (Pender &; Pender, 1986). Hammitt (1984) found no influence of subjective norm on intentions but a relatively large influence on participation level, whereas G o d i n et al. (1987) could predict neither intention, proximal or distal behavior from subjective norm. Social support, defined as direct encouragement from or positive attitudes of significant others, or normative beliefs and motivation to comply by oneself, seem to be a very important predictor of intentions to exercise as well as of I P A .  A. 1.6  Barriers  A considerable amount of research has examined why people stop exercising or what prevents them from initiating a program.  A number of perceived barriers have been  directly associated with the degree of involvement in physical activity. Experiences tell us that friends tend to give reasons such as " I do not have time" when asked why they do not exercise, which is an example of a barrier to I P A . The fact that these barriers are usually measured as perceived barriers and that the actual situations are not observed might cause a certain degree of inaccuracy. Someone might, for example, indicate that inaccessability of facilities is one of his/her major reasons for non-participation, when i n fact he/she lives within walking or cycling distance of an adequate public facility. Noland et al. (1981) and Slenker et al. (1984) found that a considerable amount of variance i n prediciting exercise behavior can be attributed to perceived barriers. Availability of time and convenience of location has been shown to have a direct influence on attitudes towards physical activity i n path analyses performed by Mullen et  Appendix A. Literature Review - Physical Activity  114  al. (1987). Jackson and D u n n (1988) classified non-participants into three categories: non-participants can be characterized as having either (a) deferred demand, that is they are prevented from exercising by barriers such as lack of time or accessibility of facilities; (b) potential demand, that is they are usually affected by economic or social constraints; or (c) no demand, that is they have no interest i n exercise at all. One of the most frequently indicated barriers to involvement i n exercise is lack of time. W h i l e there are certainly occupations and/or lifestyles that do not allow an adequate amount of leisure-time for physical activities, a reasonable intuitive approach would be that one can always make time to exercise three times a week or at least on weekends, if the intention exists. Several studies report that dropouts from exercise programs and inactive people more frequently indicate that they do not have enough time to maintain or start an activity program (Andrew et al., 1981; Desharnais et al., 1987; Dishman et a l , 1985; Lupton et a l , 1984; Noland et a l , 1981; Oldridge, 1984; Serfass & Gerberich, 1984). Similarily, the inaccessability or inconvenience of facilities has been identified as an important barrier to I P A (Andrew et al., 1981; Dishman, 1982; Dishman et al., 1985; Oldridge, 1984; Serfass & Gerberich, 1984; Sonstroem, 1982). Other important barriers that influence exercise behavior are "little attention" or "unreceptive behavior" by the staff of exercise programs (Andrew et al., 1981; Desharnais et al., 1987; Serfass & Gerberich, 1984) and cost (Noland et a l , 1981; Serfass & Gerberich, 1984). W h i l e some inactive individuals appear to be motivated and have the intention to exercise, the discussed barriers may be an important factor that prevents them from actually becoming involved i n physical activity.  Appendix A. Literature Review - Physical Activity  A.1.7  115  Demographics  Demographic variables have a substantial influence on involvement patterns i n physical activity. As Dishman et al. (1985) indicate, all other determinants as well as outcomes of I P A may vary with respect to demographics. It is, for example, quite likely that older people have different attitudes toward physical activity and that their physical health is affected differently than young adults. Stanley and M a d d u x (1986) point out that healthenhancing behaviors are generally associated with certain costs such as time, money, pain, inconvenience. Effects of negative outcomes from these barriers on the adoption of and adherence to exercise behavior should be evaluated. Sex differences with respect to I P A have been documented extensively (e.g. Lupton et al., 1984; Mullen et al., 1987) and shall not be discussed here. T h e following demographic variables have been associated with I P A .  Social/Economic Status Individuals with higher income or white-collar occupation tend to exercise more (Clignet, 1978; Dishman et al., 1985; Gale et al., 1984; Gottlieb & Baker, 1986; Hayes & Ross, 1986; McPherson, 1980; Oldridge, 1984; Ross & Hayes, 1988; Serfass & Gerberich, 1984; Sonstroem, 1982; Stephens, Jacobs & White, 1985).  Age Older people are generally less physically active (Dishman, 1986; Dishman et al., 1985; Hayes & Ross, 1986; Lupton et al., 1984; Mullen et al., 1987; Ross & Hayes, 1988; Sallis et al., 1986; Slenker et al., 1984; Stephens at al., 1985).  Appendix A. Literature Review - Physical Activity  116  Education More educated individuals tend to be more active (Dishman, 1986; Gottlieb &; Baker, 1986; Hayes & Ross, 1986; McPherson, 1980; Ross & Hayes, 1988).  Religion Catholics are generally more involved i n physical activity than protestants or jews (Hayes & Ross, 1986; McPherson, 1980; Mullen et al., 1987; Ross & Hayes, 1988).  Marital Status Physically active people are more likely to be single than married (Gale et al., 1984; Gottlieb & Baker, 1986; Hayes & Ross, 1986; Ross & Hayes, 1988). It appears as if people with a certain demographic profile are more likely to be involved in physical activities; therefore, these demographic variables should be considered when predicting exercise behavior. However, they do not contain any information about the psychological process underlying I P A .  A. 1.8  Biological Traits  Some models of exercise have included biological traits as predictors of I P A . Dishman and Ickes (1981) included "% body fat" as one of the main variables i n their psychobiological model and were able to classify 80% of all subjects accurately into eventual dropouts or adherers. In a similar study "% body fat", body weight and metabolic capacity were successfully used i n the prediction of exercise behavior (Dishman, 1981). Pender and Pender (1986) were able to double the variance explained for when predicting I P A by including body weight. The fundamental problem with the inclusion of these biological trait variables is that  Appendix A. Literature Review - Physical Activity  117  they are at least to some extent an effect of IPA; i n other words, somebody who exercises already is Hkely to have more control over bodyweight and will therefore be able to reduce body fat. In the attempt to understand the process of exercise behavior, it is of more interest, however, to identify psychological as well as demographic variables associated with I P A , because this knowledge can be directly used to develop improved motivational strategies for I P A .  A.1.9  Models of Exercise Behavior  Several researchers have developed models of determinants of I P A in order to understand the process of exercise behavior.  Others have adapted established models from other  scientific disciplines, most notably the Theory of Reasoned Action from social psychology and the Health Belief Model from health psychology.  Theory of Reasoned Action This theory was developed by Fishbein and Ajzen (1975) i n order to understand what determines behavior. They hypothesize that attitudes, consisting of beliefs about consequences and evaluation of importance of a behavior, as well as subjective norms, consisting of expectations by significant others and motivation to conform with these expectations, can adequately predict behavioral intention, which i n turn is strongly related to behavior itself. Sonstroem (1982) discusses the advantages of applying this model to the study of exercise behavior. Recently some successful applications to the study of I P A have been made. Riddle (1980) was able to support the Theory of Reasoned Action; over half of the variance i n the intention to exercise was explained by attitude and subjective norm and the association between behavioral intention and behavior was also high.  G o d i n and Shepard (1986)  found attitudes, defined within Fishbein and Ajzen's theory, to be a good predictor of  Appendix A. Literature Review - Physical Activity  behavioral intention.  118  Similarily, G o d i n et al. (1987) tested a causal model based on  the Theory of Reasoned Action; they concluded that habit predicts behavioral intention and proximal behavior, attitude predicts behavioral intention, and distal behavior can be predicted from behavioral intention as well as proximal behavior. Subjective norm, however, could not predict any of these variables. Hammitt (1984) tested a model very similar to Godin's (behavior was only measured at one point in time) and was able to explain 30% of the variance in exercise behavior and 40% of the variance in intention to exercise. Pender and Pender (1986) successfully tested the Theory of Reasoned Action, but the prediction was very weak.  Health Belief Model According to the original theory developed by Becker et al. (1974) three central concepts determine whether one engages in a behavior to avoid illness: (a) personal susceptibility, that is one has to believe that one is susceptible to illness before initiating behavior, (b) perceptions of the severity of a given condition, and (c) perceptions of the benefits of the recommended action. This last factor is then weighed against potential barriers to action before behavior is initiated. The model has been extended by several researcher by inclusion of cues to action, health locus of control, and health motivation. Even though Dishman (1986) has questioned the applicability of the Health Belief Model ( H B M ) , some successful applications have been made. Slenker et al. (1984) tested a modified version of the H B M . Readiness to undertake the behavior, susceptibility, and probability of threat reduction precede modifying and enabling factors, which in turn precede the compliant behavior. Sixty-one % of the variance i n I P A was accounted for by this model. Similarily Mullen et al. (1987) could account for 57% of the variance i n physical activity level by the H B M , confirming the appropriateness of the H B M for the study of exercise behavior.  Appendix A. Literature Review - Physical Activity  119  Other Models The  P R E C E D E model was applied to I P A by Mullen et al. (1987). It is very similar to  the Health Belief Model, but views behavior as not being directed towards health. T h e P R E C E D E model consists of three factors: (a) predisposing factors (e.g. attitudes), (b) enabling factors (e.g. environment), and (c) reinforcing factors (e.g. social support). It was tested and compared with Fishbein and Ajzen's model and the H B M . T h e variance accounted for i n physical activity level was 57%, 57% and 58% for the H B M , Fishbein and Ajzen and P R E C E D E model, respectively.  This indicates that even though the  P R E C E D E model gave a slightly better prediction, all three models can be useful for explaining exercise behavior and produce similar results. Davis et al. (1987) developed a psychosocial model i n order to identify determinants of participation i n worksite health promotion activities, but their model was not very effective i n predicting participation. Similarily, Noland et al. (1981) developed a general exercise behavior model, but they were not successful i n identifying predictors of I P A either. In an attempt to develop a health enhancement rather than a health protection model, Stanley and M a d d u x (1986) combined and successfully tested protection motivation and self-efficacy theories, which is discussed i n section A.1.3. T h e psychobiological model, mentioned earlier, was tested by Dishman, Ickes and Morgan (1980) and 80% of participants i n an exercise program could accurately be classified into adherers and dropouts by using body composition and self-motivation as predicting variables.  Got-  tlieb and Baker (1986) applied a multilevel model for lifestyle health behavior to I P A and found exercise behavior to be a function of socialization influences, social environment and social networks, and belief. In general, several models appear to be very useful for explaining exercise behavior. In particular, Mullen et al. (1987) have shown that the accuracy of prediction of I P A  Appendix A. Literature Review - Physical Activity  120  with three established models is very similar.  A.2  Outcomes of Physical Activity  The potential beneficial effects of physical activity have become more evident i n recent years and are now well-established i n the public. T h e general notion presented by mass media and the medical community is that exercise is good for you. However, slogans such as "Sport ist M o r d " (German: "exercise is murder") indicate that an awareness of the potential risks of physical activity, such as injuries, exists as well. M a n y studies have found that regular physical activity is related to general physical and psychological well-being.  T h e majority of the benefits that have been associated  with I P A are health-related and include physical fitness, disease prevention, and mental health. Evidence supporting physical and psychological benefits of physical activity is presented i n the next two sections, respectfully. Even though the discussed research represents only a fraction of the existing literature, it gives an adequate picture of the outcomes of I P A .  A.2.1  Physical Benefits  The physical benefits of exercise have traditionally been examined by conducting experiments or cross-sectional surveys. Leon and Fox (1981) provide an extensive review of the literature related to benefits of physical activity and it appears as if there is very little disagreement between researchers on the validity of these findings. M a n y studies report exercisers to generally be i n better health and more physically fit than inactive individuals. However, the pattern of physical activity has to be maintained practically throughout life i n order to optimize these health benefits (Serfass & Gerberich, 1984). T h e important  121  Appendix A. Literature Review - Physical Activity  physical benefits of physical activity are discussed in the following sections.  Good Health Individuals who exercise on a regular basis, that is who are involved i n moderate physical activity three times a week or more, tend to be i n better general health. This is indicated by reduced incidence of illness, fewer number of doctor's visits, lower incidence of absence from work, and so on. Subjects involved in physical activity have a tendency to have an increased feeling of well-being.  However, healthy individuals are more likely to be  physically active than individuals with health problems, as mentioned earlier. Therefore, good health appears to be a predictor of I P A as well. Perceived health, for example, has been identified as a motivating factor for exercise participation, as discussed in more detail in section A.1.3. Nevertheless, general health and well-being have been reported as a major outcome of physcial activity by several researchers (Blackburn, 1978; Driver 1982; Haskell, Montoye & Orenstein, 1985; Larson, 1973; Thomas, 1981).  Physical Fitness Physical fitness, as defined earlier, is improved by regular exercise, and the magnitude of this effect is dependent on intensity, frequency and duration of the exercise program. Physical fitness has a number of components and the type of physical activity determines which aspect of physical fitness is affected. Physical activity can be classified into aerobic exercises, which mainly affect the cardio-respiratory  system, and anaerobic exercises,  which are generally designed to improve strength and flexibility. One particular aspect of physical fitness is cardio-respiratory fitness. The efficiency of the cardio-respiratory  system can be improved through exercise, which is reflected  by an increase in cardiac output and V 0 2 . This has been shown by several researchers  122  Appendix A. Literature Review - Physical Activity  (Blackburn, 1978; Goldwater & CoLLis, 1985; Larson, 1973; Leon & Fox, 1981; Powell & Pfaffenbarger, 1985; Serfass & Gerberich, 1984; Thomas, 1981). Evidence suggests that other components of physical fitness, namely strength, flexibility and muscular endurance, are direct outcomes of I P A as well (Leon & Fox, 1981; Powell & Pfaffenbarger, 1985; Thomas, 1981).  Disease Prevention Haskell (1984) states, that regular physical activity can "delay or prevent the onset or reduce the severity of major chronic diseases" (p. 210). The most prominent example that has been studied extensively is the role of I P A in the prevention of coronary heart disease. It has been well established and documented that exercise greatly reduces the risk and severity of coronary heart disease (e.g. Powell & Pfaffenbarger, 1985). Exercise may have a preventive effect on other diseases such as hypertension, osteoporosis, type 2 diabetes, as well as irregular lipid and carbohydrate metabolism. have not been firmly established.  However, these relationships  Siscovick, Laporte and Newmann (1985) point out  that dose-response effect and the effect of exercise on other diseases are not known. The following authors have reported disease preventive effects of I P A : Blackburn (1978); Haskell (1984); Haskell et al. (1985); Larson (1973); Leon and Fox (1981); Powell and Pfaffenbarger (1985); Siscovick et al. (1985).  Work Capacity Driver (1982) as well as Leon and Fox (1981) showed that physical work capacity and productivity increased when employees initiated a physical activity program or exercised more often. However, improved work capacity might be rela.ted to improved psychological well-being as an outcome of exercise rather than being a direct outcome of I P A .  Appendix A. Literature Review - Physical Activity  123  Weight Control B o d y weight can be controlled and optimized by reduction of adiposity and maintenance of muscle tissue and bone mineralization through exercise (Leon & Fox, 1981).  This  potential benefit of physical activity has been shown by several authors (Haskell, 1984; Larson, 1973; Powell &z Pfaffenbarger, 1985; Serfass & Gerberich, 1984).  Stress Tolerance R o t h and Holmes (1985) showed that physical fitness was a reliable moderator for the relationship between stress and illness, that is physically active people have a greater tolerance to stress (Leon & Fox, 1981). In a controlled experiment Long (1984) concluded that an aerobic conditioning program is an effective stress management treatment. This finding was confirmed by a long-term follow-up study (Long, 1985), i n which subjects participating i n the physical activity program still showed lower levels of anxiety 15 months after the treatment.  A.2.2  Psychological Benefits  A positive relationship between physical and psychological health has been known since early civilization. One of the ancient greek life philosophies was: " a healthy mind i n a healthy body" (Sime, 1984). T h e basic underlying principle of Freud's psychoanalytic theory is that the body is the core of one's psychological identity and many theories suggest that m i n d and body constitute a unit. T h e effects of physical activity on psychological well-being or mental health have been studied by many researchers and several good reviews of this literature have been published (Hughes, 1984; Morgan, 1981; Sime, 1984; Taylor, Sallis & Needle, 1985). M a n y people who exercise report a good and relaxed feeling, an improved quality of  Appendix A. Literature Review - Physical Activity  124  life, as well as a sense of accomplishment and well-being (Sime, 1984). However, some researchers have pointed out, that this effect might be more related to aspects of social involvement and achievement rather than the physical activity per se.  Psychological  well-being might, for example, be mainly due to self-initiative by the exerciser. Even though the relationships between I P A and factors such as depression and anxiety appear to be established, results from studies examining the effect of exercise on mental health are inconsistent and some authors even question their validity.  Hughes (1984)  concludes that the empirical basis for mental health as an outcome of I P A is limited. This is mainly due to methodological deficits. Poor measures of psychological constructs are often used, experimenter or subject biases tend to exist, usually there is an a priori belief i n positive psychological benefits, and very specific treatment populations are mostly used (Hughes, 1984). Sime (1984) points out, that the problems i n providing experimental controls are very serious and that it is virtually impossible to conduct single-blind or double-blind studies. A notable exceptions is the controlled experiment conducted by Goldwater and Collis (1985), in which a placebo group was used. However, Hayes and Ross (1986) state that experiments establish causal order but do not explain whether exercise has an effect on mental health i n the general population. They suggest the use of large, generally healthy community samples. Despite these methodological problems, psychological benefits that have been associated with I P A within the limitations of the studies remain very interesting and informative. Some studies have attributed the positive association between physical activity and psychological well-being to the increased release of endorphins (e.g. Hayes & Ross, 1986; Sime, 1984). Serfass and Gerberich (1984) conclude, for example, that perceived euphoria associated with vigorous exercise is the result of an increased level of beta-endorphins. However, according to Morgan (1981), we do not understand why exercise improves affect.  Appendix A. Literature Review - Physical Activity  125  In addition to being a direct outcome of I P A psychological health can also be induced via the indirect path through physical health, which is i n accordance with most theories about the interaction of body and m i n d . Some of the aspects of psychological health that have been shown to be related to physical activity are presented i n the following sections.  Psychological Well-Being Sime (1984) concludes from his review that empirical and clinical studies provide evidence that exercise results i n a greatly improved state of mind. Stephens examined four large population surveys and found improved mental health to be directly related to physical activity. M a n y studies have identified general psychological health or well-being as one of the major outcomes of I P A (Dishman, 1986; Goldwater & Collis, 1985; Hayes & Ross, 1986; Mehrabian & Bekken, 1986; Morgan, 1981; Ross & Hayes, 1988; Stephens, 1988).  Depression Lower levels of depression have been associated with I P A and exercise has successfully been used as a therapy for depressed patients (Powell & Pfaffenbarger, 1985; Serfass & Gerberich, 1984; Sime, 1984; Stephens, 1988; Taylor et al., 1985; Thomas et al., 1981). Although most studies have examined samples from depressed populations, Ross and Hayes (1988) were able to show lower levels of depression i n active subjects from a healthy community sample as well.  Anxiety Following exercise individuals tend to be more relaxed (Bassey &: Fentem, 1981; Goldwater & Collis, 1985; Long, 1984, 1985; Powell & Pfaffenbarger, 1985; Rathbone, 1976;  Appendix A. Literature Review - Physical Activity  126  Ross & Hayes, 1988; Serfass & Gerberich, 1984; Sime, 1984; Stephens, 1988; Taylor et al., 1985; Thomas et al., 1981; Tucker, 1987).  Emotional Stability People who exercise tend to show greater emotional stability (Bassey & Fentem, 1981; Serfass & Gerberich, 1984; Sime, 1984; Tucker, 1987).  Confidence/Self-Concept Physical activity i n purely recreational or competitive form appears to give people a sense of achievement, which can result i n increased self-esteem, confidence or self-concept (Bassey & Fentem, 1981; Driver k Ratliff, 1982; Hughes, 1984; Morgan, 1981; Sime, 1984; Tucker, 1987).  Other Aspects Mehrabian & Bekken (1986) found that trait dominance and trait pleasure tended to be higher i n people who exercise; this is an indication of exuberance and relaxation when combined with high and low arousability, respectively.  I P A has also been associated  with more positive mood (Abele & Brehm, 1985; Stephens, 1988), increased creativeness (Tucker, 1987), as well as improved socialization and life enjoyment (Bassey & Fentem, 1981).  A.3  Summary  A large number of variables have been studied i n conjunction with physical activity by sport scientists. Even though some findings are controversial, researchers have repeatedly shown a positive association between increased involvement i n physical activity and  Appendix A. Literature Review - Physical Activity  127  variables discussed i n sections A . l and A.2. Past exercise behavior has been shown to influence behavioral intention and present behavior as well as physical fitness, a direct outcome of exercise. Attitudes towards I P A seem to predict I P A , provided attitudes are measured appropriately. A highly motivated individual is more likely to exercise than an individual who is not motivated. Social support is important for the intention to exercise. Barriers such as cost and time can prevent an individual to become involved i n physical activity. Some demographic variables representing social status, economic status and maturity have been associated with exercise behavior. These concepts have been defined as predicting variables i n the hypothetical model of I P A , model II. Knowledge about exercise and fitness does not seem to influence exercise behavior.  Biological traits are not of interest when attempting to understand  the process of involvement i n physical activity. The relationships between predictors and I P A are consistent w i t h the Theory of Reasoned Action and the Health Belief Model. A positive association between involvement i n physical activity and physical fitness has been well established on a physiological level. Even though there are serious problems associated with studying psychological benefits of physical activity, general psychological well-being appears to be directly related to I P A . Physical and psychological fitness were defined as outcomes of involvement i n physical activity i n model II. Other benefits such as improved health and work capacity, weight control, increased stress tolerance, decreased depression and anxiety were not examined in this study.  Appendix B Causal Modeling - Theory and General Procedural Guidelines  As mentioned i n section 1.5 the numerous statistical techniques based on the theory of causal modeling come under various names: path analysis, structural equation modeling, cross-lagged panel correlation technique, simultaneous equation systems, analysis of covariance structure, confirmatory analysis. These techniques can be viewed as a complex extension of factor analytic and regression methods, which have been developed for the evaluation of observational data. They are designed to test the fit between a hypothetical model and empirical data. T h e model has to be developed and based on solid theoretical grounds and can consist of the following elements: • Latent variables: defined abstract concepts that are abstractions and cannot be directly measured or observed (such as the concepts denned i n section 1.2 and 1.3) • Manifest variables: directly observed or measured variables that have been operationalized as indicators of latent variables (such as the variables selected in section 2.3) • Directed paths: hypothesized causal relationships between latent constructs (such as the relationships described i n sections 1.2 and 1.3). These directed paths can only occur from independent to dependent variables. Independent or x variables are known as exogenous variables and dependent or y variables are known as endogenous variables.  128  Appendix B. Causal Modeling  129  The structural equation model defines these elements i n terms of the mathematical model used to assess the fit of the model to the data. Complex computer programs are then applied to the structural equation model to estimate the unknown coefficients i n a set of structural equations. These estimated parameters represent the basis for evaluating the validity of the hypothetical model. Several generalized models have been developed by statisticians and psychometricians and are available as computer software packages. In order to clearly present the description of actual procedures i n performing causal modeling analyses some aspects of the theory behind causal modeling have to be discussed.  B.l  The Theory  B.l.l  Model Selection  The concept of fitting a hypothetical model to empirical data requires important consideration with respect to the choice of a model.  T h e general idea behind structural  equation modeling is to reduce the information contained i n the data in order to interpret phenomena.  This is the general purpose of most statistics.  One of the primary  advantages of causal modeling is that it allows the researcher to test and interpret comprehensive models of unmeasured constructs, observed variables and relationships with causal direction. These models are very useful i n explaining processes such as behaviors or sociological phenomena. Phenomena can generally be well understood and explained i n terms of a multivariate theoretical model; studying them i n isolation or only i n relation to a few selected variables can Hmit understanding and interpretability. Simpler models are easier to understand. Therefore the researcher is i n search for the simplest model that is still interpretable and can explain the phenomena under study (assuming, of course, that the researcher is dedicated to progress of science).  A p p e n d i x B.  Causai Modeling  130  However, the model also has to fit the data and, unfortunately, causal modeling works the other way. The best fitting model is the completely unrestrictive model. A restrictive model defined by the researcher has to be sufficiently simple to allow meaningful interpretation in terms of the theoretical basis. Simpler models are more difficult to fit to the data. Therefore, the fit of a model could generally be improved by relaxing more and more parameters, which would result in a more and more complex model. This defies the purpose of developing and testing a theoretical model. The ideal is a golden path or "golden model", which produces an excellent fit of model to data with simple structure. Factor scores are indeterminant. Due to their definition, there is an infinite number of factor scores corresponding to the same factor loadings. Therefore, different models that fit the data equally well can always be found. This illustrates why causal modeling is a confirmatory methodology. Exploratory model searching without a fixed theoretical model is possible using causal modeling methodology but seldom produces any useful knowledge.  Other statistical methods such as exploratory factor analysis or multiple  regression should be used for exploratory purposes. The degree of confirmatory restrictions on causal models has become a subject of ongoing controversy i n the literature on causal modeling methods.  Some researchers  (e.g., Anderson &> Gerbing, 1988) advocate a model building approach, which allows for a certain degree for exploratory model searching. Others (e.g., M c D o n a l d , personal communication) believe that causal models should only be tested i n a truly confirmatory sense, which would practically eliminate the option of respecification (discussed in section B.2.3). T h e degree to which a model can be modified has to rely on the nature of the data as well as on the soundness of the theory underlying the model. If the theoretical foundations of the model are very solid and based on existing evidence, only minor modifications of the model can be justified, whereas a model based on a new theory may be subjected to respecification as part of a model-building process.  Appendix B. Causal Modeling  B.1.2  131  The L I S R E L Model  The L I S R E L (Linear Structural Relations) model and computer program was used for most tests of models of I P A in this study. It was developed by Joreskog i n 1973 and marketed across the world as the first computer software package for the analysis of structural equation models. It is to date the most widely used model and program for the evaluation of causal models and it has been applied by many researchers i n tests of hypothetical models or confirmatory factor analyses as part of sociological or psychological research. However, L I S R E L is not necessarily the simplest or most readily understandable model. It also has its limitations and problems with respect to applicability, which shall be discussed later. In this study L I S R E L was selected for most statistical analyses, because it was easily accessible and convenient to use as it is embedded i n the Statistical Package for the Social Sciences (SPSS) as a userprocedure. Even though it is realized that there might be more precise and simpler ways to express the structural equation model as a mathematical model (such as the C O S A N model discussed later), the L I S R E L model is used here to explain the mathematical theory behind causal modeling. The general goal of causal modeling is to produce an estimated variance-covariance matrix from the model that is as close as possible to the sample variance-covariance matrix foT all observed variables. If they are close, the hypothetical causal structure is said to be consistent with the relationships between observed variables. The L I S R E L model consists of two basic parts: • T h e Measurement Model defines which observed or manifest variables measure the latent variables or abstract constructs. A test of the measurement model assesses the measurement properties of these observed variables.  Appendix B. Causal Modeling  132  • T h e Structural Equation Model specifies the hypothesized directed relationships between latent variables.  A test of the structural equation model assesses the  strength of hypothesized causal effects and the amount of unexplained variance. Let n' = (771,772, •••tVm) be a random vector of latent dependent variables and £' = (£1, £2, •••,£") be a random vector of latent independent variables. Then 77 =  Br, + T( + (  where B{m x m ) is a coefficient matrix representing direct causal effects of n variables on other n variables r(rn x n) is a coefficient matrix representing direct causal effects of £ variables on 77 variables £ = (£1, (2,  Cm) is a random vector of residuals representing errors i n the equations.  Since the vectors 77 and £ are not directly observed, they have to be measured by two vectors y' = (2/1,2/2,-^p) and X' =  (Xi,X ,  ---yXq)  2  in the following manner: V =  +  e  x = A £+ 6 x  where e is a vector of errors of measurement i n y, 6 is a vector of errors of measurement i n x, A (p x m ) is a matrix of regression coefficients of y on n, y  A (q x n) is a matrix of regression coefficients of x on £. x  133  Appendix B. Causal Modeling  T h e following assumptions are made: 1. £ is uncorrected with ( 2. e is uncorrelated with n 3. 8 is uncorrelated with £ 4. (, e and 8 are mutually uncorrelated 5. B has zeros i n the diagonal and I — B is nonsingular Let $ ( n x n) be the covariance matrix of £ $ ( m x m ) be the covariance matrix of £ 0  £  be the covariance matrix of e  0,5 be the covariance matrix of 8 z — {y',x') be the matrix of all observed variables then it follows (Joreskog, 1985) that  " A„(J - B J - ^ r ' + * ) ( / - 5 ' ) - ^ + 0e Ay(7 - B ) r $ A ^ . _1  [ A $r(j - s ' )  - 1  x  ^  A $A; + X  where E is the covariance of z. Elements of the matrices A , A , B, T, $, y  x  0  e  and 0^ consist of parameters which  can be of the following form: • fixed at an assigned value •  constrained to be equal to one or more other parameters, but unknown  • free or unknown  Appendix B. Causal Modeling  134  The latent variables in 77 and £ have an arbitrary scale. In the structural model both the origin and the unit of measurment have to be defined. Since observed variables are reported in deviation form, the origin is already fixed at zero. There are basically two ways of assigning a unit of measurement to the latent variables: • One can set the unit of measurement to be the same as the unit of one of the observed variables by fixing one of the elements of K and A y  x  at 1 in each column.  • One can alternatively fix the variances of latent variables at 1 by fixing the diagonal elements of $ and $ at 1. A n example shall illustrate the setup of a structural equation model as a L I S R E L model.  135  Appendix B. Causal Modeling  Consider model C M I 5 i n figure 6, which is actually the final version of model I. T h e following equations illustrate the location of parameters i n the equations. Structural Equation Model  7i  V 0  0 72 )  Measurement Model for y  /  A  0^  1  A  2  0  2/3  A  3  0  2/4  A  4  0  2/5  0  A  5  2/6  0  A  6  Vr  0  A  7  0  A  fi  \ «J y  /  \ ei  £2  Measurement Model for x  /  \  £7 A  9  * 1  •^10  0  An  0  Al2  0  x$  0  Al3  X  0  A 4  0  ^15  X  2  X  3  6  \  0  X 7  1  V  68  J  X  \  6  7  )  136  Appendix B. Causal Modeling  Note that all latent exogenous variables are hypothesized to be correlated as stated by the model (i.e. off-diagonal elements of $ are free parameters). In order to transform these structural equations into L I S R E L control language several matrix specifications have to be made. L I S R E L requires the specification of four types of variables: • p endogenous manifest variables • q exogenous manifest variables • m endogenous latent variables • n exogenous latent variables The pattern for these variables has to be specified i n the A  u  and A  x  matrices. For the  measurement models the matrix $ , which is the variance-covariance matrix of latent variables, is defined as a symetric matrix with fixed ones i n the diagonal. This fixes the variances of latent variables at one and has the effect of assigning a unit of measurement. In the structural model, the matrices of causal path coefficients, B and T, can either be i n fixed form, which requires freeing elements corresponding to hypothesized path coefficients, or i n free form, which requires fixing all elements corresponding to a path that has not been hypothesized.  To assign the unit of measurement i n the structural  model, one can • fix one free parameter per column i n both A matrices at one, and estimate the diagonals of $ and \? as free paramters (this sets the unit of measurement of each latent variable equal to the scale of one manifest variable, while estimating the variance of the latent variable); or • the diagonals of $ and $ are fixed at one, which fixes the unit of measurement of each latent variable.  137  Appendix B. Causal Modeling  Before a model can be tested by estimating parameters the model should be identified.  B.1.3  M o d e l Identification  The concept of model identification can be best explained with the relationship between the number of structural equations and parameters. In order for the model to be identified there has to be at least as many equations as parameters to be estimated. T h e identification problem manifests itself i n the following way. A given set of values of parameters results i n one and only one matrix S . However, there may be several sets of parameters or structures that generate the same matrix S . If two structures produce the same S , the structures are said to be equivalent. If a parameter has the same value i n both structures, it is said to be identified. If all parameters are identified the model is identified. T h e identification status of a parameter is therefore very important for the interpretation of results. Unfortunately, evaluating the identification status of a model is a rather difficult task. Berry (1984) describes two practical methods of ensuring identification. T h e order condition involves a simpler method, but is not a sufficient condition for model identification. Each structural equation is tested separately for the condition that  m +k > m — 1 e  e  where m is the number of endogenous manifest variables excluded from the structural equation e  being tested k  e  is the number of exogenous manifest variables excluded from the structural equation being tested  m  is the total number of endogenous manifest variables  In the test of the rank condition a matrix of path coefficients has to be transformed into simple form and a decision can be made whether the model is underidentified (not  138  Appendix B. Causal Modeling  enough equations), exactly identified (the right number of equations), or overidentified (too many equations).  B.1.4  Estimation of the Model  The input matrix used for model estimation is a symetric covariance or correlation matrix of all manifest variables. The correlation matrix can be used, if the units of measurement of those variables are arbitrary.  T h e following estimation procedures are available i n  LISREL: 1. Initial Estimates (IE): This procedure is non-iterative and fast and is normally used to produce starting values for maximum likelihood estimation and unweighted least squares estimation. 2. Unweighted Least Squares (ULS): This iterative procedure minimizes the following fitting function F = l/2ir((S-E) ) 2  3. Maximum Likelihood fAfLJ:This estimation procedure is iterative as well and minimizes the fitting function F = log{det(Y,)) + t r ( S E ) - log{det{S)) - (p + q) - 1  The U L S and M L methods estimate all independent parameters by minimizing the fitting function with respect to these parameters. The fitting function F is positive and would be equal to zero i n case of a perfect fit of the model (i.e. 5 = £ ) . N o distributional assumptions have to be made for the U L S function, whereas the M L estimation is based on the assumption that the observed variables have a multinomial distribution. If the assumption of multivariate normality is met, maximum likelihood gives the most precise  Appendix B. CausaJ Modeling  139  estimation of parameters and it is therefore the most often used estimation method i n model fitting.  If it is not met, parameters can be estimated but standard errors are  invalid. A positive definite input matrix is required for M L estimation. Other estimation methods such as elliptical and asymptotically distribution free methods designed for the treatment of non-normal data and generalized least squares are available i n other computer software packages, which are described below. T h e only constraint on the M L fitting function is that the estimated matrix S has to be positive definite. Solutions can therefore exist outside the admissable parameter space (e.g. correlations greater than one, negative variances). It is, however, often possible " t o use various tricks to force the program to stay within the admissable parameter space" (Joreskog & Sorbom, 1985, p. 1.32). These "tricks" are discussed i n section 3.4.2.  B.1.5  Assessment of Fit  Primary aims i n model fitting are the production of valid indices of fit and valid parameter estimates. The first step in assessing the fit of a model is to inspect all estimated parameters. If unreasonable values occur, such as correlations that are larger than one i n magnitude, unreasonable large parameter values, negative squared multiple correlations or negative coefficients of determination, the model has been misspecified or does not fit the data. If any of the matrices $ ,  0 , 0$ of estimated parameters are not positive e  definite (i.e. if they have at least one negative Eigenvalue), the model does not fit the data and no valid interpretations can be made.  Criteria for the Assessment of Overall Fit A hypothetical model is never confirmed by data; by testing the model one can only gain support of the hypthesis by failing to disconfirm the model. The main measure of overall  Appendix B. Causal Modeling  140  fit i n the L I S R E L model is the %-square value as defined by Joreskog (1985) X = (n - 1)F 2  with associated degrees of freedom  df = l/2k(k +  l)-t  where n is the sample size F is the value of the fitting function after minimization k is the number of observed variables (p + q) t is the number of parameters estimated  This x  2  value can only be considered a valid test statistic if the following assumptions  are met: 1. all observed variables have multivariate normal distribution 2. the sample covariance matrix S is given 3. the sample size n is fairly large Because these assumptions are rarely met, % should be regarded as a criterion to decide 2  whether the fit is adequate or not rather than a test statistic. corresponds to a better fit of the model. However, x  2  In general, a lower  x  2  is sensitive to sample size and  departures from multivariate normality of observed variables.  Since % is linearily de2  pendent on sample size, it is, for example, practically impossible to get a low % value 2  with large samples. Some researchers have suggested to use the ratio of Xzl^f  a s  a  relative measure of fit.  Although this technique is questionable for comparing the fit of models using different  141  Appendix B. Causal Modeling  datasets, it may be useful to describe the fit of models for one set of data.  However,  suggested standards for an acceptable fit range from 2.0 to as high as 10.0 and changes in fit are not always detectable. A n alternate way of using x  2  i to assess the change i n fit between two models. If a s  model is, for example, modified based on the results from an initial test, the improvement i n fit can be assessed by evaluating whether the change i n % i n conjunction with 2  the difference i n associated degrees of freedom is significant or not. If it is, a significant improvement of the model has been achieved and the new model therefore fits the data better. If the difference is not significant, the modifications have not produced any improvement i n model fit and the original model should therefore be retained. This procedure, known as the Sequential Chi-Square Difference test, is not dependent on sample size. Its use for the assessment of overall model fit has been suggested by Anderson and Gerbing (1988). Steiger, Shapiro and Browne (1985) showed analytically that sequential chi-square differnce tests are asymptotically independent. Another fit assessment criterion given by L I S R E L is the Goodness of Fit Index ( G F I ) and the Adjusted Goodness of Fit Index ( A G F I ) , which is adjusted for the degrees of freedom.  B o t h indices range from zero to one and represent the relative amount of  variances and covariances jointly accounted for by the model. They do not depend on sample size and are robust against departures from multivariate normality.  However,  their distributions are unknown and therefore no standards exist for comparisons. The third measure of overall model fit i n L I S R E L is the Root Mean Square Residual. It is calculated from the matrix of residuals R = S — £ as the average residual variance and covariance.  Appendix B. Causal Modeling  142  Criteria for Detecting Location of Specification Error Past experience with the application of L I S R E L to various models has shown that the program is very sensitive to minor misspecifications. If, for example, a manifest variable is excluded from a misspecified model, which produced an invalid solution, the test of this new model can very likely produce a converged fitting function and a highly improved fit based on the general criteria described i n the previous section. Because of the sensitive nature of the program, methods are necessary to specifically locate one or more parameters that appear to be misspecified. In the case of an acceptable overall fit of the model, indicated by high G F I and low R M R , one or more parameters might still be misspecified. A model could, for example, have an overall fit that is very good, but one of the predicted relationships has been falsely defined and should be eliminated as well. Such cases require methods for detecting the location of specification errors as well. T h e following descriptions of various criteria should be regarded i n light of the requirement that any modifications of a model have to be accompanied by theoretical justifications. Joreskog and Sorbom suggest a number of procedures for the detection of specification errors. Residuals can be inspected i n a matrix of raw residuals, where elements r\j are calculated as  They represent the difference between the sample covariance and the covariance estimate given by the L I S R E L model. L I S R E L also produces a matrix of normalized residuals which are raw residuals standardized by their estimated asypmtotic variance. Joreskog suggests that normalized residuals which are larger than two i n magnitude indicate a possible specification error. In such a case the relationship between observed variables i and j should be reevaluated based on the fact that their covariance could not be  143  Appendix B. Causal Modeling  reproduced by the model. A modification index is defined as n / 2 times the ratio of first order derivative and second order derivative of the fitting function with respect to a parameter. It represents the m i n i m u m decrease i n % if that parameter is relaxed and estimated as a free param2  eter i n the model. T h e highest modification index indicates which (possibly omitted) parameter could improve the overall fit of the model the most if it were included i n the model. It has to be emphasized again that any decision with respect to redefining the model based on these criteria has to be profoundly based on theoretical considerations.  That  is, if a new parameter is entered into the model it has to be interpretable i n terms of the theoretical model; if a parameter is ehminated, its exclusion from the model has to be justifiable.  Other Criteria The fit assessment criteria suggested by Joreskog have been criticized by several psychometricians and statisticians.  Dillon and Goldstein (1984) conclude that G F I and  likelihood-ratio statistic (% ) should be replaced by other statistics. M c D o n a l d and Marsh 2  (in press) point out that most available fit assessment methods depend largely on sample size or on expressing fit relative to the fit of a chosen nullmodel. T h e nullmodel is defined as the most restrictive theoretically defensible model for relative fit indices such as the Bentler-Bonett  normed fit index (Bentler, 1985). T h e Tucker-Lewis Index and the  Unbiassed Relative Noncentrality Index (McDonald) are suggested as relative fit indices by M c D o n a l d and Marsh. However, they suggest that comparing two indices gives more information than evaluating one relative index. Steiger and Lind's Badness of Fit Index and MacDonald's Measure of Centrality are the only absolute measures of fit that do not depend on sample size, according to M a c D o n a l d . Confidence bounds can be constructed  Appendix B. Causal Modeling  144  to assess whether specific parameters are significant or not.  B.1.6  Other Models  The perhaps simplest and most general model representing structural equation systems is the C O S A N model, which was developed by M c D o n a l d . It states that any model can be expressed as  £ =  F F ...F PFi..F! F[ 1  2  k  i  where £ is the variance-covariance matrix of a population for-a set of variables, P is symetric, and elements of any F or P matrix may be constrained to be equal to each other or to a specified numerical value. A L I S R E L - t y p e causal model can easily be defined as a C O S A N model of order 2 by applying the R A M system developed by M c A r d l e and McDonald. Bentler developed the E Q S computer program for testing structural equation models, which has been embedded i n the Biomedical Computer Programs ( B M D P ) package.  statistical  It gives estimates of multivariate normality and has alternative estimation  methods for the analysis of non-normal data. EZPath, which was developed by Steiger and is available under S Y S T A T , is a very userfriendly and efficient program that allows the user to set up models i n a quasigraphic representation. model.  T h e program then transforms this input into a C O S A N - t y p e  Minimization of the fitting function can be followed visually and the resulting  parameters are written into the original model, ensuring easy interpretability of results. It is presently the only program that provides measures of non-centrality i n addition to various other fit assessment criteria. Confidence intervals for the Goodness of F i t indices are given as well, which allows the researcher to evaluate the fit of the model to the data more appropriately.  145  Appendix B. Causal Modeling  B.1.7  Categorical Data  M a n y sociological studies include variables of categorical nature, that is variables that can only be measured on ordinal or nominal scales of measurement. They typically only have a few possible values, such as general categories. These variables are often treated as variables with continuous underlying distributions i n statistical analyses, which implies violating the assumptions of many statistical tests.  In particular, the assumption of  multivariate normality is most likely not met by categorical variables.  In a test of a  structural equation model involving such variables maximum likelihood estimation could possibly produce invalid parameters. Several alternative estimation methods have been developed.  M u t h e n (1985) de-  veloped and tested the Categorical Variable Method ( C V M ) as an alternative estimation method and implemented it into the computer program L I S C O M P . T h e program P R E L I S was developed by Joreskog as a preprocessor for categorical data. T h e program produces detailed information about distributional characteristics of the variables.  Tables and  statistics are calculated for three types of variable pairs: • continuous vs. continuous: T h e product moment correlation is calculated for all observations with no missing data. • continuous vs. categorical: T h e mean value of the continuous variable for all subjects indicating one category is calculated. This produces a table with means for each category, which is used to estimate the polyserial correlation between the two variables under the assumption of bivariate normality. • categorical vs.  categorical: A contingency table or crosstabulation is given and  used to estimate the polychoric correlation, again under the assumption of bivariate normality.  Appendix B. Causal Modeling  146  This produces a new correlation matrix consisting of product moment, polyserial and polychoric correlations, which is then used as input for the L I S R E L model. The L I S R E L computer program has a built-in option to automatically calculate these correlations and estimate the parameters i n the model with it.  B.1.8  Non-Normal Data  One of the major assumptions underlying the distribution of the M L function is multivariate normality.  Several other estimation methods have been developed that do not  require this assumption. Unweighted Least Squares ( U L S ) or Generalized Least Squares ( G L S ) can be used to estimate parameters for models with non-normally  distributed  data. Unfortunately, the fitting functions produce parameter estimates, which are not as precise as m a x i m u m likelihood estimates. Bentler developed elliptical estimation methods and Asymptotically Distribution Free ( A D F ) methods to give more precise solutions for non-normal data. They are available under E Q S along with criteria for the assesment of multivariate normality (e.g., Mardia's K a p p a Coefficient). Anderson and Gerbing (1988) report that several researchers have tested the robustness of estimation procedures with respect to violations of the assumption of multivariate normality i n Monte-Carlo studies. In general, maximum likelihood estimations appear to be robust with respect to parameter estimates, but standard errors are likely to be affected.  B.2  General Procedural Guidelines  Practical guidelines for the development and evaluation of causal models have been given by a number of authors (e.g., Bentler, 1985; Dillon Sz Goldstein, 1984; Everitt,1982; James, Mulaik & Brett, 1982; Joreskog Sz Sorbom, 1985; Long, 1983). Although specific  Appendix B. Causal Modeling  147  suggested procedures vary, researchers appear to agree on their general outline. One of the most important and most often neglected steps i n causal modeling is the development of a sound theoretical model with justifiable hypothesized causal relationships. T h e development of model I and model II, which are the causal models examined i n this study, is discussed i n sections 1.2 and 1.3. The next important step is finding indicators of the unmeasured variables or latent constructs, that have good measurement properties, i n the operationalization of variables, which is discussed i n section 2.3. In studies involving primary data analyses established measures of latent constructs with known validity and reliability should be selected as variables for the study. In studies involving secondary data analysis, only the variables which satisfy that condition should be selected from the given variables. Several researchers have suggested a two-step approach to testing causal models (e.g. Anderson & Gerbing, 1988; Joreskog & Sorbom, 1985). It is suggested to first test the measurement model by itself and then employ a satisfactory solution into the structural equation model before testing it. T h e mathematical definitions of these models have been described i n section B.1.2, whereas practical procedures are explained i n the following sections.  B.2.1  Measurement Model  The first step i n testing a hypothetical model is a test of the measurement model. T h e hypothesized factor structure is tested by applying confirmatory factor analysis. Structural equations and therefore the hypothesized relationships between latent variables are ignored.  The test of the measurement model attempts to establish the validity of the  hypothesized factor pattern. It indicates how well the manifest variables measure the latent variables. B y testing the measurement model first, the researcher would, i n a sense, like to ensure that the abstract concepts, which are defined on the basis of a theoretical  Appendix B. Causal Modeling  148  model, are appropriately measured by observed variables, before assessing the strength of relationships between them. The measurement model can be tested for endogenous and exogenous variables separately or for all observed variables jointly, depending on the size of the model. In order to run a confirmatory factor analysis, parameters have to be specified i n the following manner: In a chosen A matrix (it makes no difference whether A  y  or A  x  is selected)  each column contains free paramters for the manifest variables, which are hypothesized to measure the latent variable corresponding to that column, and fixed zeros elsewhere. Therefore each row only has one free parameter, unless a manifest variable is hypothesized to load on more than one factor.  This means that observed variables are only  allowed to load on the factors they are hypothesized to measure. The number of factors is given by the specification of latent variables. In exploratory factor analysis the number of factors is generally selected during the analysis (such as in the procedure of retaining factors with an Eigenvalue greater than one) and all manifest variables are allowed to load on all latent variables. This illustrates the distinction between exploratory and confirmatory analysis. Furthermore, off-diagonal elements of the matrix $ are estimated as free parameters i n testing the measurement model, which allows for correlated factors. The L I S R E L program is then run on the covariance or correlation matrix of the observed variables.  The estimated parameters i n the A matrix can be interpreted as  factor loadings, generally ranging from zero to one. Criteria for the assessment of fit, which are described above, are then used to decide whether the measurement model is adequate or not. If it is, the structural equation model is tested. If it is not, respecification and testing of a modified model is considered, which will be described below.  Appendix B. Causal Modeling  B.2.2  149  Structural Equation Model  In the case of an acceptable fit of the measurement model, its structure is directly implemented as part of the structural model. In addition, hypothesized causal relationships have to be specified as demonstrated in the example in section B.1.2. A l l elements of the B and T matrices set to a free parameter represent a hypothesized path coefficient.  All  other elements should be set to zero. The unit of measurement of the latent variables has to be fixed by applying either of the two procedures described in section B.1.2. The structural equation model can then be tested using the L I S R E L program. Again, the fit of the model is assessed, and respecification considered on the basis of fit assessment. If an acceptable fit has been found, the standardized solution can be used to interpret the strength of hypothesized relationships. The overall fit and estimated parameter values should then be interpreted with respect to the original theoretical model.  B.2.3  Respecification  If a model is misspecified there are four possible scenarios resulting from its test: 1. The model has an acceptable overall fit and cannot be improved significantly without major changes to the structure. 2. The model has an acceptable overall fit, but the fit could be significantly improved by making justifiable modifications, which do not alter the general structure. 3. The model has an overall fit that is not acceptable, and the fit could be significantly improved by making justifiable modifications, which do not alter the general structure. 4. The model has an overall fit that is not acceptable and cannot be improved significantly without major changes to the structure.  150  Appendix B. Causal Modeling  Case 1 represents the simplest and most satisfying situation, since the final solution is reached and the model can be interpreted in light of this solution.  Case 4 is almost  hopeless and would require a redevelopment of the theoretical model or collection of new data.  Case 2 and 3 are the most common and require additional work, the nature of  which is discussed in this section. It should be pointed out that sampling error might be a cause for case 3 and 4 as well. The location of potential specification errors can be detected by procedures discussed in section B.1.5. T h e following modifications can be implemented i n order to improve the fit of a measurement model i n cases 2 and 3: • Relate a manifest variable to a different latent variable. • Eliminate a manifest variable. • Relate a manifest variable to a second factor as well. • Correlate measurement errors. These modifications can only be done if, and only if, they are justifiable on solid theoretical grounds. Only one modification should be implemented per respecification of the model. If no indicators appear to properly measure a latent variable, its ehmination can be considered. This should be viewed, however, as a last resort. Cases 2, 3 or 4 should normally not occur for the structural model if the measurement model has been properly specified or respecified. If they do occur, the above options for modifications should only be used if there is strong theoretical support for them.  In  extreme cases causal path can be eliminated, added or redirected, but this option should be used with extreme caution. After respecification the model is tested again and evaluated according to the same procedure. Experience with previous models has shown that the length of this process  Appendix B. Causal Modeling  151  is highly variable. W h i l e some models only require minor respecification, others have to be modified many times before a satisfactory solution is found.  Appendix C Questionnaire of the 1981 Canada Fitness Survey  152  Appendix C. Questionnaire of the 1981 Canada Fitness Survey  PHYSICAL ACTIVITIES WHAT YOU DO AT WORK OR AT SCHOOL OR IN THE HOME. PLUS YOUR ACTIVITY IN YOUR LEISURE TIME ALL CONTRIBUTE TO YOUR CURRENT LEVEL Of FITNESS. THE FOLLOWING QUESTIONS WILL PROVIOE A COMPLETE PICTURE OF ALL YOUR ACTIVITIES. TO HELP QUESTIONS WEEK, ONE FOR THOSE  YOU OESCRI8E YOUR ACTIVITIES. WE HAVE DESIGNED FOUR - ONE FOR THOSE YOU DO DAILY, ONE FOR THOSE YOU DO EACH FOR THOSE YOU HAVE DONE IN THE LAST MONTH, AND THE FOURTH ACTIVITIES YOU HAVE DONE IN THE LAST YEAR.  DAILY ACTIVITIES For those activities which you do most days of the week (such as work, school and housework), how muchtime'doyou spend. . .  1.  HxxA 1/4 of 9* arm  AVTMHI of i f . oma  • • in • •  • • • • •  Sitting Standing Walking Walking up • u i r a L i f t i n g or c a r r y i n g h e a v y o b j e c t s  Airmail* of i n *  AbQUX 1/4 of tha dm*  • • • • •  of tf* fjmt  • • • • •  2. WEEKLY ACTIVITIES Please refer to the reference card for a list of activities. Answer the following for the physical activities you do each week. L i g h t h o o a a w o r k a n d K a n d y w o r f c w » t h i n g dbjhea. ironing, m a k i n g b e d a , m o w i n g l a w n , ate Ught Brno tan»  Numtwr of occAttont ••eft men fh J  »  M  A  M  J  J  A  1  O  M  O  from PKKKUWA >MMn  Mtxfcjm  Hoavy  sagr« (M^i  prrrMn Ate**  pw» prrean  wn«  biMfh^f  bnMtfwvj  I • I . I • II • I . I . II • I • 1 . II • I . I • 1 U L J  nemm  •  Mmtvy  •  •  H a a v y h o u a a w o r k a n d h a n d y w o r k w a t h i n g a n d w a x i n g f l o o r * , p a i n t i n g , ate light  MnoVim  am* Nvmbar of  f  J  M  A  M  J  rrrmmrm J  A  J  O  N  O  l-  ,  I . I • I • II . I. I • II . I , I , II • I • I • I U L J  ,  •  ,  •  •  L. , • I  N a m a of activity OryaWarJ  J  U  M  Morr*-»f of occ«My« •axhrron* U j J A  A  O  %  M  A^t^. am* t+t «»w«  O  Intarwfv M«Sum  L-^M  I . I . I. ii • I. I . il . i. i. i i . i . I. I I M , l • a  a  a  a  a  »  H«arvt  •  * « tn • t»*gu« rm Ho  jm  No  •  •  L7J  •  a  •  a  a  1, ,• 1  N a m a of activity  Hvtvb* of o c c a u n  Avtx»ot  »»cn month J  *  M  A  M  J  oma  J  A  J  O  N  LV  kmnt HAtxSurn  1 1  O  I • I • I. II. I. I. M . l. I, l l , I , I, I I II • I. • a  a  a  J  f |  M I  A II  a  I Nurriw of o c t w o r a Mch month  N a m a of activity  I  a  M I  J I  J II  A I  a  S  O I I  M I  I  I  I  I I  XW» I  0»OAn«Md  ComortrtA.  I*  'lit. £2.  *°  •  kttararly M«drum  light  <*n  O  •  a  Av»»»»ot tima  I  •  HO«VY  I  1 Htavt TM  I  I  '  I  1  • UJ  « I MO  ' r*»  I  ' 1 Mo  endix C. Questionnaire of the 1981 Canada Fitness Survey  3.  ACTIVITIES IN THE LAST MONTH L Please refer to the reference card for a list of activities. Answer the following for the physical activities yoo have done at least once in the last month. I Do not include activities already listed m Weekly Activities) Gardening and cultivating *uch as spading, digging, weeding MMwn Ligm  *c*v*etH «p«m on Men occiMn Hnj Mirw  monfri  U  •  L J  •  Shovelling mow  lm»nsffy VUOaj^ Vsr^e '«(*• enor  Light  OccMton* in tr* tag*  Av*r»Q4 ami aciuatv « f H on **chocca*>on Hn) Mr«  U  •  LxJ  K M W  •  Mowing the lawn (pushing a power mower)  •  InunMy M«*u<n Light  Av*r»gt WW  •  on OOCA acceaxy Hn Uirw  u Name of activity  •  •  i  OccM*om  •  Medium  •  Hww  Light  •  fcUdum  •  HNV«  Away* Hm Min*  Ugnt  M«oVjn  K«9vy  A w i g i torn* Hn Mint  LtgM  Light  L J  Mnj  U  Mina  L J  in krvwr, or in • i n g m y«* HO  • • • •  Cornp«tiOv»,  YM  NO  •  Name of activity  Avinjoi orm  L J  Hn  U  mm  L J  • • • • YM  No  YM  •  No  Nam* of activity in  Tm tat  L J  U  L J  •  •  • • • • Y  M  NO  YM  No  •  Name of activity Occa**onft in 9* loci  U  L J  •  trnaognV M*dwjr*  •  H*#w  •  • • • • Organoid  YM  NO  Comp#vtK>«  YM  NO  Name of activity in tf* IMI month  •  light Hr»  U  Mina  L J  Vi Howry Medium  • • • • • • Heavy  OoJivjexj  Y M  NO  Cornp«fjtrv»j  YM  NO  2  s  Appendix  C. Questionnaire of the 1981 Canada Fitness Survey  154  ACTIVITIES IN THE LAST YEAR Please refer to the reference card for a list of activities. Answer the following for-the physical activities you have done in the last 12 months. i*ioir«nti»oi (Do not include activities you have already listed) Nurriow Of iwXitM loonl on MontT* n wft*cn *cwf» •ocr* occAwon OCCJwOOt ww Gont •n 1M1 S « Jl II  J ' M A M J J A S O * 0 •  •  •  •  •  •  •  •  •  •  •  ' W « ww  1 0  40  Walking lor axtxcise  •  LJ''[TLJTJT]  Jogging lusing short strides)  • • • • • • • • • • • •  LJ• • •  •  Running lusing long strides)  •  •  •  •  •  •  •  •  •  •  •  •  L  J •  •  BicycJing  •  •  •  •  •  •  •  •  •  •  •  •  L  J•  Home exercise (push-upa, sit-upsl  • • • • • • • • • l f ] D D  • • • • • • • • • • • • • • • • • • • • • • D O • • • • • • • • • • • •  Exercise classea Weigtit draining Yoga  J F M A M J J A S O N D  Gorf (walking and carrying club*) Rscquetbal Squeeh Tennia  B j > n a v w « « ] O w w «  • • • •  • • • •  • • • •  • • • •  • • • •  • • • •  • • • •  • • • •  • • • •  • • • •  • • • •  n  o  M  S  s  i  C  w  w  a  n  c  • •  •  • la <0  •  U"D"D'D*D  LJ• • • LJ• • • LJ• • • >*  IS 1 1 il  w wX  o  • • •  «0  a LjTrDTra a L J• • • • a L J• • • • a L J• • • •  J F M A M J J A I 0 N 0  Basebal  •  a  it i « ii « i i 5 «0 «»»  «  Ice hockey  • • • • • • • • • • • a LJ • • • • • • • • . • • • a L J• • • •  Curling  • • • • • • • • • • • • L J •  Softbea  • •  • • • • • • • • • • • a L J • •1w0 • • • • • • • • • • • • • •  Swimming at a pool  LJ  • • • • • • • • • • • a L J • • • • • • • • • • • • • • • a L J• • • • • • • • • • • • • • • a L J • • •it •  Dots country skiing AJpine/Downhill skiing lea tkabng Names of scovrtjea:  m  J • • • • • • • • • • • •  J L  JL  •  11 w *3  L^TDTTCrn  J • • • • • • • • • • • •  L J •  •  •  •  J  •  •  •  •  •  •  •  •  •  •  •  •  L  J•  •  •  •  J  •  •  •  •  •  •  •  •  •  •  •  •  L  J•  •  •  •  J •  •  •  L  J•  • • IS to X  •  •  •  •  •  •  •  •  •  •  M J J  j • • • • • in • >o• "I• • • • •  •  Lj^CT'trrm  endix C. Questionnaire of the 1981 Canada Fitness Survey  PHYSICAL ACTIVITY IN YOUR LEISURE TIME 5. Here is a list of reasons why some people do physical activities during their leisure time. How *>< important is each of these to you? Of homtOf »n>« fDoonani «npon£nt •mporunc*  • • • • • • • • • • •  .•  To 'eei better mentally end phytically To be with other people For pleasure, fun or excitement To control weight or to look better To move better or to improve flexibility Ai a challenge to my abilities To relax or reduce tvesa To learn new thing* Becauae of fitnese apeciefitt'a advice for improving health in general Became of doctor'! order* for therapy or rehabilitation Other 6.  • • • • • • • • • • •  •  •  •  • •  • • • • • •  With whom do you usually do your physical activities in your leisure time? Noon*  „l_I Fnandi  14 I—I oridjovw  Co~<wxUri  ,1 I itKnoof  „'  I CWwi  7. When do you usually do your physical activities? (Indicate one only) Wnutn  8.  LLI WMMnai  LU so*  At what time do you usually do your physical activities? (Indicate more than one if you usually do activities mora than once a day) In fTtamoan [ J lntfu«v*ning  »CJ  N  9.  Where do you usually do your physical activities? (Indicate one or more) I—I 1—I ScNxH. or „l I Wort „i I ufwwwty faolhy • Mom.  • 10.  At f  CorrvTwcitf TlolrtV  | I O^tuo* utV>g no  How long have you been doing some activity in your leisure time at least once a week? I don't do *n f 1 Fo/lewtt«0 I 1 from 3 month* to j—| f/omfimonlrn n' J juH und* 6 monihi l J juit un0#H J y»J • •ctjvitv t*:h w*«k t I 3 rnonth* |—^ From 1 v«*v to fu»t f—\ from 3 y«*r» to '—' "-~ s  a  r  ppendix C  12.  Questionnaire of the 1981 Canada Fitness Survey  It you want to participate more in physical activities than you do now, why aren't you able to? (Check at most 3 reasons.) l doo l warn v D«n>Op«U rtxjr*  »• .•  .• .•  Iryxy or ha^rjicjQ Lack of  VTt  L*c* of rtrrm b t O U M Of wort laC*OOt}. Lack of Dm* bacauat of otftar a * * * * acuvioa*  Avfteb-* ^otrba* * n tnaOaQuata No f o » r . yysjaibaj  .• .•  Kaourai too nxich ia»*1-di*cip-»** Lack tT»» rvcatsa/Y rJuttl  .•  1  Coats too fnucn  13.  Nof»c*it*M naaroy  if you wanted to participate more in physical activities, which of the following would increase the amount of physical activity you do? (Check at most 31  JO JO JO JO JO  .• „• .•  Ftoo** taxi wnh p*K»ory»J activity proorwn rvaaafita 8«Rar or ctoaar t*c*tim frffarant facaftaa L o t ajuwnvv* t*cHhim Mora inforrrtjoon on Uha b*n«ftta of doing pnv**=* actStfy Ernptovw or i***»»on tponaorad acVvttMl *v**4atta  .• .• .•  iHop-a wnti «rhom to partxap*ta Common r t t a r « i of f»maV Cornrrion r a r w i of tri»nrji MoraH 09m  Oro*nix*d •port] .tvarfaba) Oryantzad fttnaw  Which of the following programs have you heard of? JO  CtnarJan Homa Rmaaa T a n  JO  Canada Gamal  B  O  »CH  15.  Canada H i r a i A«rm»: HTlUT  S  D  INFORMacoofl  A  D  PAXTICIP^rBon  .• ,•  .• .• .• ,•  Sta^darrJo*d Taai of Ftraai Rtn*a» ant) A/nrtaur Sport Ftaaa* Cavvada  Cinad* f^tnaaa facM  What is the name of your provincial fitness program? No provincial progr%m Don't fcnow  N»ma of p*oo/«vn:  Off"<* U*a  endix C  Questionnaire of the 1981 Canada Fitness Survey  panneiPdcnon  ID. Have Y O U ever seen this symbol?  No - Go to oucroon 17  •  Not Sum - Gotoxwoon 17  Where have y o j heard of or s««n the PAfiTlCIPacbon symbo* or measag,«? (Indicate ell applicable)  In m*>gu>n*M  in ooc*J*ti or p4im©n***  .•  Onbirtboarda  On pcatam  Onbuve* or tuowar*  „•  On mrk cariona  .•  In PtP—•: Tha Fae»'  -•  At acnoor  At PirriciPaA*  Sudani notabooAa  Oon'l know  . Have you previously taken t physical fitnet* test? No - Gotoouwtion IS  Whet type of cerdto-vescular laerobkl exercise did this test use? ,D  In r^wioapari  On radio  On f thins  17  „•  On Mkivwon  Q  SMOOX«  •  Don't know - Go » quonon Ii  •  Wl»V Jog/Hun  Where did you take this fitness test? Commaroai ofcjo or t*G*«V  •  front % manrttv) II  •  O W 1 r « r igo  •  Notllduta  1  » Q  YMCA/YWCA  Lt3  Q  WoitorKNjol  Q  When did you take this teat? jp L J .3 Intf>aavt 4 montfai  •  Inarlgo  Were you satisfied with the way the tesl was explained and administered? -CD  Vvyomf*}  CD  Saoxflad  Has taking the fitness test increased the amount of physical activity you do? »  •  » .  •  NO  •  Don't know  18.  In the past year, what physical activities have you stopped doing? {Do not include those stopped due to a change in the season) OffcaUaa Nona or Actrrfty Atry did TOU tlop doing thai acOVrty?  m Qtf<m Uaa  dix  C.  19.  Questionnaire  of the 1981 Canada  Fitness  Survey  1  What physical activities would you like to start in order to improve your fitness and health? U3  Man*  or  AcDvffy wh«t •  m*m ra**o« rou h*v« not rat n i n M in*?  Acrvny Wh*n « tf* m*«n outon you n*v* no* y*l itartx] M >  OtVaOw AcDvrty  CKtV* U M  Wh*rt * tf** matn r**»on you Kav* not r*i rtartad tm)  L J  20.  How important are each of the following to you in gaining a feeling of well being? Vary lUMlim  Of *ona> tmeorunca  • • • • • • • • • • •  Adaquatt r**1 and * X l p AoooddWl Low caloria anacls barwaan  rrtnU  Ma«^t»n*nc* of propar » * i q N rVixapabon in aooai and oufturaf actfvroaa Co*'trod of f v a M Ragoia/ phya>cai actMry A*cn aa * x * r c a * . <xjra or gama* U*ng atconof mcOanjtary or oaing • rkor^oVinMr Ba»ng a rwrvamofcar A^oouatv rrwoVa* and dantai car*  0* Irrda Importance  • • • • • • • • • •  Of no Imponanca  • • • • • • • • • • •  LIFESTYLE AND YOUR HEALTH What do you usually eat for breakfast? that appty. »L)  1 d o n l M I braairtaai  aO  (»gi  1 s  Check a all week.'. [Usually means at least four days  .MO*  a  1  }  aVaarJ. daniah or donul  aO  O w n  X,0  CW»r caraaa)  .  Al W t • our<m  O  Chaoaa  „Q  Yogurt  a CD  Taa or coflaa  a  1 S w y i or <rtfiar moat, IWl or poultry  D  ofm*  In the last year, have you been eating twaat food* and cindlaa  j,[D  Mora  •  Laaa  frun and v«o«t»b»aa  B  CD  Mora  CD  laaa  • •  S*ma • mount as bafora Sama amount U txfon>  Appendix  C. Questionnaire  o f the 1981 Canada Fitness Survey  8 23.  About how often do you usualfy drink alcohol?  Gj  4 to 7 «ma> i  E  «r*»M  Gj ! to J oma« « M «  lata  than one* a mont*  Gj looft'iorrt alcohol - Go loovaaaon 24  About how many drinks do you usually have at a time? Whe<e one drink m: — one pint of beer - 12 ounce* — on* imall gles* o< win* — one »hot ol liquor o> Jpi/m i.e. 1 • 1 1/2 ounces with or without mix.  • • 24.  Ona  ED Saoriwvao  Two Of Irm  [jD C*}M Or fTVOn  Four or flva)  Which of the following best describes your experience with tobacco. Check all that apply.  • • • • • 25.  I currant** trnofca:  I Hope-ad amoaJng:  bgaraRa-f occaa«x>»aV  dg*v«ttaa rncanAV  an  tan  1/5  c*g*v«f-»a  • • •  p a c k of  4a*Jy  a b o u t a p o c k of d o a r v n a a oaJy t w o or m o r a p a c k s o t o g a v v n a a da»V a p i p a . cigar or c » o a r * o  ciganmaa ovar a v*ar ago a pipa. cigari or aganioa racanOV • ptpa. 6 9 a m or cJQaHtaa pvax a yaar ago  • p i p a . o o a r or c i g a n l o daaV  Here is a fat that describes some of the ways people feel at different times. During the pest few weelts, how often have you fert . . . Ottan On «oo of lha world? Varyfc>rtaryor rafTX7ta rrom crtTw p*oo*a? rSnKuavtr «jot*d or iniaraatad in »omathing i*  OapraaairJ or vf+^CKnt PWaaad about having ac^ompT«»n#d »c«T»»thing? Soradr r>CAAJ baCaXrM »v>T»»or»t  oonar*  CO*r^rr«e>nL*vJ you on t o m a t f a i n g you had  So ra^dnst you COu*dn't »it long in a chaW Thattftingj»v*f t goir»g ytw wry?  tom«timai  • • • • • • • • •  Nov*  • • •  Q  • • • • •  Appen dix C  26.  Questionnaire  of the 1981 Canada  Fitness  Survey  About how many hours of sleep do you usually get each day?  LD  p  Sb houri or laaa  CU S*««n  0 Nina Q Tan Oovan Noun or mora  27. Are you limited in the type or amount of work you can do (or school you can attend) because of an illness, injury or handicap?  • • •  28.  I—| Yae. bacauaa of 9 LiJ tamponry «*ajry i—i Yaa. bacaun of a LiJ parmanant injury or handicap  Are you limited in the iyp« or amount of physical activity you can do during your leisure time because of an illness, injury or handicap?  •  •  29.  Ho Yaa. baouMoTi ttamporary aYiaaa Yaa. bacauaa of a crvorac or long-tarm aViaaa  Y M . b*c*uM of a WnpOfWY * f —  j—i LiJ  Y M . tectuM of • ptnnantnt injury or ha-"»dca©  Y M . b i c t u M of I chnwwc or long-tarrr. ttrwM  In general, how would you describe your state of health?  Vary good CZ1 Good  LiJ »oor 0 Vary'oor  Q Avar*,.  SOME FACTS ABOUT YOU 30.  Were you born in Canada?  Y.  0  H.  31 . What language do you use all or most of the time? Check one only  Sngaan Gl! frvx*. Carman  32.  LlJ ItaSan 0 LU Orhar |  Is there another language that you are in the habit of using? B  Q  Nona  O Itatan  Engbah  LU Uk/a*iian  160  endix C.  Questionnaire of the 1981 Canada Fitness Survey  10  33.  Are you . . . •  31  34.  r.  How old are you?  IF YOU ARE 14 YEARS OF AGE OR YOUNGER, YOU HAVE FINISHED THE QUESTIONNAIRE.  T H A N K YOUI WE W O U L D BE GRATEFUL FOR YOUR C O M M E N T S . A S P A C E FOR THIS HAS BEEN LEFT ON THE LAST P A G E .  IF YOU ARE 15 YEARS OF AGE OR OLDER, . . . 35.  What is your present marital status? Are you presently . . D  CD 36.  Uarrwd  •  Saparatad  Widow**  Q  S«ngfctIN#va/  KnM  What's the highest level of education you have reached?  • • • •  Cmr+niari  or  am  at  37.  Secondary £pic*m«  |—J Cornrr^unrty coftao* LU or CK£f <*>oma  f—| UJ  Ona or mom LWvarvtv da^aaa  Soma poa TV* C or*Sa*"V  Are you . . . ICheck alt that apply)  • • • • • 38.  Soma t*cora3*vy  LlJ or canificata  «*wad t^Yiptoyad"  Hc«mama* ar/Hc»^aaWa ^ -» tut-oma  Empiovad pa^-orna StwJant hj4-0ma  • • •  Moma^kar/Houaawrfa pani lJna*r»?_oY*d or on nrfca Ornar |  SiwSam pavvoma  How many hours a week do you spend doing your main activity? (work, going to school, housework) I  J  noum  01  39.  How many hours a week do you spend doing other chores? hewn  endix  C  Questionnaire  of  the  1981  Canada  Fitness  Survey  !1V i  41 . Have you worked or had a job in the past 2 weeks?  G r.  G  HO - Go toov«*t>on M  W h a t k i n d of work d o y o u d o ? l e g . p o s t i n g i n v o i c e s , selling » h o e s . etc.)  Please p r o v i d e  as m u c h  detail as  possible.  For w h o m  do  you  work?  (Name  of  business,  government depertment.  agency,  person,  or  are  you  serf  employed?!  W h a t k i n d of b u s i n e s s , i n d u s t r y or s e r v i c e is this? (eg. paper box m a n u f a c t u r i n g , retail s h o e s t o r e , b o a r d of e d u c a t i o n . I  42.  Is there an opportunity for physical recreation where you work? G  Yaa. atlunct.  Q  Yaa. « ooTfaa braas.  G  Yaa. afar Mart  •  43.  G  m  No  Approximately what was your family's total income last year, before taxes? Q a  taaa tfwi H.000  Q a  tZ.OCOtt> t29.Ht  •  16.000 » 19 9BB  LiJ  IX.000 lo U6.Q0O  Q  llO.OOOto l<.99»  G  uvatWo.OOO  G  Don't know  Q  municipal  Appendix D SPSS Control Commands for Transformation of IPA Variables  164  Appendix  D. SPSS Control Commmands  For  164  University of British Columbia  Use INFO OVERVIEW for more information on: INCLUOE • To bring in command files RENAME VARS • To rename variables AUTORECOOE - To recede strings as numbers Relinking Usercode 0 0 0 4 0 5 0 6 0 7 0 0 8 0 9 0 10 0 11 12 0 13 0 14 0 15 0 16 0 17 0 16 0 0 19 0 20 0 21 22 0 23 0 24 0 0 25 0 26 1 ? 3  License Number 12495  Improvemen t s in: MANOVA TABLES 1  TITLE ' CFS • MALES. 20 TO 40, DESCR STATS ALL OTHERS 4 ALL CORR FILE HANDLE OATA/NAMEr'CFSDATA TOT' DATA LIST FILE =0ATA REC0R0S=7/ AGE DAYS AOHERENC LIMITED ACTIVSCA WALK TYPE WALK INT WALKYEAR WALKLMON WALK TIME JOGGTYPE J0GG1NT JOGGYEAR JOGGLMON JOGGTIME RUNNTYPE RUNNINT RUNNYEAR RUNNLMON RUNN TI ME BICYTYPE 81CYI NT BICYYEAR BICYLMON 8ICYTJME GOLFTYPE GOLF INI GOLFYEAR GOLFLMON GOLF TIME RACOTYPE RACOINT RACOYEAR RACOLMON RACOTIME TENNTYPE TENNINT TENNYEAR TENNLMON TENNTI ME 8ASETYPE BASE INT BASEYEAR BASELMON BASE T]ME ICEHTYPE ICEHlNT ICEHYEAR ICEHLMON ICEHTIME SOFT TYPE SOFT I NT SOFTYEAR SOFTLMON SOF T TI ME SWIMTYPE SWIMINT SMI MYEAR SWIMLMON SWIMTIME SK1ATYPE SKI A INT SK1 AYEAR SKlALMON SKIA TI ME SKICTYPE SKICINT SKICYEAR SKICLMON SKICTIME SKATTYPE SKATINT SKATYEAR SKATLMON SKATTIME ROLLTYPE ROLL INT ROLL YEAR ROLLLMON ROLLTIME CALITYPE CALIINT CALIYEAR CALILMON CALIT1 ME EXERTYPE EXERINT EXERYEAR EXERLMON EXERTI ME WEIGTYPE WEIGINT WEIGYEAR WEIGLUON WE IG TIME BA0M7YPE 8A0MINT BAOMYEAR BAOMLMON BAOMTIME BASKTYPE BASK1NT BASKYEAR BASKLMON BASKTIME FOOTTYPE FOOTINT FOOTYEAR FOOTLMON FOOTTIME SOCCTYPE SOCCINT SOCCYEAR SOCCLMON SOCCTIME VOLL TYPE VOLLINT VOLLYEAR VOLLLMON VOLLTIME FRISTYPE FRISINT FRISYEAR FRISLMON FRI ST I ME fll TO R10 MATE1 TO MATE7 FITNESS BAR 1 TO 8AR13 PARTICIP  LIFE 1 TO LIFE11 ALCFREO ALCAMOUT SMOKETYP SMOKING SMOKSTOP 8RA0P0S BRADNEG 8RA0SCAL SLEEP HEALTH MARITAL EDUCAT INCOME SKINFOLD AEROBIC GRIPSTR PUSHUPS FLEXION SITUPS (T3.F2.0.T8.4F1.0.4(/T3.6(Fl.O.F4.1.F3.0.F2.0.F3.0))./T3.4 3F1.0./. T3.5F1.0.3F2.0,5F1.0,F4.1,F2.0.4F30)  THE ABOVE OATA LIST STATEMENT WILL READ VARIABLE AGE DAYS ADHERENC LIMITED ACTIVSCA WALKTYPE WALK INT WALKYEAR WALKLMON WALK TI ME JOGGTYPE JOGGINT JOGGYEAR  REC START 1 1 1 1 1 2 2 2 2 2 2 2 2  ENO 4 3 8 8 9 9 10 10 11 11 3 3 4 7 8 to 1 1 12 13 15 16 16 17 20 21 23  7 RECORDS FROM FILE DATA FORMAT WIOTH DEC F 2 0 F 1 0 F 1 0 F 1 0 F 1 0 F 1 0 F 4 1 F 3 0 F 2 0 F 3 0 F 1 0 F 4 1 F 3 0  Appendix D. SPSS Control Commmands  JOGGLMON JOGGTIME RUNNTYPE RUNNINT RUNNYEAR RUNNLMON RUNNTI ME BICYTYPE BICY1NT• BICYYEAR BICYLMON BICYTIME GOLFTYPE GOLFINT GOLFYEAR GOLFLMON GOLFTIME RACQTYPE RACOINT RACOYEAR RACOLMON RACQTIME TENNTYPE TENNINT TENNYEAR TENNLMON TENNTI ME BASETYPE BASEINT BASEYEAR BASELMON BASETIME ICEHTYPE ICEHINT ICEHYEAR ICEHLMON ICEHTIME SOFT TYPE SOFT INT SOFTYEAR SOFTLMON SOFT TI ME SWIMTYPE SWIMINT SWIMYEAR SWIMLMON SWIMTIME SKI A TYPE SKI A INT SKI AYEAR SKIALMON SKI ATIME SKICTYPE SKICINT  2 2 2 2 2 2 2 2 2 2 2 2 2 ' 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4  24 26 29 30 34 37 39 42 43 47 50 52 55 56 60 63 65 68 69 73 76 78 3 4 8 1 1 13 16 17 21 24 26 29 30 34 37 39 42 43 47 50 52 55 56 60 63 65 68 69 73 76 78 3 4  25 28 29 33 36 38 4 1 42 46 49 51 54 55 59 62 64 67 68 72 75 77 80 3 7 10 12 15 16 20 23 25 28 29 33 36 36 41 42 46 49 51 54 55 59 62 64 67 68 72 75 77 80 3 7  165  F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F .F -. F F F F  2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4  0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1  166  Appendix D. SPSS Control Commmands  SKICYEAR SKICLMON SKICTIME SKATTYPE SKAT INT SKATYEAR SKATLMON SKATTIME ROLL TYPE ROLL INT ROLLYEAR ROLLLMON ROLLTIME CALITYPE CALIINT CALI YEAR CALILMON CALITIME EXERTYPE EXERINT EXERYEAR EXERLMON EXERTIME WEIGTYPE WEIGINT WEIGYEAR WEIGLMON WE IGTI ME BAOMTYPE BAOMINT BADMYEAR BAOMLMON BADMTIME 8ASKTYPE BASK INT BASKYEAR BASKLMON BASKTIME FOOTTYPE FOOT INT FOOTYEAR FOOTLMON FOOTTIME SOCCTYPE SOCCINT SOCCYEAR SOCCLMON SOCCTIME VOLL TYPE VOLLINT VOLLYEAR VOLLLMON VOLLTIME FR1STYPE  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 S 5 5 5 5 5 5 5 5 5 5 5  8 1 1 13 16 17 21 24 26 29 30 34 37 39 42 43 47 SO 52 55 56 60 63 65 68 69 73 76 78 3 4 8 1 1 13 16 17 21 24 26 29 30 34 37 39 42 43 47 50 52 55 56 60 63 65 68  10 12 15 16 20 23 25 28 29 33 36 38 41 42 46 49 51 54 55 59 62 64 67 68 72 75 77 80 3 7 10 12 15 16 20 23 25 28 29 33 36 38 41 42 46 49 51 54 55 59 62 64 67 68  F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F  3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1 4 3 2 3 1  0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0  Appendix D. SPSS Control Commmands FRISINT FRISYEAR FRI SIMON FRISTIME Rl R2 R3 R4 R5 R6 R7 R6 R9 R 10 MATE 1 MATE? MATE 3 MATE 4 MATES MATE6 MATE 7 FITNESS BAR 1 BAR2 BARS BAR4 BARS BAR6 BAR7 BARS BAR9 BAR 10 BAR 1 1 BAR 1 2 8AR13 PARTICIP LIFE1 LIFE2 LIFE3 LIFE4 LlFES IIFE6 LIFE7 LIFE8 LIFE9 LIFE10 L I F E 11 ALCFREQ ALCAMOUT SMOKETYP SMOKING SMOKSTOP BRAOPOS BRAONEG BRADSCAL SLEEP HEALTH MARITAL EDUCAT INCOME SKINFOLD AEROBIC GRIPSTR PUSHUPS FLEXION SITUPS END OF OATALIST T A B L E .  5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7  69 73 76 78 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 3 4 5 6 7 8 10 12 .14 15 16 17 18 19 23 25 28 31 34  167  72 75 77 80 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 36 37 38 39 40 41 42 43 44 45 3 4 5 6 7 9 11 13 14 15 16 17 18 22 24 27 30 33 36  F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F \ F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F  4 3 1 1 1 1 1 1 1 1 l 1 1 1 1 1 1 1 1 1 1 1 1 \  1  \  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 4 • 2 3 3 3 3  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0  Appendix D. SPSS Control Commmands  168  2?  0  28  0  I I MI T E D ( 0 )  29 30  0 0  PART1C1P10) LIFE) TO L 1 F E 1 K 0 ) ALCFREO(O) 8RADP0S TO B R A O S C A L ( O O ) S L E E P ( O ) HEALTH(0l  31 32  0 0 0  INC0MEI0.8)  33 34 35 36 37  0 1 1  MISSING  VALUES »CTIVSCA(4)  ADHERENC(O)  SKINF0LDI999  8)  R1  AER0BIC(98)  PUSHUPS F L E X I O N S I T U P S ( 9 9 5 , 9 9 6 . 9 9 8 ) R E C O D E A L C F R E Q I 6 = 0 ) ( 5 = 1 ) ( 4 = 2 ) < 2 = 4)< 1 = 5 ) 00 IF ( A L C F R E Q EQ 0) • •  COMPUTE ELSE IF  TO R 1 0 ( 0 )  FITNESSIO)  SMOKETYP(O) MARITAL(O)  EDUCATIO  G R I P S T R ! 9 9 5 . 9 9 6 . 998)  ALCAM0UT(8)  ALCAMOUT=0 (ALCAMOUT E O 0 )  38  1 1  • RECOOE END IF  39  0  RECOOE  40 41  0  WALKYEAR  JOGGYEAR  RUNNYEAR  BICYYEAR  GOLFYEAR  RACOYEAR  0  ICEHYEAR CALIYEAR  SOFTYEAR EXERYEAR  SWIMYEAR WEIGVEAfi  SKIAYEAR 8ADMYEAR  SKICYEAR BASKYEAR  FRISYEAR(998=0)  ALCAM0UT(0=8)  4?  0  B A S E YEAR ROL L VE AR  43 44  0 0  S0CCYEAR RECOOE  V0LLYEAR  TENNYEAR SK A T Y£ AR FOOT YE AR  TENNLMON  45  0  WALKLMON  JOGGLUON  RUNNLMON  81CYLMON  GOLFLMON  RACOLMON  46 47  0 0  BASELMON R O L L LMON  ICEHLMON CALILMON  SOFTLMON EXERLMON  SWIMLMON WE I G L M O N  SKIALMON BAOMLMON  SKICLMON SKATLMON BASKLMON FOOTLMON  48 49 50  0 0 0  SOCCLMON  VOLLLMON  FRISLMON(98=0 I  RECOOE WALKT1ME  JOGGTIME  R U N N T I ME  B1CYTIME  G O L F T I ME  RACOTIME  TENNTIME  51  0  BASETIME  ICEHTIME  SOFT TIME  SWIMTIME  SKI ATIME  SKICTIME  SKAT TIME  52 53 54  0 0  ROLL TIME SOCCTIME  CAL1TIME VOL L TI ME  E X E R T I M E WE I G T I M E FRISTIME(998=0)  BADMTIME  BASKTIME  FOOT TIME  58 59  0 0 1 1 1 1  60 6 1 62 63 64  1 1 1 1  55 56 57  65 66 67 68 69 70 7 1  1 1 1 1  72  1 1  73 74  1 1  75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 9 1 9? 93 94  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  95 96 97 98 99 100  1 1 1 1 0  RECOOE LIMITE0(4=2)(5=3) 00 I F ( W A L K T Y P E E O 2) • COMPUTE WALKFREQ=WALKLMON • ELSE • COMPUTE END IF  WALKFREQ=WALKYEAR/12  0 0 I F ( J O G G T Y P E E Q 2) • COMPUTE JOGGFREO=JOGGLMON • ELSE • COMPUTE JOGGFREO=JOGGYEAR/12 ENO IF D O I F ( R U N N T Y P E E O 2) • COMPUTE RUNNFRE0=RUNNLMON • ELSE • COMPUTE END IF  RUNNFREQ=RUNNYEAR/12  DO IF ( B I C Y T Y P E E O 2) • COMPUTE 81CYFRE0=BICYLMON • ELSE • COMPUTE END IF  8ICYFREQ=8ICYYEAR/12  0 0 I F ( G O L F T Y P E E O 2) • COMPUTE GOLFFREQ=GOLFLMON • ELSE • COMPUTE G0LFFREO=GOLFYEAR/12 END IF DO IF (RACQTYPE  EO 2)  • COMPUTE RACQFRE0=RAC0LMON • ELSE • COMPUTE RACOFREO=RACOYEAR/12 END IF DO IF ( T E N N T Y P E E O 2) • COMPUTE TENNFREQ=TENNLMON • ELSE • C O M P U T E T E N N F R E Q = 1 E N N Y E A R / 12 END IF DO I F I B A S E T Y P E EO 2) • COMPUTE BASEFRE0=BASELMON • ELSE • COMPUTE B A S E F R E O - B A S E Y E A R / 1 2 END IF DO IF ( I C E H T Y P E EQ 2) • • •  COMPUTE ELSE COMPUTE  ICEHFREO=ICEHLMON ICEHFREO=ICEHYEAR/12  END IF DO I F ( S O F T T Y P E  E Q 2)  Appendix  D. SPSS Control Commmands 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 14 1 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 17 1 172  1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 T 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 l 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1  • COMPUTE S0FTFREQ=S0FTLMON • ELSE • COMPUTE SOFTFREQ=SOFTYEAR/12 ENO I F DO IF (SW1MTYPE EO 2) • COMPUTE SWIMFREQ=SWIMLMON • ELSE • COMPUTE SWIMFREO-SWIMYEAR/12 END IF DO I F ( S K I A T Y P E EO 2) • COMPUTE SKIAF REQ=SKIALMON • ELSE • COMPUTE SKIAFREQ=SKIAYEAR/12 END IF DO IF ( S K I C T Y P E EO 2) • COMPUTE SKICFREQ=SKICLMON • ELSE • COMPUTE SKICFR£Q=SKICYEAR/12 END IF DO I F (SKATTYPE EO 2) • COMPUTE SKA TF REO=SKATLMON • ELSE • COMPUTE SKATFREQ=SKATYEAR/12 END I F 0 0 I F (ROLLTYPE EO 2) • COMPUTE ROLLFREQ=ROLLLMON • ELSE • COMPUTE ROLLFREQ=ROLLYEAR/12 END IF DO I F ( C A L I TYPE EO 2) • COMPUTE CALIFREQ=CALILMON • ELSE • COMPUTE C A L I F R E 0 = C A L I Y E A R / 1 2 END IF 0 0 IF (EXERTYPE EO 2) • COMPUTE EXERFREQrEXERLMON • ELSE • COMPUTE EXERFREQ=EXERYEAR/12 END I F 0 0 I F (WEIGTYPE EQ 2) • COMPUTE WEIGFREQ=W£IGLMON • ELSE • COMPUTE WEIGFREQ^WEIGYEAR/12 • END I F DO I F (BADMTYPE EO 2) • COMPUTE BADMFRE0=BADMLMON • ELSE • COMPUTE BADMFREQ=8ADMYEAR/12 • END I F 0 0 IF (BASK TYPE EO 2) • COMPUTE BASKFRE0=8ASKLMON • ELSE • COMPUTE B A S K F R E Q = B A S K Y E A R / 1 2 • END IF DO IF (FOOT TYPE EQ 2) • COMPUTE FOOTFREQ=F0OTLMON • ELSE • COMPUTE FOOTFREQ=FOOTYEAR/12 • ENO IF DO IF (SOCCTYPE EO 2) • COMPUTE S0CCFRE0=S0CCLMON • ELSE • COMPUTE S0CCFREQ=S0CCYEAR/12 • END I F DO I F (VOLLTYPE EO 2) • COMPUTE V0LLFREQ=V01LLM0N • ELSE • COMPUTE VOLLFREQ=VOLLYEAR/12 • END I F DO I F ( F R I S T Y P E EQ 2) • COMPUTE FRISFREQ=FRISLMON • ELSE  169  170  Appendix D. SPSS Control Commmands  173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 19 1 192 193 194 195 196 197 198 199 200 201 202 20 3 204 205 206 207 208 209 210 21 1 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226  1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1  • COMPUTE F R 1 S F R E Q = F R I S Y E A R / 1 2 • END IF COMPUTE YEARPA I R=GOLFFREQ*RACQFREQ+ TENNFREQ + BADMFREQ COMPUTE YEARTEAM=BASEFREQ*ICEHFREQ+SOFTFREQ* BASKFREQ•FOOTFREQ' • SOCCFREQ• VOLLFREQ COMPUTE YEARFIT=JOGGFREQ+RUNNFREQ BICYFREQ+SWIMFREQ SK ICFREQ+ CAL IFREQ + EXERFREQ-* WE IGFREQ COMPUTE YEARL EIS=WALKFREQ*SKIAFREQ* SKATFREQ*ROL L F R E Q • F R I S F R E O COMPUTE YEARGAME=YEARPAIR+YEARTEAM COMPUTE YEARACTI=YEARFIT+YEARLEIS COMPUTE YEARTOT=YEARGAME*YEARACTI COMPUTE WALKTME=WALKFREQ'WALK I N T ' W A L K T I M E / 6 0 COMPUTE JOGG TME = JOGGFREO•JOGGINT *JOGGT I M E / 6 0 COMPUTE RUNNTME=RUNNFREQ'RUNNINT'RUNNTIME/60 COMPUTE B I C Y T M E = B I C Y F R E 0 ' B I C Y I N T * B I C Y T l M E / 6 0 COMPUTE GOLFTME=G0LFFREQ'GOLF I N T ' G O L F T I M E / 6 0 COMPUTE RAC0TME=RACQFREQ'RACQINT'RACQTIME/60 COMPUTE TENNTME=TENNFREO*TENNINT'TENNTIME/60 COMPUTE BASETME=BASEFREQ"BASE I N T ' B A S E T I M E / 6 0 COMPUTE ICEHTME=ICEHFREO*ICEHINT* I C E H T I M E / 6 0 COMPUTE SOFTTME=S0FTFREQ*SOFT I N T ' S O F T T I M E / 6 0 COMPUTE SWIMTME=SWIMFREQ*SWIMINT*SWIMTIME/60 COMPUTE SKI ATME=SKIAFREO*SKI AINT*SKI A T I M E / 6 0 COMPUTE S K I C T M E = S K I C F R E Q * S K I C I N T * S K I C T I M E / 6 0 COMPUTE SKATTME=SKATFREQ*SKAT I N T * S K A T T I M E / 6 0 COMPUTE ROLL TME=ROL LFREQ'ROLL INT'ROLL T I M E / 6 0 COMPUTE C A L I T M E = C A L I F R E Q ' C A L I I N T * C A L I T I M E / 6 0 COMPUTE EXERTME=EXERFREQ*EXERINT*EXERTIME/60 • COMPUTE WEIGTME=WEIGFREO'WEIGINT'WE I G T I M E / 6 0 COMPUTE BADMTME=BADMFREO*BADMINT'BADMTIME/60 COMPUTE BASKTME=BASKFREQ*6ASKINT *FJASKT I M E / 6 0 COMPUTE FOOTTME=FOOTFREO*FOOTINT'FOOTTIME/60 COMPUTE SOCCTME=SOCCFREQ*SOCCINT'SOCCTIME/60 COMPUTE VOLLTME=VOLLFREO*VOLLINT * V O L L T I M E / 6 0 COMPUTE F R I S T M E = F R I S F R E O * F R I S I N T ' F R I S T I M E / 6 0 COMPUTE TMEPA1R=GOLFTME*RACQTME* TENNTME*8ADMTME COMPUTE TMETEAM=BASE TME »ICEHTME*SOFTTME•BASKTME•FOOT TME•SOCC TME• VOLLTME COMPUTE TMEF I T = JOGGTME*RUNNTME*BICYTME + SWIMTME*SK ICTME + C A L I TME* EXERTME'WEIGTME COMPUTE TMELEIS=WALKTME*SKIATME*SKATTME ROLLTME+FRISTME COMPUTE TMEGAME=TMEPAIR»TMETEAM COMPUTE TMEACTI=TMEFIT*TMELEIS COMPUTE TMETOT=TMEGAME*TMEACTI COMPUTE RHF=R1«R4»R5*R7 COMPUTE RSOC=R2-R3 COMPUTE R S E L F = R 6 * R 8 COMPUTE RADV=R9•R 10 DO IF (MATE 1 EO 1) • COMPUTE MATE=0 • ELSE IF (MATE2 EO 1) • COMPUTE MATE= 1 • ELSE • COMPUTE MATE=2 ,  +  +  +  171  Appendix D. SPSS Control Commmands  227 228 229 2 30 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254  1 0 0 0 0 0 0 0 1 1 1 t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  END I F COMPUTE BAR=BAR1-»BAR2 BAR3*BAR4*BAR5 BAR6+BAR7*BAR8*BAR9 B A R 1 0 * B A R 1 1 + BAR 1 2*BAR13 RECODE P A R T I C I P ( 3 = 2 ) COMPUTE LIFE=LIFE1*LIFE2 LIFE3 LIFE4+LIFE5 LIFE6 LIFE7*LIFE8*LIFE9* L I F E 10»LIFE11 COMPUTE ALC=ALCFREQ"ALCAMOUT DO I F (SMOKING EO 1) OR (SMOKING EO 5) OR (SMOKING EQ 7) • COMPUTE SM0KE=4 • ELSE • COMPUTE SM0KE=5 END I F IF (SMOKSTOP EO 2 ) OR (SMOKSTOP EQ 4) OR (SMOKSTOP EO 6 ) SM0KE=2 IF (SMOKSTOP EQ 1) OR (SMOKSTOP EQ 3) OR (SMOKSTOP EQ 5 ) SM0KE=3 IF (SMOKETYP EO 1) SMOKE=1 RECOOE H E A L T H ( 4 = 2 ) ( 5 = 3 ) RECODE MARITAL<5=1)< 1 = 2 X 2 = 5 ) M I S S I N G VALUES WALKFREQ TO F R I S F R E Q ( 6 0 THRU HIGHEST) YEARPAIR TO YEARTOT(90 THRU HIGHEST) MATE(O) SELECT I F (TMETOT L E 1500) FREQUENCIES V A R I A B L E S = DAYS ADHERENC L I M I T E D ACTIVSCA RHF TO RADV MATE BAR L I F E ALC SMOKE F I T N E S S P A R T I C I P BRADPOS BRADNEG BRADSCAL S L E E P HEALTH MARITAL EOUCAT INCOME SKINFOLD TO S I T U P S /FORMAT ONEPAGE L I M I T ( 2 5 ) /HISTOGRAM NORMAL / S T A T I S T I C S = ALL +  +  +  +  +  +  +  THERE ARE 31536 BYTES OF MEMORY A V A I L A B L E . THE LARGEST CONTIGUOUS AREA HAS 31536 B Y T E S . MEMORY ALLOWS A TOTAL OF THERE ALSO MAY BE UP TO  1433 VALUES, ACCUMULATED ACROSS ALL V A R I A B L E S . 358 VALUE L A B E L S FOR EACH VARIABLE  Appendix D. SPSS Control Commmands  Bibliography  [I] Abele-Brehm, A . & Brehm, W . (1985). Einstellungen z u m Sport, Praferenzen fiir das eigene Sportreiben u n d Befindlichkeitsveranderungen nach sportbcher A k tivitat. (Attitudes towards sports, preferences for one's own sport, and changes in perceptions of well-being after participation i n physical exercise) Psychologie in Erziehung und Unterricht, 32(4), 263-270. [2] Achen, C. H . (1987). A s statisticians see us: comments on Freedman's paper "as others see us Journal of Educational Statistics, 12(2), 148-150. [3] Anderson, J . C. & Gerbich, D. W . (1988). Structural equation modeling i n practice: a review and recommended two-step approach. Psychological Bulletin, 103(3), 411423. [4] Andrew, G . M . et al. (1981). 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