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Predictors and consequences of involvement in physical activity : a causal model of the 1981 Canada Fitness.. Haag, Gerald Gunnar 1989-09-02

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PREDICTORS AND CONSEQUENCES OF INVOLVEMENT IN PHYSICAL ACTIVITY: A CAUSAL MODEL OF THE 1981 CANADA FITNESS SURVEY By Gerald Gunnar Haag B. P.E. University of British Columbia 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 this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ^VAJ <,'. ^Aoxl\-^ov\ <^cV Wvt^QvN The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract Involvement in physical activity (IPA) represents a complex lifestyle behavior. In order to gain a better understanding of the concept of IPA and the relationships with other factors, two comprehensive theoretical models of predictors and consequences of IPA were tested. The 1981 Canada Fitness Survey (CFS) 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 CFS to measure the abstract concepts of past experience, attitude, motivation, social status, barriers, modifiers, IPA, physical fitness, and psychological fitness. Causal modeling techniques were applied to test the conceptual model of fitness, presented in the CFS manual (model I), and a model of IPA 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 LISREL computer program. Both models revealed a good fit to the data (GFI=.95 and GFI=.93, respectively). Model 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 IPA, followed by barriers and social status. Past experience and IPA improve physical fitness. Attitudes and past experience could not predict IPA and neither IPA 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 viList of Figures viii Acknowledgement ix 1 Introduction 1 1.1 Canada Fitness Survey 2 1.2 Model I 5 1.3 Model II1.4 Uni- vs. Multivariate Analysis 8 1.5 Causal Modeling 11 1.6 Purpose 4 2 Methods and Procedures 15 2.1 Data 12.2 Involvement in Physical Activity 16 2.3 Operationalization of Variables 22.3.1 Attitude 22.3.2 Barriers 8 2.3.3 Modifiers 9 2.3.4 Past Experience 30 iii 2.3.5 Motivation 30 2.3.6 Social Status 1 2.3.7 Physical Fitness2.3.8 Psychological Fitness 32 2.4 Practical Versions of Models I and II 33 2.5 Causal Modeling 33 Results and Discussion 40 3.1 Model I 43.1.1 Measurement Model 43 3.1.2 Structural Equation Model 9 3.1.3 Categorical Data Treatment 54 3.1.4 Non-Normal Data Treatment 7 3.1.5 Summary 60 3.2 Model II 2 3.2.1 Measurement Model 63.2.2 Structural Equation Model 68 3.2.3 Summary 73 3.3 Predictors and Consequences of IPA 74 3.3.1 Model I3.3.2 Model II 78 3.3.3 Comparison of Models 84 3.4 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 8 4.2 Causal Modeling 9 4.3 Recommendations for Future Research 100 Appendices 101 A Literature Review - Physical Activity 101 A.l Determinants of Physical Activity 3 A.1.1 Past Experience . ' 106 A. 1.2 Attitude 107 A. 1.3 Motivation 9 A. 1.4 Knowledge Ill A. 1.5 Social Support 112 A. 1.6 Barriers 3 A. 1.7 Demographics 115 A. 1.8 Biological Traits 6 A. 1.9 Models of Exercise Behavior 117 A.2 Outcomes of Physical Activity 120 A.2.1 Physical BenefitsA. 2.2 Psychological Benefits . 123 A. 3 Summary 126 B Causal Modeling 8 B. l The Theory 129 B. l.l Model Selection 12B.1.2 The LISREL Model 131 v B.1.3 Model Identification 137 B.1.4 Estimation of the Model 8 B.1.5 Assessment of Fit 139 B.1.6 Other Models 144 B.1.7 Categorical Data 5 B.1.8 Non-Normal Data 146 B.2 General Procedural GuidelinesB.2.1 Measurement Model 147 B.2.2 Structural Equation Model 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 32.3 Operationalized Variables for Model II 5 3.4 Descriptive Statistics for Manifest Variables in Model I (n=3032) .... 41 3.5 Correlation Matrix for Manifest Variables in 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 Data Treatment for Model I 56 3.9 Steps in Non-Normal Data Treatment of Model I 9 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 Matrix of Manifest Variables from Model II 64 3.13 Steps in Development of Measurement Model II 65 3.14 Alternate Tests of Measurement Model II (MMII5) 9vii List of Figures 1.1 Theoretical Model I (from CFS Data Tape Manual) 6 1.2 Theoretical Model II (based on the literature review in Appendix A) . . 9 2.3 Testable Version of Model I 36 2.4 Testable Version of Model II 7 3.5 Parameter Values for Final Measurement Model I 50 3.6 Parameter Values for Final Version of Structural Equation Model I . . . 53 3.7 Parameter Values for Final Version of Measurement Model II 69 3.8 Parameter Values for Final Version of Structural Equation Model II . . . 72 3.9 Flowchart of Suggested General Causal Modeling Procedures 89 vm Acknowledgement The 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. Dr. R. W. Schutz has shown continued support as my advisor with all aspects of my study. He gave numerous suggestions relating to the theoretical models, their measure ment and many different statistical procedures. He showed interest and offered help with tests of hundreds of models. I was able to use his personal IBM 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. Dr. G. Sinclair deserves thanks for his helpful comments. Finally, I was very fortunate to receive support from Deborah Killam during the last stages of my thesis, and I would like to thank her very much. ix Chapter 1 Introduction Many people find enjoyment in being physically active. Even though opportunities to engage in various forms of recreational physical activities are available, there still is a significant proportion of the Canadian population that is completely sedentary. Why are some people physically active while others are not ? What 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 in physical activity as well, although a large proportion of research in this area is lacking validity due to insufficient research designs. How strong is the association between involvement in 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 IPA, its role for the individual and complex interrelationships with other important concepts, IPA needs to be examined in 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 in the area of physical ac tivity has been restricted to focus on either predictors of IPA, or the outcomes of IPA, but never have both been examined in 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 general-izability 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 IPA and in order to generalize results from tests of a comprehensive model of IPA, a survey based on a large sample and measuring many variables is necessary. Fortunately, such a survey has recently been conducted in Canada. 1.1 Canada Fitness Survey Canadians have shown an increasing interest in physical activity and its effects on phys ical fitness and health in the past two decades. The government, industry and private organizations have promoted the inclusion of regular exercise in lifestyles of the general public and offered suitable physical activity programs. The 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, con tained 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 in 1980, upon proposition from the National Conference of Fitness and Health, which was held in 1972. It was established as a permanent insti tution providing periodic assessments of Canadians' physical activity habits and related information. The major purposes of the Canada Fitness Survey (CFS) 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 CFS took place from February to July, 1981, covering spring, summer and fall in order to account for any seasonal differences. A CFS ques tionnaire and physical fitness test procedures were developed and data were collected throughout Canada. The 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 in the 1981 CFS Data Tape Manual (1987). This first administration of the CFS is one of the most comprehensive fitness and lifestyle surveys conducted anywhere in the world. From the wide variety of variables available from the questionnaire and physical fit ness 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 char acteristics. Analyses of physical activity patterns for activities ranging from jogging to gardening have been performed by the CFS 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" (CFS, 1983). Bimonthly one-page summaries of a specific aspect of the data, entitled "Highlights", have also been published between April 1983 and June 1985. These publications give informative de scriptions 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 CFS data tape in 1983, a number of researchers in 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 CFS and have reported some of the key results (Ferris, Kisby, Craig & Landry, 1987; Ferris, Landry & Craig, 1987; Gilmore, 1983; Hunter,1985; Newton, 1984; Peepre, 1984; Shepard, 1986; Stephens, 1983; White, 1983). White (1983) desribed the potential use of the CFS 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 CFS. Shepard (1986) compared anthropometric and physical fitness data from the 1981 CFS 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 in providing a benchmark of physical condition for the year 1981" (p. 299). These publications provide useful descriptive information about physical activity pat terns and related variables. However, no attempt has been made to explore relationships between these variables and involvement in leisure time physical activity. Chapter 1. Introduction 5 1.2 Model I In the 1981 CFS Data Tape Manual a conceptual "Model of Fitness and its Interrela tionships" (p. 4) was developed in order to select variables to be included in 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. The amount of physical activity deter mines 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 ac tivity, 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 in physical activity. Model I represents a conceptual model of fitness consisting of variables and relation ships based on the 1981 CFS Data 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 in physical activity and what the outcomes of physical activities are, such a theoretical basis is necessary. This requirement manifests itself particularity in two aspects: Chapter 1. Introduction 7 1. The use of any statistical methodology for the test of a model of IPA can only be justified on the grounds of such a theory. 2. Any interpretations of results from statistical tests are very difficult to make and not legitimate without a theoretical base. Therefore, a new model of IPA based on existing theories had to be developed. Al though a number of researchers have attempted to explain involvement in physical activ ity 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 scien-cists and a direct relation between physical activity and general well-being has been well established. The identification of determinants of IPA represents a much more complex issue. This is a common phenomenon in 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 ex perimental research designs, several researchers have identified factors that are directly associated with IPA. A detailed review of the literature examining predictors and outcomes of involvement in physical activity is given in Appendix A. Based on the findings summarized in 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 IPA, no specific psy chological 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 IPA in order to form a general model of IPA. Figure 1.2 shows a schematic representation of Model II, the hypothetical model Chapter 1. Introduction 8 developed in this study. Since some social behavioral theories emphasize the importance of distinguishing be tween 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. IPA is hypoth esized to directly predict physical fitness and psychological fitness. Physical fitness may influence psychological fitness. The amount of past experience with physical activity may have a direct effect on physical fitness. The goal of this study was to test Model I, the Canada Fitness Survey conceptual model of fitness, and Model II, the hypothetical model of IPA 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 in 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 mul tivariate data analysis procedures to experimental designs and to comparative research in physical education and sport. Schutz argues, that in order to study complex interre lationships 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 im portant results which univariate techniques cannot reveal. In their study of processes underlying involvement in physical activity Godin et al. (1987) identified three major factors that "can explain our lack of fundamental under standing of exercise behavior" (p. 146): 1. Most studies have inappropriately omitted development or adaptation of a theo retical model. 2. Prospective designs have to be employed in order to establish causal order within relationships. 3. Multivariate statistical techniques have been largely ignored. Godin et al. applied path analytic procedures based on an intricate theoretical model in 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 attempt ing 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 IPA, Model I and Model 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 in order to test the validity of these models. 1.5 Causal Modeling Causal modelling has recently been developed and become available as an empirical pro cedure for the evaluation of complex multivariate interrelationships. Linear Structural Relations (LISREL), Structural Equation Modeling, Analysis of Covariance Structure, Path Analysis and Confirmatory Analysis all represent similar statistical procedures de signed to test the fit between a theoretical model involving relationships and empirical data. Latent or unmeasured abstract variables such as the concepts in Model I and Model 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 in a confirmatory sense. These techniques have been called the greatest promise and the most important sta tistical revolution in 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. Ac cording to Bentler (1987) the major advantages of applying structural equation modeling techniques in social and behavioral sciences are that mathematical models can be used to conceptualize problems and data in 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 methodol ogy. 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 in reality as well as drawing invalid inferences about causal relationships that do not exist in 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 in applied studies. The 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 funda mental 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 there fore, 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 hy pothetical 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 in 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 estab lished. 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 "toss ing 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 in 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 in 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 mod elling (e.g. Everitt, 1982; James et al., 1982; Joreskog, 1978; Long, 1983; Mulaik, 1972). However, terminologies and approaches vary considerably throughout this literature, pre senting 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 cor rect approach; in 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 inves tigators, who have developed some of the methodologies and computer software packages, the practical application of these statistical procedures often presents tremendous prob lems. Analytical procedures for minimization of the loss function from the estimation process are very complex and sensitive. Especially when evaluating more complex func tions, 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 IPA. 1.6 Purpose The purpose of the study is to test the conceptual model of fitness presented in the Canada Fitness Survey Data Tape manual (model I) and a hypothetical model of predictors and consequences of involvement in 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. The appropriateness of models will be evaluated and results will be interpreted in light of hypothesized relationships. Chapter 2 Methods and Procedures 2.1 Data All data subjected to statistical analyses were taken from the household-based sample of the 1981 Canada Fitness Survey. Data were collected from randomly selected house holds across Canada. Every person present in the household was asked to fill out the Canada Fitness Survey Questionnaire (see Appendix C) and to complete the Canadian Standardized Test of Fitness (CSTF). 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 in involvement in leisure time physical activity. Since the intent of this study was to identify important predictors of IPA 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. An 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 in 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 maximum objectivity and accuracy is desirable, more subjective methods such as self-report procedures have to be chosen in larger studies and population surveys due to practical and financial reasons. Blair (1984) identifies some of the important issues with respect to exercise assess ment: • Data Treatment: The estimation of group means may be useful for assessing exercise habits of large samples in research studies, but accurate information about the single individual is more appropriate in clinical settings. • Type of Exercise: Even though the measurement of vigorous physical activity is relatively easy and useful in 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 in the study of specific groups. • Accuracy of Measurement: The estimation of daily caloric expenditure appears to Chapter 2. Methods and Procedures 17 be relatively accurate, but unfortunately still relies on imprecise methods. Classi fication 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 objec tive 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 de sirability bias. Recall surveys are most commonly used in studies of physical activity habits. Brooks (1987a) describes problems with present assessment sytems: "inadequate mea surement 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 in 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 in a review of 13 population surveys Lupton et al. (1984) note that most collected survey data assesses only participation in specific forms of exercise. Both 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 in physical activity is the main focus of this study and the central component of both models, its accurate assessment appears to be necessary in 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 in the 1981 CFS. In the questionnaire subjects were asked to identify activities which they were participating in on a weekly basis, within the last month, and within the last year in three different sections of the questionnaire (see CFS questionnaire in 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). The 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. On page 2 of the questionnaire, subjects were asked to report all activities performed in the previous month. Activities that respondents participated in 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 in one of these three sections. The CFS used the concept of Metabolic Expenditure as a measure of physical activity: ME = FREQ * INT * DUR where ME represents metabolic expenditure FREQ is the frequency of participation in an activity per month INT is the intensity of an activity, which is represented by an assigned METS value DUR is the duration of participation in an average activity session in hours Metabolic expenditure METS values were developed by Bouchard, Godin, Landry, Shep-ard and Skinner to represent the physical effort an individual undertakes when partici pating in a physical activity. They were adapted by the CFS as described in the CFS data tape manual (1981). Values were assigned based on the activity and reported inten sity. Walking for exercise, for example, was assigned METS 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 in 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 did not consider intensity of activities. In order to adequately assess the concept of IPA additional measures of IPA based on the design of the CFS questionnaire had to be developed. Several data checks were undertaken initially in 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 in the CFS data manual were confirmed. The following procedures were applied for the development of new measures of IPA (for exact mathematical transformations see the SPSS control commands in Appendix D). Based on the frequencies in the total population, which are reported in the CFS data manual, the following twenty-four major activities were identified: Walking for Exercise, Jogging, Running, Bicycling, Golf, Racquetball, Tennis, Base ball, Ice-Hockey, Softball, Swimming, Alpine Skiing, Cross-Country Skiing, Ice-Skating, Roller-Skating, Calisthenics, Exercise Classes, Weight Training, Badminton, Basketball, Football, Soccer, Volleyball, Frisbee. An average frequency per month was calculated for each activity. The sum of all fre quency scores produced a score YEARFREQ, which represents the average occurence of participation in physical activity per month, based on recall data from the previous year. Additionaly, each frequency score was multiplied by the assigned METS value, which represents the intensity of the activity, and by the average duration per session in hours, to produce a TME (Total Metabolic Expenditure) score for each activity. The sum of Chapter 2. Methods and Procedures 21 all TME scores produced a score YEARTME, 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 in 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 TME 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 overesti-mation, perhaps due to a social desirability complex. In order to prevent the distributions of IPA variables to be disturbed by these outliers the following restrictions were applied to indicators of IPA: • Frequency: Any subject participating in an activity more than 60 times per month or in all activities more than 90 times per month was eliminated from the sample. • TME: Any 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 IPA. Since recall procedures are more reliable for a shorter time span, summary measures from the previous month only were defined. LMONFREQ represents the frequency of all major activities in the last month, based on data from that previous month. LMONTME represents the metabolic expenditure from all major activities in the last month, based on data from that previous month. Before testing model II additional analyses of IPA scores were performed to possibly identify an underlying structure important to the measurement of IPA 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. PAIR: Games played with a partner • Badminton • Golf • Racquetball • Tennis 2. TEAM: Games played as a member of a team • Baseball • Basketball • Football • Ice-Hockey • Soccer • Softball • Volleyball 3. FIT: 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. LEIS: Activities that stress enjoyment and social aspects • Alpine Skiing • Frisbee • Roller-Skating • Skating • Walking Categories 1 and 2 were combined into a GAME category. Categories 3 and 4 were combined into an ACTI category. Frequency and TME 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 in activities than in games, the total metabolic expenditure from activities was only twice as high as the total metabolic expenditure from games. The last column in table 2.1 represents the ratio of TME and FREQ, which is the product of duration and intensity: TME IFREQ = DUR * INT As shown in 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. The frequency value for FREQFIT indicates that 20 to 40 year old Canadian males participate in fitness-oriented activities such as cycling or running over half the time they decide to be physically active. Chapter 2. Methods and Procedures 24 Table 2.1: Means and Standard Deviations for Various Activity Categories Category No of Acti X s TME/Freq Freq Pair 4 1.39 3.15 Freq Team 7 2.16 4.30 Freq Fit 8 9.33 13.35 Freq Leis 5 6.04 9.72 Freq Game 11 3.55 5.72 Freq Acti 13 15.03 16.94 Year Freq 24 18.24 17.97 TME Pair 4 11.64 33.84 8.4 TME Team 7 19.42 49.63 9.0 TME Fit 8 38.49 84.06 4.1 TME Leis 5 24.74 62.87 4.1 TME Game 11 31.07 64.45 8.8 TME Acti 13 62.70 108.21 4.1 Year TME 24 93.39 132.67 5.1 The standard deviations are very large, indicating that involvement in physical ac tivity is quite variable across this sample. The distribution of these scores is strongly affected by the large number of completely inactive subjects, that is subjects with scores of zero on IPA variables. By inspecting table 2.1 it can be concluded that the total measures of FREQ and TME of all 24 activities combined have the smallest variability, indicated by the lowest coefficients of variation CV =x/s. Correlations between all frequency and TME measures and other variables from mod els I and II were calculated and some interesting results emerged. The Pearson product-moment r between Activities and Games was only .15 for the frequency measure and .14 for the TME measure, which indicates that they are two distinct concepts. In general, people who play games do not participate in fitness activities as much and vice versa. Fitness activities correlated much higher with total scores ( r = .95 and r = .88 for FREQ and TME scores, respectively) than did games (r = .42 and r - .60 for FREQ and TME Chapter 2. Methods and Procedures 25 scores, respectively). This indicates that most of the variance in combined activity scores can be accounted for by fitness activities. Correlations with other variables revealed some differences. For example, measures for the GAME category correlated higher with social and personal development reasons for exercise, and measures for the ACTI 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 in models I and II and the derived physical activity measures, the largest were found for the total measures of all twenty-four activities combined in all cases. The derived categories of actvities were therefore not used for the indication of IPA in tests of the hypothetical models. Based on these preliminary analyses the following measures of IPA were chosen as manifest variables: Model I • Activity Scale: as defined by the CFS (see above) • YEARFREQ: frequency of all activities based on data from previous year • LMONFREQ: frequency of all activities based on data from previous month • YEARTME: total metabolic expenditure of all activities based on data from the previous year • LMONTME: total metabolic expenditure of all activities based on data from the previous month • Adherence: Question 10 of the questionnaire, indicating the amount of past expe rience with physical activity Chapter 2. Methods and Procedures 26 Model II Only Activity Scale, YEARFREQ and YEARTME were selected as indicators of IPA in model II, based on results from analyses of model I. 2.3 Operationalization of Variables All abstract concepts defined in models I and II are represented as latent variables that cannot be measured directly. Manifest or observed variables had 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. The Canada Fitness Survey had designed both the questionnaire and fitness test in order to receive baseline information about fitness and related factors in 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. The 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 in 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 in order to get more detailed information about different types of attitude. Chapter 2. Methods and Procedures 27 The Alberta General Factor Analysis Program (AGFAP) was applied to the correlation matrix of all ten items and a maximum likelihood analysis with oblique rotation (Promax-type 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. The second factor clearly represented Social Reasons for involvement in 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 rela tively high (r=.52), a second exploratory factor analysis restricted to three factors was run with the AGFAP 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 in section A.1.2, all four factors from the original exploratory factor analysis solution were included as measures of attitude in model II. Item 7 of question 20 required a rating of how important regular exercise is for a gen eral 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 indica tors of attitude in 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 CFS. All 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 in 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. All but the latter variable were of dichotomous nature, and produced highly skewed distributions. The amount of information contained in 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 all barriers listed in question 12 was computed and used in conjunction with a measure of limitations due to health (question 28) as indicators of barriers to physical activity in model II. Chapter 2. Methods and Procedures 29 2.3.3 Modifiers Model I includes the concept of modifiers which can effect the relationship between IPA and fitness. A number of variables are identified as modifiers in the CFS 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 IPA in 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 in 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 al cohol 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 in 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 CFS (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 in model I. 2.3.4 Past Experience The only indicator of past experience with physical activity that could be taken from the CFS was adherence to exercise, which was measured in question 10 of the questionnaire ("How long have you been doing some activity in your leisure time at least once a week?"). In model I this variable was combined with measures of involvement to represent a general IPA factor. In model II, however, adherence was defined as a different concept than involvement per se, based on research findings discussed in the literature review. 2.3.5 Motivation Two items were selected from the CFS as measures of motivation in model II. Question 11 of the CFS 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 in behavioral models such as the Health Belief Model and were therefore considered to be adequate indicators of motivation. Chapter 2. Methods and Procedures 31 2.3.6 Social Status As described in 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. The 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. Marital 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 in 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 CFS administration. The following were chosen as established measures of different aspects of physical fitness (see Haag, 1975): • Predicted Aerobic Power from steptest: aerobic/cardiovascular fitness • Pushups: muscular endurance, muscular strength • Situps: muscular endurance • Gripstrength: muscular strength • Trunkflexion: flexibility 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 in 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 in 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 with 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. An inspection of distributional characteristics within the 1981 Canada Fitness Survey data showed that the information contained in 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 in models I and II. Chapter 2. Methods and Procedures 33 2.4 Practical Versions of Models I and II All selected manifest variables are presented in 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 in the practical version of the model II, which was developed in this study. Variables that were used as measures of latent constructs in the final version of the models after completion of analysis are indicated by an asterisk in both tables. On the basis of these selected variables practical versions of both hypothetical models were defined. The testable version of model I is shown in figure 2.3. It consists of 5 latent and 29 manifest variables. The testable version of model II is shown in figure 2.4. Twenty-four manifest variables were defined to measure 8 latent variables. No measures of behavioral intention or social support could be found in the 1981 Canada Fitness Survey data and these concepts were therefore eliminated from the model. All hypothesized causal relationships are based on evidence discussed in the literature review (see Appendix 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 in testing a model, rather than just producing statistical test results in 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 retained ATT Lifestex * Reason Health * Reason Social * Reason Self * No Intention No Energy No Discipline Knowledge BAR Time Facilities Illness Skill Cost Perceived Health MOD Alcohol Amount * Alcohol Frequency * Smoking * Skinfolds *(FIT) Importance of Diet Importance of Rest IPA Activity Scale * Year Frequency * Last Month Frequency * Year Total Metabolic Expend. * Last Month Total Met. Expend. Adherence FIT Predicted Aerobic Power * Pushups Situps Flexibility * Gripstrength Bradburn Chapter 2. Methods and Procedures 35 Table 2.3: Operationalized Variables for Model II Latent Manifest retained PEP Adherence * ATT Reason Health * Reason Social * Reason Self * Reason Advice MOT Lifestex Perceived Fitness * Perceived Health * BAR Barriers * Health * SOC Age Marital * Education Income * IPA Activity Scale * Game Frequency Activity Frequency *(Tot) *(Tot) Game Total Met. Expend. *(Tot) *(Tot) Activity Total Met. Expend. PHY Predicted Aerobic Power Pushups * Situps Flexibility Gripstrength Skinfolds * * PSY Bradburn * Llfestex • RHealth • RSocial • RSelf • Nolntent • NoEnergy NoDlsclp • Knowledge Time • Facilities • Illness G Skill • Cost • PerHealth • AlcAmount • AlcFreq Smoking D Skinfolds • Diet • Rest • YearTME LmonFreq LmonTME ActSc^""' • ••••• psn J O Aerobic /^~~"\/ • Pushups • Situps T ^ • Flex GripQtr PSI2 Figure 2.3: Testable Version of Model I Adherence • ^ ^PEP^ RHealth RSocial RSelf R Advice Ufe8tex PerFit PerHealth Barriers Health Age Marital Education Income • • • • • v_y_ Act ActlTME GameFr GameTME ActiFr • Aerobic D Pushups • Sltups • Flexibility • Gripstrength • Skinfolds • Bradburn PSI3 Figure 2.4: Testable Version of Model II 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 in conjunction with the results in 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 LISREL 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. The 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. The measurement structure was tested with the LISREL computer program and modified if necessary. Manifest variables were eliminated, respecified or added, based on results from analyses and theoretical considerations. The measurement model was modified until a satisfactory solution was achieved. The 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 PRELIS computer program was used to calculate a matrix including polyserial and polychoric correlations in order to account for the categorical scale of measurement of many variables. This matrix was subjected to further tests with the LISREL program. Elliptical and arbitrary estimation procedures were applied with the EQS program to account for non-normality of the data. Results from all analyses were compared and interpreted in 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 SPSS computer programs on the U.B.C. mainframe system. Frequencies, sev eral 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 descrip tive statistics were carefully examined. Because most of the units of measurement for manifest variables were arbitrary, a Pearson product-moment correlation matrix was cal culated, which is presented in table 3.5. Several variables are not normally distributed, indicated by high skewness and kurtoses values, which are shown in 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 in section 3.1.4. The 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 in Model I (n=3032) Variable Latent Scale X Min Max Skew Kurt xl Lifestex ATT Ord 66 1.66 1.00 4.00 1.04 .45 x2 Reas HF ATT Ord 157 7.48 4.00 16.00 .67 .11 x3 Reas SO ATT Ord 124 3.90 2.00 8.00 .57 .06 x4 Reas SE ATT Ord 155 4.65 2.00 8.00 .29 -.60 x5 No Exer ATT Nom 0 0.12 0.00 1.00 2.29 3.23 x6 No Ener ATT Nom 0 0.10 0.00 1.00 2.70 5.30 x7 No Disc ATT Nom 0 0.15 0.00 1.00 2.01 2.03 x8 Know ATT Ord 0 3.66 0.00 11.00 .45 -.13 x9 Time BAR Nom 0 0.72 0.00 1.00 -.97 -1.05 xlO Facil BAR Nom 0 0.22 0.00 1.00 1.95 3.02 xll Health BAR Nom 0 0.07 0.00 1.00 3.41 9.64 xl2 Limited BAR Ord 36 1.21 1.00 3.00 2.54 5.08 xl3 Skill BAR Nom 0 0.04 0.00 1.00 4.08 18.05 xl4 Cost BAR Nom 0 0.13 0.00 1.00 2.25 3.09 xl5 Skinf MOD Int 45 53.87 15.90 146.60 1.00 1.02 xl6 AlcFreq MOD Ord 15 3.46 1.00 6.00 .49 -.18 xl7 AlcAm MOD Ord 0 2.14 0.00 5.00 .37 .00 xl8 Smoke MOD Ord 14 3.08 1.00 5.00 -.03 -.18 xl9 Rest MOD Ord 31 1.30 1.00 4.00 2.05 4.38 x20 Diet MOD Ord 40 1.54 1.00 4.00 1.46 1.95 yi Act Sea IPA Ord 33 2.55 1.00 3.00 -.85 -.27 y2 Year Freq IPA Int 0 18.24 0.00 112.25 1.59 3.01 y3 Year TME IPA Int 0 93.39 0.00 5475.00 5.35 34.61 y4 Lmon Freq IPA Int 0 15.24 0.00 112.25 1.79 4.08 y5 Lmon TME IPA Int 0 216.67 0.00 5475.00 5.31 33.74 y6 Adher IPA Ord 106 4.72 1.00 7.00 -.53 -.15 y7 Aerobic FIT Int 383 44.15 26.00 62.00 .50 -.64 y8 Strength FIT Int 351 108.07 47.00 161.00 -.01 .39 y9 Situps FIT Int 442 30.44 0.00 70.00 .09 .60 yio Flex FIT Int 389 29.74 1.00 73.00 -.25 .17 yii Bradburn FIT Ord 108 8.31 1.00 19.00 .10 .16 00 (/» W» o */» * S r- « m rr rt- r n * m -• 9 iA B T) ~ Q n — Owc^—OOO » * * I O-trori-wmFii'i c » o •* — — »•»*/» 0 ^ g . g g o « * • ^ZI^ZZSB*^ f- t- f~ CO — U r Q ^ W — mmj i _ — « r» -o o - <C OOOOOOOOOOOO -o^ — o - - -oooogojg ooooooaooooooooooooooo-r ooggooooogogogooooooo*gp ooooooooooo. 000000000 - — c W — — 'WM-UAAVC — w • » k « O « O — < oooooooooooooaooooooo• ooooogooooogooogoogooj OOOOOOOOOO-OQOOOOQOO'VJC • O » » - aoa^ui; — "\j — ~- <o — c oooooooooooooooaoooo-OO — OOQOOOOOQOOOOOOOOC O » ^ * — >. _ tf> _ ^ ooooooooo -00-0000000 oooooooo-ooooooo -oooooooo Q» - w O MQ 1= OOOOOOOOOOOOOOOOOOO -OOOOQQOOQOOOQOOOOOOQ w — i^'OOy 0*JM»0-'U - — <\> O Q OOOOOOOOOOOOOOOOOO-OO-OOQ — OOOOOO^ — w Q •o.i*»-*Ajt»0**-Od»<»0'VJwO<»0 OOOOOOOOOOOOOOOOO. 00-000-QOOOOO-w^,t»C «M^W — — - «VJ^O-^O — I O O O O O O — O W » W - I* 8 * O -J> » w »"• O O O O O O -O O O - ^ o oooooooooooooooo-OO -QOQ-OQOQQO-wwC *j Ok — 0"s>0*J"wO»00 »\j » C OOOOOOOOOOOOOOO — O o o o - OOOOOOOOOOOOOO OO -OOOOOOOOOOOO • MM A O 9 O • • »MOO O - O O *J> — <• o o» « a» O OOOOOOOOOOOOO-OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO-V* O O - O O O — «s< »v — O a — <M O Q — — — OOOOOO - O O — - * of-vji a «) — — AtwMO O — ' O <a t_j » » — ^ <^ ««WM*oi^Qt* ooooooooooooooooooooooooooooooo-OOOOOOQ** — OOOQ-OO — — — OOQOOOOOO— wwO - »V> tji . - 00>^^ - «jO*j»0-o*'MA>-0*0»iOOOOt*i*Q OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO — 1 <v — <M <S O W 1 OOOOOOOOOOOOOOOOOOOOOOOOOOOOO— OO—OOOO— — OgOOOOOOOOOOOQOOOOOOg OOOOOOOOOOOOOOOOOOOOOOOOOOOO -ooooogoooogooogggoooooo- w o o o c H p» cr ?** o o si tu o' » S3 01 SU a. Ul c o Ss: ooooooooooooooooooooboooooo-OOOOOQOOOOOOO-00000000000000 lO •> w <VJ O lO - — 4»maOMM •> kMUlO — — 0» *> w <» O >^)Uww 0 « fctOAAAhrfwtt'VJwwO — *Vt O 3 oooooobooooooboooooooooooo-OOOOOO — QOQOOO-OOOOOOOOO- -o o i^N^wA.uO — o^«^**wu*<»a»»» * » w w O O O • t*w»M«oitf«»»au'w«»k — » u — O o» o» O ooooooooooooooooooooooooo-OO-OOOOOO-OOQ-OOO - - ooooooo tf>x*9fe - — * W * — M»ON(>a»0'0' «M «• O » O Aw9«»ll ' (•••*«Ji^-»»»l»0»»^»> - C»0 Ol Ol O OOOOOOOOOOOOOOOOOOOOOOOO — OOOOOOOOOOOOOOOOOOOOOOOOO cr 5 2 o oooaooooooooooooooooooo-Chapter 3. Results and Discussion 43 3.1.1 Measurement Model The measurement model was constructed as described in Appendix B and as shown in figure 2.3. Each latent variable is measured by a number of manifest variables and their measurement errors. All 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 MMI1 consisted of 31 observed variables and 5 latent variables, related in the following manner: • Attitude (ATT) - 8 indicators • Barriers (BAR) - 6 indicators • Modifiers (MOD) - 6 indicators • Involvement (IPA) - 6 indicators • Fitness (FIT) - 5 indicators This model was set up as a LISREL model under SPSS and several versions of the measurement model were analyzed. Table 3.6 provides a list of steps taken in 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> associated degrees of freedom, X2/df ratio, Goodness of Fit Index, Root Mean Square Residual, and CPU time used in 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 combi nations. Sometimes LISREL prints error messages such as "TIME LIMIT EXCEEDED", "LIKELIHOOD FUNCTION WAS NOT EVALUABLE FOR INITIAL ESTIMATES" Chapter 3. Results and Discussion 44 Table 3.6: Steps for the Development of Measurement Model I Model Var Conv x2 df X2/df GFI RMR CPU MMI1 31 n - - - - - 64.0 EXI1 20 n - - - - - 26.0 EXI2 12 n - - - - - 6.0 EXI3 7 y 120 13 9.2 .98 .04 .6 ENI1 12 n - - - - - 5.2 ENI2 10 y 3642 43 84.7 .76 .13 1.0 ENI3 9 y 1655 26 63.7 .87 .09 .8 ENI4 8 y 7388 19 388.8 .79 .14 .9 MMI2 16 y 2009 98 20.5 .89 .07 3.3 MMI3 15 n - - - - - 3.2 MMI4 15 y 614 85 7.2 .96 .06 2.7 or "JOB CANCELLED", which indicate that the solution is invalid, because the min imization of the fitting function has not been completed. LISREL also gives warnings if any matrix is not positive definite, which indicates an improper solution. The 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 x2 value. If the estimation procedure has not located a minimum 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 with the measurement of that latent variable. Sometimes LISREL prints a warning mes sage 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 in 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 LISREL 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: The original measurement model was tested and the program did 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: The first version of the exogenous measurement model included 8 indica tors of ATT, 6 indicators of BAR and 6 indicators of MOD. The program did not converge to a proper solution, indicated by a negative x2 value. The 20 manifest variables were reevaluated in light of their descriptive statistics, and several deci sions were made. The 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 indicat ing these barriers. Their dichotomous nature and the fact that these means were rather low imply that they do not contain information that is useful in explaining or measuring the concept of attitude. As shown in table 3.4 all three variables are highly skewed and kurtotic, which violates on of the major assumption of maxi mum likelihood estimation. Since they do not represent measures of attitude that Chapter 3. Results and Discussion 46 are established in the literature, these three variables were eliminated from further analyses. Two 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 impor tance 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 repre sent 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 in 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. The 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 IPA), but on the con clusion that no valid indicators of barriers to physical activity could be found in the Canada Fitness Survey data. Examination of indicators of ATT 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 in the literature, this variable was eliminated as a measure of attitude. ei 3. Results and Discussion 47 EXI3: This model consisted of only two factors and 7 manifest variables and it yielded a proper solution. All factor loadings were reasonably high and the total coefficient of determination of z-variables was above .9. The high GFI (.982) and low RMR (041) indicated that this factor structure fits the data very well. Inspec tion of modification indices and residuals showed no high values, which means there did not appear to be any locations for possible specification errors. Model EXI3 was therefore accepted as measurement model for exogenous variables of model I. ENI1: The initial model of endogenous variables consisted of 6 indicators of IPA and 6 indicators of fitness. Skinfolds had been eliminated as an indication of modifiers. Since it has been utilized in many fitness tests as a measure of anthropometric characteristics, it was respecified to be an indicator of fitness. The program did not converge for this model. An inspection of the nature of the Bradburn scale as a measure of psychological fitness revealed that it was virtually unrelated to any other variable; in particular, it showed no significant relationships with the measures of physical fitness. It was therefore excluded as an indicator of fitness. The 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: This model yielded a proper solution, but the fit was very poor, indicated by a GFI of .76 and RMR of .13. An inspection of the residuals showed that some of the IPA measures had correlations that could not be reproduced by the model very well. In particular the total metabolic expenditure of activities performed in the last month appeared to create problems. In light of this, and because LMONTME was correlated very highly with LMONFREQ (r=.99), LMONTME 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 RMR=.09). All 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: The solution for model ENI4 produced a significantly worse fit (GFI=.79 and RMR=.14) as measured by the x2-difference test. The difference in x* was A = 7388 — 1655 = 5733 with associated df = 26 — 19 = 7, which is significant. Therefore, the exclusion of skinfolds resulted in a structure that has a worse fit to the data; it adds important information in measuring physical fitness. Model ENI3 was therefore accepted as the measurement model for endogenous variables. • MMI2: This model consists of a combination of the models EXI3 and ENI3. ATT is measured by 4, MOD by 3, IPA by 5 and FIT by 4 manifest variables. The estimation of this model converged and yielded an acceptable solution (GFI=.89 and RMR=.07). Adherence revealed a low factor loading as an indicator of IPA as well as high residuals. It was conceptually different from other measures of IPA in that it measured past experience or habit rather than the behavior itself. It was therefore eliminated as a measure of IPA. • MMI3: An invalid solution was the result of testing this model. The problem could be directly located by examining the estimated parameters. YEARFREQ 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 IPA factor than any of the three other variables. The 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 in that they represent short-term and long-term involvement, respectively. However, these concepts should have equal importance in measuring exercise behavior, which is represented by the general concept of IPA. The parameters for these two variables were therefore constrained to be equal in the Ax matrix. • MMI4'- The estimation of the parameters specified by this model converged and produced a good fit (GFL=.96 and RMR=.06). All parameter estimates had reason able 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 Model MMI4 was used as underlying structure for the structural equation model. It was constructed as a LISREL model as described in Appendix B. The elements of B and T were defined according to the hypothesized relationships in model I. The following paths were defined as free parameters: • from ATT to IPA • from MOD to FIT • from IPA to FIT ATT and MOD are hypothesized to be correlated by definition of the LISREL model. It was decided to fix one A per latent variable at 1 in 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 in the following section. Lifestex RHealth RSocial RSelf • ^.556 • .48 • S .41 950 .057 .334^. • .973 • AcfScale YearFreq \^973 • LmonFreq .427N* YearTME AlcFreq • ^485 782 (MOD) AlcAmount D Smoking D .662^ • "T560 • Aerobic Skinfold Situps .290 • 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 Model I Model Var Conv x2 df X2/df GFI RMR CPU CMI1 15 n - - - - - 2.5 CMI2 15 y 626 86 7.3 .95 .06 2.4 CMI3 15 y 625 87 7.2 .95 .07 3.4 CMI4 15 n - - - - - 3.6 CMI5 15 y 595 86 6.9 .95 .06 3.4 CMI1: This model was the "causal" version of MMI3. It was originally hypothe sized that the constraint put on the paramaters representing frequency of activities in the last month and frequency of activities in the last year would not be neces sary since structural paths were included. However, the solution for model CMI1 indicated, that this is not the case. The estimation did not converge, indicated by a non positive definite 0£ matrix. This was clearly due to a negative 9e value for the variable "YEARFREQ", just like in model MMI3. Therefore, the con straint of equal factor loading was put back onto the variables "YEARFREQ" and "LMONFREQ". CMI2: The test of this model revealed a very good fit. The model suited the data well (GFI=.95 and RMR=.06). All factor loadings were reasonably high and 3 and 7 coefficients were acceptable as well. However, the value for IPA was very high (32), indicating that the error in the structural equation for IPA is very high. This situation was also reflected in a very low total coefficient of determination for structural equations (.02). Therefore the model had to be respecified in 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: The solution for this model was satisfactory (GFI=.95 and RMR=.07). All 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 "YEARFREQ" and "LMONFREQ" had large modifi cation indices. Since they were measured in 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 in the matrix 0£ corresponding to these two variables. CMI4'- Unfortunately, this model did not yield a proper solution, indicated by a non positive definite 0£ matrix. The problem was still related to the two variables, whose measurement errors had been allowed to correlate. A negative element in the diagonal of Oe indicated that one of the factor loadings was probably too high. It was decided to constrain the elements of Ay corresponding to "YEARFREQ" and "LMONFREQ" to be equal, just like in model CMI2. CMI5: A valid solution was achieved that produced a good fit. The model fit the data well (GFI=.95 and RMR=.06). All parameters had reasonable values and no large residuals or modification indices were found. The total coefficient of determination for structural equations was, however, still very low, indicating that the structural parameters should be interpreted with caution. Model CMI5 was chosen as the best fitting causal model resembling the structure of theoretical model I. Parameter values of the standardized solution of model CMI5 are presented in figure 3.6. to c o 3 O a Lifestex • ^544 .826 RHealth • ^_ (ftfj) RSocial U .46&/ r-, ^424 RSelf • AlcFreq • ^493 782 (MOD) AlcAmount Smoking • GFI - .952 RMR - .061 .203 .276 .012 .742 ActScale D YearFreq t -392 .742 • LmonFreq .54 • YearTME T 10 .662,, • • ^648 • .288 • Aeorblc Skinfold Situps Flexibility Figure 3 6: Parameter Values for Final Version of Structural Equation Model I Chapter 3. Results and Discussion 54 3.1.3 Categorical Data Treatment Despite receiving a good fit in 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 in 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 in 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 in order to account for the categorical nature of some variables. This can be done in 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. Two methods were chosen to account for the categorical nature of some of the vari ables from model I. Firstly, LISREL provides a built-in option for the computation of an input matrix as described above. One has to read raw data and set the MV parameter in the RA card of LISREL control commands equal to the minimum number of categories a continuous variable consists of. The program will then calculate polychoric and poly-serial correlation coefficients for variables that have less than MV categories and test the model with this new input matrix in the usual fashion. Secondly, the program PRELIS was designed as a preprocessor of data for LISREL and is very useful for the analysis of categorical data. It gives detailed information about each variable, provides all con tingency 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 in 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. The program PRELIS was run on an IBM XT 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 in order to produce a valid input matrix. This correlation matrix was used for all analyses using the PRELIS input matrix. Table 3.8 lists several steps taken in testing model I with the polychoric option of LISREL and Chapter 3. Results and Discussion 56 Table 3.8: Steps in Categorical Data Treatment for Model I Model Conv x2 df X2/df GFI RMR CPU MMI5 y 755 72 10.5 .93 .07 2.5 CMI6 y - - - .95 .07 5.9 CMI7 y - - - .95 .06 6.2 CMI8 y 732 86 8.5 .93 .07 2.9 CMI9 n - - - - - 84.3 CMI5 y 595 86 6.9 .95 .05 3.4 with PRELIS input. • MMI5: A measurement model was developed similarily to MMI4 described above using the input matrix calculated with PRELIS. The structure of the model is iden tical to that of MMI4. The fit of the model is acceptable (GFI=.93 and RMR=.07), but is slightly worse than the fit of MMI4. All parameters are very similar as well. This model was then taken as the basic structure for the structural equation model of model I. • CMI6: The structural model was constructed in a manner similar to the con struction of CMI1. Because the adjustment of the input matrix may violate the as sumption of multivariate normality, which is required for maximum likelihood (ML) estimation of the model, a different estimation procedure was chosen. Unweighted Least Squares (ULS) is an estimation method, that is not as precise as ML, but does not require distributional assumptions about the data. Model CMI6 was therefore estimated with ULS. The analysis produced valid parameter estimates that are very similar to the ones for model CMI5, presented in figure 3.6. As shown in table 3.8, ULS does not have an underlying %2 distribution and can therefore not produce a %2 value. Other criteria for overall fit are very similar to the values for model CMI5 (GFI=.95 and RMR=.07). Values for model CMI5 are listed in the Chapter 3. Results and Discussion 57 last row of table 3.8 for comparison. Due to reasons described for model CMI4, the measurement error between "YEARFREQ" and "LMONFREQ" was respecified as a free parameter for this model as well. • CMI7: The estimation of the model converged and produced a slightly better fit than model CMI6 (GFI=.95 and RMR=.06). Because no locations for potential specification errors could be detected, this model was accepted as the final struc tural model of model I using PRELIS input data. Although the factor loadings of the solution were very similar to those of model CMI5, the structural coefficients representing the hypothesized causal relationships were slightly higher. • CMI8: Model CMI7 was also tested using maximum likelihood estimation. The estimation converged and produced a solution very similar to CMI7 and CMI5. The fit is slightly worse (GFI=.93 and RMR=.07), but factor loadings are very similar. Causal path coefficients are lower than in model CMI7, but still slightly higher than in model CMI5. • CMI9: It was attempted to run a test with the built-in option of LISREL, 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 in 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 in table 3.4, and it was discovered that a number of variables had large kurtosis values. • Bivariate normality: gooodness-of-fit tests via PRELIS indicated that many pairs of variables do not satisfy this assumption. • Multivariate normality: Mardia's coefficient of multivariate kurtosis calculated with the EQS 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. The program EQS 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 (ADF) procedure to estimate parameter values, requires no restrictions on skewness or kurtoses of variables. The estimation is, however, computationally very demand ing 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 in detail in the EQS manual (Bentler, 1985). Chapter 3. Results and Discussion 59 Table 3.9: Steps in Non-Normal Data Treatment of Model I Model Conv x2 df X2/df GFI RMR CMI10 y 595 86 6.9 .91 .05 CMI11 y 492 86 5.7 .89 .05 CMI12 y 539 86 6.3 .96 .06 Table 3.9 provides a list of analyses performed with the EQS program. A PC version of the EQS program was installed and run on an IBM XT to perform the following model tests. • CMI10: In order to insure that the results generated by EQS are directly compara ble with LISREL results, model CMI5 was analyzed with the standard maximum likelihood estimation of EQS. Parameter estimates and goodness of fit criteria were almost identical with those obtained from LISREL. Because Bentler reports his own normed fit index the value for GFI is slightly different. However the fitting function has an identical value at its minimum, indicated by equal %2 values. o CMI11: The model was then subjected to elliptical generalized least squares esti mation followed by elliptical maximum Hkelihood estimation. Model CMI10 had similar parameter values to model CMI9. Although the %2 dropped by over 100, the GFI was slightly lower (GFI=.89 and RMR=.05). • CMI12: Arbitrary generalized least squares were then applied to the model and again a similar solution was found. The x2 value dropped again and the GFI was quite a bit larger, indicating a better fit (GFI=.96 and RMR=.06). All three methods (ML, EML, AGLS) 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 maximum likelihood esti mation, 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 in 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 MMI4 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 CMI5 represents the final version of the structural equation model. It has a reasonable overall fit and interpretable parameter values. The 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. An overview of all final solutions for the structural equation model of model I is given in table 3.10. The 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 cri teria 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 in traditional maximum likelihood estimations of the parame ters. The PRELIS program was applied to the dataset in order to produce a new input matrix. This matrix included polychoric and polyserial correlations, which account for the assumption of continuous distribution in categorical variables. Results from testing Chapter 3. Results and Discussion 61 Table 3.10: Summary of Solutions for Structural Equation Model I Model Input Missing Estim. Conv GFI CMI5 LISREL PPM Pairwise ML y .95 CMI9 LISREL Poly Listwise ML n -CMI7 PRELIS Poly Listwise ULS y .95 CMI8 PRELIS Poly Listwise ML y .93 CMI10 EQS PPM Listwise ML y .91 CMI11 EQS PPM Listwise EML y .89 CMI12 EQS PPM Listwise AGLS y .96 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. Maximum likelihood and unweighted least squares solutions were very similar for the PRELIS input. It can be concluded from this study that adjusting the data for categorical variables can be performed by using the PRELIS 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 PRELIS input with the Canada Fitness Survey dataset. The assumption of multivariate normality was tested on the CFS data, and found to be violated on the three levels of univariate, bivariate and multivariate normality. Two alternate estimation procedures available under the EQS computer program were then applied to the model in order to test whether they can produce a different solution or an improved fit. Both 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 in 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 in table 3.12. 3.2.1 Measurement Model The measurement model for model II was constructed as described in Appendix B and shown in figure 2.4. Two latent variables defined in 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 (PEP). The Bradburn scale was the only indicator that was available from the CFS data that measured psychological fitness (PSY). These variables represent a single indicator and therefore no measurement structure exists for them. In the LISREL 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 (ATT) - 4 indicators • Motivation (MOT) - 3 indicators • Barriers (BAR) - 2 indicators Chapter 3. Results and Discussion 63 Table 3.11: Descriptive Statistics for Manifest Variables of Model II Variable Latent Scale nmiss X Min Max Skew Kurt xl Adherenc PEP Ord 106 4.72 1.00 7.00 -.53 -1.45 x2 Reas HF ATT Ord 157 7.48 4.00 16.00 .67 .11 x3 Reas SO ATT Ord 124 3.90 2.00 8.00 .57 .06 x4 Reas SE ATT Ord 155 4.65 2.00 8.00 .29 -.60 x5 Reas ADV ATT Ord 258 5.81 2.00 8.00 -.46 -1.08 x6 Lifestex MOT Ord 66 1.66 1.00 4.00 1.04 .45 x7 Per Fit MOT Ord 42 1.97 1.00 3.00 .01 -.25 x8 Per Hea MOT Ord 36 1.21 1.00 3.00 2.54 5.08 x9 Barriers BAR Ord 0 1.73 0.00 4.00 .41 -1.08 xlO Health BAR Ord 36 1.21 1.00 3.00 2.54 5.08 xll Age SOC Int 0 29.28 20.00 40.00 .13 -1.14 xl2 Marital SOC Nom 11 1.38 1.00 2.00 .50 -1.75 xl3 Educat SOC Ord 51 4.10 1.00 7.00 .27 -1.33 xl4 Income SOC Ord 438 4.52 1.00 7.00 .03 -.63 yi Act Sea IPA Ord 33 2.55 1.00 3.00 -.85 -.27 y2 Year Game IPA Int 0 3.55 0.00 69.67 3.08 15.76 y3 Year Acti IPA Int 0 15.03 0.00 89.58 1.50... 2.10 y4 TME Game IPA Int 0 31.07 0.00 892.00 4.53 30.72 y5 TME Acti IPA Int 0 62.70 0.00 1267.88 4.06 24.51 y6 Aerobic PHY Int 383 44.15 26.00 62.00 .50 -.64 y7 Pushups PHY Int 415 21.70 0 110.00 1.01 2.67 y8 Situps PHY Int 442 30.44 0.00 70.00 .09 .60 y9 Flex PHY Int 389 29.74 1.00 73.00 -.25 .17 ylO Strength PHY Int 351 108.07 47.00 161.00 -.01 .39 yii Skinfold PHY Int 45 53.87 15.90 146.60 1.00 1.02 yi2 Bradbum PSY Ord 108 8.31 1.00 19.00 .10 .16 CORRELATION MATRIX TO BE ANALYZEO RHF RUT RSOC RSELF. RAQY PfRHEALI LIFE; PERfll. BAHBILBS HEAL IM MARITAL.. i. 000 RSOC 0 195 1 000 RSELF 0. 4 1 3 0. 421 1. 000 RADV 0. 379 0. 154 0. 262 1. 000 PEflHEALT 0 065 0. 045 0. 055 -0 040 1 000 LIFE 7 ', 0 45 1 0 236 0. 260 0 138 0 121 I . 000 PERF1T -0. 075 -0. .046 •0 113 0. 069 -0 400 -0 183 1 . 000 BARRIERS •0 .018 •0 .012 -0. 006 -0 .04 7 0. .074 •0. 006 •0 083 1 .000 HEAL TM 0 .00 7 0 .028 0 018 -0 .06 7 0 128 •0. 00 7 •0 075 "049 * 000 MARITAL -0 .013 -0 .043 •0. 059 0 . 123 0. 029 -0. 078 0 054 -0.1)34 0 Cl* 1.000 EOUCAT •0 on 0 .048 0 073 0 . 203 •0 034 -0. 092 0 056 0 007 •0 018 0.059 INCOME •0 .01? 0 .037 0 052 0 .072 •0 .066 -0. 008 0 064 •0 001 -0 063 •0 232 ACE •0 .046 0 . 134 0 129 •0 .117 •0 .057 0. 102 0 002 0.004 0 061 •0.493 YEARCAME -0 .077 •0 . 176 •0 . 145 0 079 -0 .117 •0. 237 0 1 38 0.015 •0 031 0 119 YEAflAC T, I -0, 177 0 033 •0 045 0 .058 -0 . 122 -0. 188 0 174 •0.008 0 024 0.206 TUEGAME •0. 068 •0 163 -0 131 0 .06* -0 114 •0. 20 3 0 . 129 0.008 •0 .028 0. 105 TMEACT1 •0. 140 •0. 006 -0. 070 0 .027 •0. . i 3r> •0. 154 0 1 78 •0 033 0 001 0.191 AC TIVSCA -0 . 114 -0 . 103 •0. 1 16 0 091 •o. 085 •0. 187 0 157 0.059 •0 008 0.093 SKINFOLD •0 043 0 048 0. 063 -0. .074 0 143 0 088 -0 258 0.072 u 018 -0.165 AEROBIC 0 .000 -0. 121 -0 101 0 .081 •0. 153 -0. 128 0 250 -0.065 •0 031 0.191 GRIPSTR 0 024 •0 .057 •0. 083 0 .018 -0. 058 0. 012 0 056 0.014 •0 020 •0.074 PUSHUPS -0. 07? -0. .036 •0. 105 0 102 -0. 191 •0. 176 0 298 •0 086 •0 .040 0.231 FLEXION -0 037 •0. 040 •0. 073 0. 044 -0. 098 -0 065 0 165 •0.038 0 000 0.044 SI TUPS •0 054 •0. 090 -0. 146 0. , 158 •0. 123 -0. 196 0 262 •0.055 •0 023 0.287 EOUCAT EOUCAT INCOME . AGE 1 . 000 INCOME 0 23 1 1 000 AGE 0 024 0 258 i. 000 YEARGAME 0 122 0 .047 -0 207 YEARACTI 0 ..i* 1 -0 .027 -0. 114 TMEGAME 0 094 0 .024 -0. 188 TMEACT I 0 .084 -0 U20 •0. 157 ACTIVSCA 0 . 148 0 .08 1 -0. 102 SKINFOLO •0 001 0 . 1 15 0. 171 AEROBIC 0 .001 -0 .113 •0 353 GRIPSTR -0 .07? 0 .092 •0. 019 PUSHUPS 0 .088 -0 .015 -0. . 308 FLEX ION 0 009 -0 028 -0 128 SI TUPS 0 169 0 006 •0 433 TEARGAME YEARACU 1MEGAME_ TMEACT I ACTIYSCA SKINFOLD AEROBIC 1 000 0. 148 1.000 0.871 0.114 I 000 0.146 0.870 0.139 1 000 T.246 0 416 0.205 0 266 -0.074 -0.10T -0.087 .C 116 0.180 0.137 0.171 0.164 0.044 -0046 0.048 0 028 0.149 0.202 0.123 0.192 0.071 0.064 0.052 0.080 0.258 0 215 0 219 0.215 1 000 o. 074 1 000 0 103 •0 431 1 . 000 0 .052 0 080 -0 127 0 162 •0 354 0. 32 l 0 023 •0 199 0 129 0 222 -0 323 0 33? GRIPSTR . PUSHUPS.. FLEXION SITUPS CRIPSTR 1.000 PUSHUPS 0.140 1.000 FLEXION 0.123 0.254 1.000 SIT UPS 0.094 0.505 0.21? 1.000 DETERMINANT = 0.265731E-02 Chapter 3. Results and Discussion 65 • Social Status (SOC) - 4 indicators • Involvement (IPA) - 5 indicators • Physical Fitness (PHY) - 6 indicators Only two endogenous latent variables were defined in model II. Since they both had fairly distinct indicators, separate tests of the exogenous and endogenous variables were not considered necessary. The complete measurement model was constructed as a LISREL model under SPSS and several modified models were tested in 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, x2/df ratio, Goodness of Fit Index (GFI), and Root Mean Square Residual (RMR). Each step is described in the following section: Table 3.13: Steps in Development of Measurement Model II Model Var Conv x2 df X2/df GFI RMR MMII1 24 y 6057 237 25.5 .85 .09 MMII2 20 y 4244 155 27.4 .88 .08 MMII3 18 y 1191 120 9.9 .94 .05 MMII4 17 y 869 104 8.4 .96 .04 MMII5 17 y 676 104 6.5 .97 .04 • MMII1: The test of the original measurement model did, surprisingly, produce a valid solution. Some parameters were very low, however. The overall fit was not very good (GFI=.85 and RMR=.09). A closer look at parameter estimates revealed several potential weaknesses in the factor structure. The 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. The 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 in 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 IPA. Both 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 IPA were retained. The 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 IPA per se. Therefore, they were eliminated as indicators of physical fitness. The variable importance of exercise had the largest modification index (MI = 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 in %2 of almost 2000, which indicated a significant improvement. However, the fit was still unsatisfactory (GFI=.88 and RMR=.08). The lowest factor loadings, highest modification indices and largest residuals occured for the two measures of IPA relating to activities. It appeared as if LISREL wanted to treat the IPA factor as two separate factors. The correlation between ACTI and GAME 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 IPA scores, which are discussed in section 2.2.7, it was decided to only include total measures of all major activities combined as measures of IPA. MMII3: The substitution of IPA measures improved the fit of the measurement model tremendously. The %2 value dropped by over 3000, and the overall fit was now very good (GFI=.94 and RMR=.05). All 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 in the questionnaire. MMII4- The estimation of model MMI4 produced a superior solution. The dif ference in x2 was 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 RMR=.04). Except for measures of barriers and income, all factor loadings were above .4. The total coefficient of determination Chapter 3. Results and Discussion 68 of ai-variables was .999, indicating that the data fits the hypothesized factor struc ture well. No 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 in physical activity, somatotype is dependent on a hereditary compo nent 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 correla tions 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: The estimation for this model converged and produced a very good solu tion. The x2 value dropped almost by 200, which indicated that the fit improved. The overall fit of the model was good (GFI=.97 and RMR=.04). The parame ter values were very similar to the ones produced by MMII4, and indicated that the data fits this hypothesized factor structure very well. All modification indices were reasonably low, and no large residuals emerged. No location for a potential specification error could be found, and therefore MMII5 was accepted as the final measurement model for model II. Parameter values for model MMII5 are shown in figure 3.7. 3.2.2 Structural Equation Model The final version of the measurement model was used as the underlying measurement structure for the structural equation model. The structural equation model was con structed similarily to model I. In order to assign the unit of measurement for latent to RHealth RSocial RSelf GF1 • .965 RMR - .040 .910 c .0 V) c 3 PerFit PerHealth Barriers Health Age Marital Income .893 Figure .619 _ • Aerobic D Pushups .494 e_ • Situps • Flexibility .722 .770 • • • Act YearTME Year Freq 3.7: Parameter Values for Final 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. Two 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 8e, respectively) was fixed at zero. This procedure ensured identification of the model. Even though the two variables are defined as latent variables in 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 in model II (see figure 2.4). The following directed causal relationships were included in the model: • from PEP to IPA • from PEP to PHY • from ATT to IPA • from MOT to IPA • from BAR to IPA • from SOC to IPA • from IPA to PHY • from IPA to PSY • from PHY to PSY PEP, ATT, MOT, BAR and SOC were hypothesized to be mutually correlated by def inition of the LISREL model. Only one version of the structural equation model was tested: Chapter 3. Results and Discussion 71 • CMII1: The original version of the structural equation model of model II was an alyzed as a LISREL model and the estimation converged. A satisfactory solution was achieved. The overall fit of the model was good (GFI=.93 and RMR=.08). The standardized solution revealed factor loadings that were very similar to the parameters from the final measurement model. All structural parameters had rea sonable values and were interpretable. The matrix $ contained no unreasonable values. The correlation between barriers and motivation was high (r=.61). Model CMII1 was therefore accepted as the final version of the structural equation model for model II. All parameters from the standardized solution of the structural equa tion model are shown in figure 3.8. The largest modification indices occured for structural path coefficients in the matrices B and T. The modification index for the path from physical fitness to IPA, for example, is 776, which is fairly large and would imply a minimum reduction in %2 of almost one third. In terms of the model the high value of this index means, that relaxing this paramater would result in 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 relation ship between IPA and physical fitness, which contradicts the defined hypothetical model. This structural parameter can therefore not be relaxed. As mentioned in Appendix B, relaxing a structural paramater after a model has been defined defies the purpose of causal modeling and should only be done in 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 3 O O 3 DO > — (» 09 CD 2. 3" 2 "0 I 9 0 ~0 ft 73 CO ft 13 CO o o 37 I ft » — 3" > Q. (V 3 O ft Chapter 3. Results and Discussion 73 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 in physical activity could change one's attitude towards physical activity and one's motivation to participate in them. Other high modification indices occurred for paths between MOT and PHY, BAR and PHY, SOC and PHY. Increased motivation to participate in an activity could im prove general well-being which affects physical fitness. Barriers towards participation in physical activity could prevent an individual from participating in 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 Model II was theoretically developed based on findings reported in the literature review. A measurement model was constructed as a LISREL model and after several tests a model with a very good fit was achieved (MMII5). This model consisted of 6 latent and 17 manifest variables. The measurement structure was then implemented into the structural equation model. Two single indicator variables were defined and included as latent variables as well. The 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. The overall fit of model CMII1 was acceptable. Chapter 3. Results and Discussion 74 Parameter values for manifest variables were of reasonable magnitude. The structural path coefficients were reasonably large and interpretable. Therefore, the hypothetical model of IPA, model II, was found to fit the Canada Fitness Survey data well. 3.3 Predictors and Consequences of IPA Two models of involvement in 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. The parameter estimates from these models can now be used to interpret the results in terms of the theoretical models. Findings are interpreted for model I and II in the next sections, followed by a comparison of results. 3.3.1 Model I Model 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 model-building approach. This approach is different from the truly confirmatory approach often required in testing causal models in that it gives the researcher more freedom to respecify the model in 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 in the dataset. Many tests did not converge and "respecification tricks" had to be used as described above. The final solution for the structural equation model CMI5 has a good fit, indicated by a high Goodness of Fit 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. The 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 in 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. • ATT: 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. • MOD: Alcohol and tobacco habits formed a factor of modifying variables. The number of drinks consumed per drinking occasion, representing the intensity of the drinking habit, was the strongest measure of this factor. • IPA: Involvement in 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. The 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 in measuring IPA. They are the strongest measures of IPA, indicated by high factor loadings. Chapter 3. Results and Discussion 76 • FIT: Fitness was adequately measured by predicted aerobic power, the sum of five skinfolds, situps and flexibility. Flexibility had 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 FIT. The structural path coefficients from the standardized solution of the final version of the structural equation model indicate the strength of relationships between latent vari ables. Model CMI5 produced very low path coefficients, indicating that the hypothesized relationships are probably not very strong. The 1981 Canada Fitness Survey was a cross-national 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 IPA to FIT (8. = .28). This confirms the strong evidence in the literature, which suggests that exercise can improve physical fitness. Although the relationship is not very strong in this model, the significant pa rameter suggests, that a Canadian 20 to 40-year old male, who participates in physical activities is more physically fit than an individual from the same population, who does not exercise very much. The path coefficient from ATT to IPA was 7 = .20. According to this model, individ uals who have a positive attitude towards being physically active do in fact participate in physical activities to a greater extent than those with less positive attitudes. The path coefficient from MOD to FIT was insignificant (7 = .01). It can be con cluded that drinking and smoking habits do not affect physical fitness. Comparing the paths MOD to FIT and IPA to FIT it can furthermore be concluded that it is probably more important to become more physically active than to change drinking or smoking Chapter 3. Results and Discussion 77 habits in order to improve physical fitness. Finally, attitudes towards participation in 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 in order to account for categorical data and non-normally distributed data. Categorical and non-normal data was present in the CFS dataset and some basic un derlying assumptions were therefore violated, which might have produced invalid results. Model estimations with a PRELIS input matrix, accounting for categorical data, were performed with unweighted least squares and maximum likelihood estimation methods. Elliptical and arbitrary estimation methods available under EQS were utilized to test model CMI5, accounting for violations of the assumption of multivariate normality. The only analysis that produced significantly different results from standard maximum likeli hood estimation was the unweighted least squares estimation of model CMI5. Although factor loadings were very similar to the ones presented in figure 3.6, structural path co efficients were all larger. The estimated coefficients were 8 = .38 for the path from IPA to FIT, 7 = -.30 for the path from ATT to IPA, and 7 = .04 for the path from MOD to FIT. These results suggest, that accounting for categorical data may produce estimations which suggest stronger relationships than in 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 CMI5 was accepted as the final version of model I. In summary, the above conclusions have to be regarded with caution for two rea sons. Firstly, model I was not developed on a strong theoretical basis and therefore the final version of the model was developed in a mo del-building process. As explained in Appendix B, many valid structures can be found for the same dataset, and therefore a Chapter 3. Results and Discussion 78 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. No 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. Model 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 involve ment in physical activity, model II was developed as a model of IPA, 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 theoret ical considerations, a more confirmatory approach was taken with respect to testing the model. This implied more restrictive analyses in the sense that only minor respecifications were performed and not as many tests were performed as for model I. All respecifications were justifiable with theoretical arguments. A measurement model of latent variables, Chapter 3. Results and Discussion 79 except for two single indicators, was tested and after a few respecifications a measure ment 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 hypoth esized in model II, rather than finding the strongest possible relationships between the defined latent variables. The overall fit of model CMII1 was good, indicated by a high Goodness of Fit Index (.93) and low Root Mean Square Residual (.08). No locations for potential fit improve ments, which would not alter the basic theoretical structure of the model, could be detected. As discussed above, relaxing additional structural parameters could have pos sibly improved the fit of the model, but the confirmatory nature of the model eliminated this option. It can be concluded, that model CMII1 fits the data well. Parameter values for the standardized solution of model CMII1 are shown in figure 3.8. The following conclusion could be drawn with respect to the measurement of latent variables. • ATT: Attitudes towards participating in physical activities were adequately mea sured by the three scales representing Health and Fitness, Social and Personal Development reasons for involvement. The Personal Development scale was the strongest measure of attitudes. • MOT: Motivation was well represented by a measure of perceived health and a measure of perceived fitness. • BAR: Barriers were measured by a sum of barriers to physical activity and by a measure of limitations due to illness or injury. The factor loadings were very low, Chapter 3. Results and Discussion 80 indicating that these variables did not form a strong distinct factor. • SOC: Social status was measured adequately by age, marital status and income. Age was the strongest measure. • IPA: After elimination of scores representing "games" and "activities", as described above, three variables were retained to form a strong measure of IPA. The 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 IPA. • PHY: 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 in model II, are of reasonable magnitude. Past experience with exercise, as measured by adherence to exercise, is strongly related to physical fitness. The path coefficient from PEP to PHY is 7 = .33. Many benefits from physical activity have a long term effect on physical fitness. The onset and duration of improvements in physical fitness is dependent on the type of physical activity performed. Individuals who have been involved in physical activities in the past are more likely to be physically fit now, as indicated in the physical activity literature (e.g., Dishman, 1982; Godin 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 PEP to IPA. Therefore, people with experience in exercise do not necessarily Chapter 3. Results and Discussion 81 become more involved in 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 Godin et al. (1987) and Hammitt (1984). These authors found relatively strong relationships between habit and behavioral inten tion and physical activity behavior. However, these studies did not include consequences of the behavior in their model. The rather weak relationship between past experience and IPA found in model II might be due to the strong relationship between past experience and one consequence of IPA, physical fitness. According to the model, attitude has no influence on exercise behavior. The path coefficent from ATT to IPA is insignificant (7 = .00). One's attitude towards being physically active does not predict exercise behavior. This finding is in direct contrast to major behavioral models. However, as described in 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), Godin 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 in this study might have limited the attitudinal model and affected the relationship with IPA. 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 in physical activity than an individual who has a negative attitude towards physical activity. This is very important information for planning of activity pro grams. 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 in physical activity. The path from MOT to IPA had the highest coefficient in the model (7 = .42). According to the model, highly motivated individuals will participate in physical activities more than individuals with low motivation. This has been shown in 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 IPA. Although the intention to exercise may depend more on other factors (this issue was not tested in the model), actual involvement in 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 in physical activity. The second largest loading occured for the path from BAR to IPA (7 = .37). This is probably the most obvious finding. If someone does not have adequate facilities in 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 in 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 in turn improve their health, which would decrease these hmitations. Social Status has a significant effect on involvement in physical activity. The path coefficient between SOC and IPA is lower but still of reasonable magnitude (7 = .25). As has been repeatedly shown in 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, Chapter 3. Results and Discussion 83 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 in mentalities between social classes. Increased involvement in physical activity improves physical fitness as indicated by the path coefficient from IPA to PHY (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 in the review by Leon and Fox (1981). The strongest path to PHY, however, is from PEP (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 in 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 IPA nor by physical fitness. Both path coefficients are insignificant (8 = —.02 from IPA to PSY and 8 = .03 from PHY to PSY). 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 PSY, the insignificant effects of IPA 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. Third, 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 CMIIl. The 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 IPA and past experience with physical activity had a small influence on present involvement. Past experience did, however, predict physical fitness. People who exercise more have improved physical fitness. Psychological fitness, as measured by the Bradburn scale, is not affected by IPA 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 Two models of IPA have been tested using causal modeling techniques. Model I was defined as a conceptual model, but was not developed in terms of a causal model. Model II, however was carefully developed based on existing evidence. This apparent difference in 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. Many of the tests performed in building model I did not produce a proper solution inside the permissable parameter space, and several "tricks" had 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 (GFI=.95 and GFI=.93, respectively). Model I has a much simpler structure, consisting of only four latent vari ables 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 in model I, model II contained several coefficients of reasonable magnitude. Only two paths from the two models could be compared. The path from ATT to IPA had structural coefficients of 7 = .20 and 7 = .00 for models I and II, respectively. The significant parameter in model I might be due to the fact, that no other latent variables were hypothesized to cause IPA. Paths from IPA to PHY had similar coefficients (3 = .28 and 3 — .22 for model I and II, respectively), indicating that this relationship was con firmed 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 in model II are therefore accepted as conclusions with respect to predictors and consequences of involvement in physical activity. These conclusions are given in the previous section (3.3.2). 3.4 Recommended Causal Modeling Procedures Causal modeling appears to be a very powerful statistical technique for testing hypothet ical models with observational data. When examining behavioral processes, for example, the analysis of comprehensive models provides a better understanding of underlying rela tionships 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 on going 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 (LISREL, COSAN, EQS, EZPATH) 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 in this section. From the variety of different procedures and analyses reported in 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 in 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 in 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 in 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 Chapter 3. Results and Discussion 87 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. All 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. The fact that the estimation procedure for the parameters cannot find a minimum 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 inad equately defined. • Technical: the model is not identified, because parameters have been defined inap propriately in 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 non-convergence 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 ap proach for their analysis. Models profoundly based on theoretical grounds should be tested in 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 Chapter 3. Results and Discussion 88 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 in Appendix 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 in 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. Two basic assumptions for the use of structural equation modeling have to be con sidered for the test of a model and the interpretation of a given solution. • Causality cannot be inferred. • Maximum 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. The guidelines are shown in a flowchart in figure 3.9. Although they are based on and discussed with reference to the LISREL methodology, they can easily be applied to other methodologies as well. All procedures are discussed with relation to a correlation input matrix. Chapter 3. Results and Discussion Consider redevelop-ment of model Define tneoretloal model Operational!** variable* E All latent var. measured o.k. ? 1 yes no Eliminate latent variables with Inappropriate measures I • 1 I Teat Measurement Model l I l • I • 1 Did estimation oonverfte ? no Modify model by applying 'tricks* feepsolfloallon poaa. •nd promising 7 Retain Measurement Model 1 Reepeoifioatlon Test Measurement Model I > M8q (l-D - CM8q (i); "o \ significant ? Fit acceptable ? )•«-Structural Model T fespeoifioatton poss and promising ? / /•* no 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 liter ature relating to the defined constructs and the hypothesized relationships is absolutely necessary in order to define a valid model. Each predicted causal relationship should be supported by existing evidence in 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. As mentioned in Appendix 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 in 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. Two indicators often cause serious estimation problems by causing Heywood cases (discussed in 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 in figure 3.9, the index i is now set to one. The measure ment model should then be constructed as exemplified in Appendix B. An example of the appropriate LISREL control commands is given in Appendix D. The 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 in the section 3.4.2. Non-convergence is indicated by so lutions outside the permissable parameter space (e.g., negative variances) or by LISREL 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, resid uals 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 92 • Parameters: 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 gen erally indicates a constrained parameter that should be relaxed. If one variable has several high modification indices, its inclusion in 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. Any 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 %2 difference test should be used to assess whether an improved fit to the data has been achieved or not. If the difference in %2 with the associated difference 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 Chapter 3. Results and Discussion 93 promising and useful. If the difference in %2 between the present and the previous model is significant, the present model shall be retained. If it is not, the previous model shall be retained. The final step in 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. • The Goodness of Fit Index (GFI) should be above .9 for a good fit and above .95 for a very good fit. e The Root Mean Square Residual (RMR) 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 Appendix B. Both methods of fixing the scale of latent variables were applied in tests of models of IPA 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 in 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 in A matrices) should only be made if absolutely necessary. Strutural parameters should only be added or eliminated in very extreme cases. The 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 equa tion model, all parameters can be interpreted in light of the theoretical model. Missing Data Treatment Model MMII5 was retested several times in 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 LISREL. However, especially in a model with a large number of variables or in 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 MMII5 are listed in table 3.14. As can be seen in this table, listwise deletion caused the deletion of over 1200 subjects. The 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. LISREL cannot produce a covariance matrix with pairwise deletion of cases; it was produced using a descriptive Chapter 3. Results and Discussion 95 Table 3.14: Alternate Tests of Measurement Model II (MMII5) Input Missing n x2 df X2/df GFI RMR Pearson Pairwise 3032 676 104 6.5 .965 .040 Pearson Listwise 1807 517 104 5.0 .967 .039 Covariance Pairwise 3032 676 104 6.5 .965 12.5 Covariance Listwise 1807 517 104 5.0 .967 21.1 Polychoric Pairwise 3032 1263 104 12.1 .953 .044 program under SPSS. 3.4.2 A List of "Tricks" Several procedures have been successfully used in applications of causal models for pro ducing a better fit. Most of these procedures have been applied in 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. Heywood Cases If a Heywood case exists in a model, an invalid solution is produced. The typical case for a Heywood case is a latent variable with two indicators where only the sum of the two factor loadings Ai -f A2 is identified. Any combination of Ai and A2 that produces this sum satisfies the restrictions implied by the equations in the model. Therefore the model is not identified. The most common and easily detectable sympton for a Heywood case is one factor loading above one in 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. The factor loadings can be constrained to be equal (Ai = A2). If this does not work, the parameter that produced the higher A should be 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 encoun tered by the estimation procedure in attempting to find a global minimum 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 0e 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 in the test of the respecified model. This generally produces an improved fit. Chapter 4 Summary and Conclusions Involvement in physical activity is a complex behavioral process, which has become an integral lifestyle component for many Canadians. Two comprhensive models of IPA and relating factors were tested in 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. Model II was developed on the basis of a review of the literature (see Appendix A). The 1981 Canada Fitness Survey contained many variables relating to IPA 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 IPA and to evaluate the strength of the hypothesized relationships. Both models were transformed into LISREL 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. The 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 in model 97 Chapter 4. Summary and Conclusions 98 development. 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 IPA 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 im portance of long-term involvement in physical activity. • Motivation has the strongest influence on physical activity behavior. • Barriers tend to prevent Canadians from becoming involved in physical activities, o Social status is an important factor influencing IPA. • Attitudes and past experience appear to have little effect on participation in phys ical activity. • For the general population of 20- to 40-year old males IPA seems to improve physical fitness. • IPA has, however, no effect on psychological well-being, as measured by the Brad-burn 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, in particular in 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. The finding that physical fitness tends to improve with increased involvement in physical activity can be used to promote the benefits of IPA 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 LISREL. The interpretation of parameters is often very difficult. It appears as if a certain degree of experience is required in order to use LISREL 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 EZ-Path 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 in this study. A flowchart of general procedures is presented in figure 3.9. It is rec ommended that these procedures are followed in 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 in sub-disciplines such as sport psychology or sport sociology. Secondly, more research is needed on predictors of IPA as well as on the effect of physical activity on psychological well-being. Thirdly, a very interesting data base will become accesible in early 1990. A revised version of the Canada Fitness Survey was administered in 1988 and data has been col lected from over 5000 subjects. These subjects are from the original sample used in 1981. Therefore, the Canada Fitness Survey represents a very comprehensive longitudi nal dataset, which should be subjected to analyses in order to assess longitudinal trends. In particular, the model of IPA that was developed in this study (model II) could be tested with 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 in 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. The 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 in 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 ac tivity 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 well-being have been well-established. In general, the purported benefits of physical activity are widely accepted by the public, and have been strongly promoted in 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 in the literature. 101 Appendix A. Literature Review - Physical Activity 102 Despite the strong evidence regarding the benefits of regular physical activity, it ap pears that the majority of North American adults do not engage in regular physical activity. Lupton, Ostrove and Bozzo (1984) compared results from twelve North Ameri can 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 exer cise 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 in one or more activities in 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. The Canada 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 in vigorous activity. From these and other sources reporting physical activity involvement patterns it is safe to conclude that in general, less than half of the North American pop ulation engages in regular physical activity, with participation rates being slightly higher in Canada than in 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. While the benefits and risks of physical activity should be subject to further investi gation, it is also important to examine why people engage in 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 limited" (p.118). In order to receive any of the benefits associated with physical activity, people have to be motivated to exercise in the first place, and, once an activity program has been initiated, they must be sufficiently Appendix A. Literature Review - Physical Activity 103 rewarded to continue. An average dropout rate from supervised exercise programs of about 50% after the first six months, which has been reported repeatedly in the liter ature (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 in 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 in 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 sponta neous 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 IPA. First, the assessment and quantification of physical activity involvement patterns represents a very complicated and difficult problem in itself; it is discussed in section 2.2. Second, the theoretical basis for gaining an understanding of exercise behavior is of ten insufficient or non-existant. Although quite a few factors have been associated with IPA 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 phys ical 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. Godin 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 IPA is that relationships between determinants and IPA 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 exer cise in 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 IPA 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 IPA. 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; Godin et al., 1987; Sonstroem, 1982). Despite all problems mentioned above, the factors identified in Dishman's review are very helpful in understanding some of these processes leading to IPA. Factors that have been shown to have a significant relationship with IPA in more than 50% of the reviewed studies examining these factors are: • Personal characteristics: past participation, occupation, smoking, overweight, risk of coronary heart dis ease, 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 in routine. • Activity characteristics: perceived exertion. In this review a number of studies that have shown single factors to be associated with IPA and studies presenting exercise behavior models are identified. The reviewed research has defined either intention to exercise or actual involvement in physical activity as the dependent variable and examined its relationship with selected potential predictors. Be havioral 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 IPA as well. In the following section, selected findings relating to personal and environmental characteristics of people who become involved in 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 in 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. Godin et al. (1987) and Valois, Shepard and Godin (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 in sports and/or physical activity was a significant predictor of intentions and the strongest predictor of participation level. More than 50% of the variance in exercise behavior was accounted for by past experience Appendix A. Literature Review - Physical Activity 107 (measured eight to nine months previous) in 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 in a cardiac rehabilitation program (Oldridge, 1982) and in healthy populations (Dishman, 1982; Gale et al., 1984). The important role of past exercise participation in the social motivation to become or remain involved in physical activities is emphasized by Heinemann (1978). The degree of involvement in leisure behavior in the past has been shown to have a strong relationship with various types of exercise behavior, which is consistent with findings in the field of psychology. In particular, past experience in physical activity appears to have a strong influence on present involvement in 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 in 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 attitude-behavior relationship as well as the use of invalid measures and incorrect designs (Bentler & Speckart, 1981). The 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 in a simple attitude-behavior 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 Rea soned 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. The general Attitude Toward Physical Activity (ATPA) 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 (CATPA) has been applied extensively with children and young adults (e.g. Smoll, Schutz & Kenny, 1976; McCready & Long, 1985). Godin 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. Godin and Shepard (1986) and Sonstroem and Kampper (1980) have shown that the Attitude Toward Act (Aact) and Physical Estimation and Attraction Scale (PEAS), respectively, are better predictors of exercise behavior than the ATPA 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 in vigorous physical activity. Dishman (1982, 1986) argues that although relationships between attitudes and in tentions to exercise and between intentions and actual exercise behavior may exist, there appears to be no relationship between attitudes and behavior. This finding is in contrast with several studies that have shown a direct relationship between attitude and mainte nance 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 ini tiating 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 IPA, 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). An 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 in an urge for higher performance. Contracting and goal-setting have been successfully used as extrinsic mo tivators 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 in 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 Appendix A. Literature Review - Physical Activity 110 (SMI) to measure intrinsic motivation and this measure was included in a psychobio-logical 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 under take 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. Within the Health Belief Model perception of one's own health status was found to be an important motivational component for IPA 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 phys ical activity level (McPherson, 1980). On 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 protec tion motivation and self-efficacy theory by Stanley and Maddux (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 in turn leads to increased involvement in physical activity. General motivation to exercise has been related directly to IPA 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 IPA. 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 Model (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 IPA; 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 in the literature supporting the influence of knowledge on exercise participation and health; exercise knowledge can therefore not necessarily be considered a determining factor of IPA. Appendix A. Literature Review - Physical Activity 112 A.1.5 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 IPA. In their review, Serfass and Gerberich (1984) reported several studies in which spouses of inactive individuals have been shown to be indifferent or have negative attitudes to wards 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 involve ment in physical activity. On 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 involve ment 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 in 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 ex pectations 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). The 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 Godin 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 signifi cant 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 IPA. 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 IPA. 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 in 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 in prediciting exercise behavior can be attributed to perceived barriers. Availability of time and convenience of location has been shown to have a direct in fluence on attitudes towards physical activity in path analyses performed by Mullen et Appendix A. Literature Review - Physical Activity 114 al. (1987). Jackson and Dunn (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 in exercise at all. One of the most frequently indicated barriers to involvement in exercise is lack of time. While 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 al, 1985; Lupton et al, 1984; Noland et al, 1981; Oldridge, 1984; Serfass & Gerberich, 1984). Similarily, the inaccessability or inconvenience of facilities has been identified as an important barrier to IPA (Andrew et al., 1981; Dishman, 1982; Dishman et al., 1985; Oldridge, 1984; Serfass & Gerberich, 1984; Sonstroem, 1982). Other important barri ers 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 al, 1981; Serfass & Gerberich, 1984). While 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 in physical activity. Appendix A. Literature Review - Physical Activity 115 A.1.7 Demographics Demographic variables have a substantial influence on involvement patterns in physical activity. As Dishman et al. (1985) indicate, all other determinants as well as outcomes of IPA 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 Maddux (1986) point out that health-enhancing 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 IPA have been documented extensively (e.g. Lupton et al., 1984; Mullen et al., 1987) and shall not be discussed here. The following demographic variables have been associated with IPA. 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 in 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 IPA. A. 1.8 Biological Traits Some models of exercise have included biological traits as predictors of IPA. Dishman and Ickes (1981) included "% body fat" as one of the main variables in 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 in the prediction of exercise behavior (Dishman, 1981). Pender and Pender (1986) were able to double the variance explained for when predicting IPA 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; in 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 IPA, because this knowledge can be directly used to develop improved motivational strategies for IPA. A.1.9 Models of Exercise Behavior Several researchers have developed models of determinants of IPA 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) in order to understand what determines behavior. They hypothesize that attitudes, consisting of beliefs about con sequences and evaluation of importance of a behavior, as well as subjective norms, con sisting of expectations by significant others and motivation to conform with these expec tations, can adequately predict behavioral intention, which in 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 IPA have been made. Riddle (1980) was able to support the Theory of Reasoned Action; over half of the variance in the intention to exercise was explained by attitude and subjective norm and the association between behavioral intention and behavior was also high. Godin and Shepard (1986) found attitudes, defined within Fishbein and Ajzen's theory, to be a good predictor of Appendix A. Literature Review - Physical Activity 118 behavioral intention. Similarily, Godin 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 (HBM), some successful applications have been made. Slenker et al. (1984) tested a modified version of the HBM. 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 in IPA was accounted for by this model. Similarily Mullen et al. (1987) could account for 57% of the variance in physical activity level by the HBM, confirming the appropriateness of the HBM for the study of exercise behavior. Appendix A. Literature Review - Physical Activity 119 Other Models The PRECEDE model was applied to IPA by Mullen et al. (1987). It is very similar to the Health Belief Model, but views behavior as not being directed towards health. The PRECEDE 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 HBM. The variance accounted for in physical activity level was 57%, 57% and 58% for the HBM, Fishbein and Ajzen and PRECEDE model, respectively. This indicates that even though the PRECEDE 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 in order to identify determinants of participation in worksite health promotion activities, but their model was not very effective in predicting participation. Similarily, Noland et al. (1981) developed a general exercise behavior model, but they were not successful in identifying predictors of IPA either. In an attempt to develop a health enhancement rather than a health protection model, Stanley and Maddux (1986) combined and successfully tested protection motiva tion and self-efficacy theories, which is discussed in section A.1.3. The psychobiological model, mentioned earlier, was tested by Dishman, Ickes and Morgan (1980) and 80% of participants in 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 IPA 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 IPA 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 in recent years and are now well-established in the public. The general notion presented by mass media and the medical community is that exercise is good for you. However, slogans such as "Sport ist Mord" (German: "exercise is murder") indicate that an awareness of the potential risks of physical activity, such as injuries, exists as well. Many studies have found that regular physical activity is related to general physical and psychological well-being. The majority of the benefits that have been associated with IPA are health-related and include physical fitness, disease prevention, and mental health. Evidence supporting physical and psychological benefits of physical activity is pre sented in the next two sections, respectfully. Even though the discussed research repre sents only a fraction of the existing literature, it gives an adequate picture of the outcomes of IPA. A.2.1 Physical Benefits The physical benefits of exercise have traditionally been examined by conducting experi ments 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. Many studies report exercisers to generally be in better health and more physically fit than inactive individu als. However, the pattern of physical activity has to be maintained practically throughout life in order to optimize these health benefits (Serfass & Gerberich, 1984). The important Appendix A. Literature Review - Physical Activity 121 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 in moderate physical activity three times a week or more, tend to be in 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 IPA 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 V02. This has been shown by several researchers Appendix A. Literature Review - Physical Activity 122 (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, flexi bility and muscular endurance, are direct outcomes of IPA 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 IPA 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. However, these relationships have not been firmly established. 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 IPA: 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 IPA. Appendix A. Literature Review - Physical Activity 123 Weight Control Body 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 Roth 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), in which subjects participating in 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 in a healthy body" (Sime, 1984). The 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 mind and body constitute a unit. The effects of physical activity on psycho logical 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). Many 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 IPA 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 IPA is limited. This is mainly due to methodological deficits. Poor measures of psychological con structs are often used, experimenter or subject biases tend to exist, usually there is an a priori belief in positive psychological benefits, and very specific treatment populations are mostly used (Hughes, 1984). Sime (1984) points out, that the problems in provid ing 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 in the general population. They suggest the use of large, generally healthy community samples. Despite these methodological problems, psychological benefits that have been associ ated with IPA within the limitations of the studies remain very interesting and informa tive. 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 IPA psychological health can also be induced via the indirect path through physical health, which is in accordance with most theories about the interaction of body and mind. Some of the aspects of psychological health that have been shown to be related to physical activity are presented in the following sections. Psychological Well-Being Sime (1984) concludes from his review that empirical and clinical studies provide evidence that exercise results in a greatly improved state of mind. Stephens examined four large population surveys and found improved mental health to be directly related to physical activity. Many studies have identified general psychological health or well-being as one of the major outcomes of IPA (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 IPA 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 in active subjects from a healthy community sample as well. Anxiety Following exercise individuals tend to be more relaxed (Bassey &: Fentem, 1981; Gold-water & 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 in purely recreational or competitive form appears to give people a sense of achievement, which can result in 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 in people who exercise; this is an indication of exuberance and relaxation when combined with high and low arousability, respectively. IPA 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 in conjunction with physical activity by sport scientists. Even though some findings are controversial, researchers have repeat edly shown a positive association between increased involvement in physical activity and Appendix A. Literature Review - Physical Activity 127 variables discussed in 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 IPA seem to predict IPA, provided attitudes are measured appropriately. A highly motivated individual is more likely to exercise than an individual who is not motivated. Social sup port is important for the intention to exercise. Barriers such as cost and time can prevent an individual to become involved in physical activity. Some demographic variables rep resenting social status, economic status and maturity have been associated with exercise behavior. These concepts have been defined as predicting variables in the hypothetical model of IPA, 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 in physical activity. The relationships between predictors and IPA are consistent with the Theory of Reasoned Action and the Health Belief Model. A positive association between involvement in 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 IPA. Physical and psychological fitness were defined as outcomes of involvement in physical activity in 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 in 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 co-variance 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. The 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 in section 1.2 and 1.3) • Manifest variables: directly observed or measured variables that have been opera-tionalized 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 in 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 in 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 in 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 in performing causal modeling analyses some aspects of the theory behind causal modeling have to be dis cussed. B.l The Theory B.l.l Model Selection The concept of fitting a hypothetical model to empirical data requires important con sideration with respect to the choice of a model. The general idea behind structural equation modeling is to reduce the information contained in the data in order to inter pret 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 com prehensive models of unmeasured constructs, observed variables and relationships with causal direction. These models are very useful in explaining processes such as behaviors or sociological phenomena. Phenomena can generally be well understood and explained in terms of a multivariate theoretical model; studying them in isolation or only in relation to a few selected variables can Hmit understanding and interpretability. Simpler models are easier to understand. Therefore the researcher is in 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). Appendix 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 inter pretation 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 in 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., McDonald, personal communication) believe that causal models should only be tested in a truly confirmatory sense, which would practically eliminate the option of respecification (discussed in section B.2.3). The 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 131 B.1.2 The LISREL Model The LISREL (Linear Structural Relations) model and computer program was used for most tests of models of IPA in this study. It was developed by Joreskog in 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 in tests of hy pothetical models or confirmatory factor analyses as part of sociological or psychological research. However, LISREL is not necessarily the simplest or most readily understand able model. It also has its limitations and problems with respect to applicability, which shall be discussed later. In this study LISREL was selected for most statistical analyses, because it was easily accessible and convenient to use as it is embedded in 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 COSAN model discussed later), the LISREL 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 LISREL model consists of two basic parts: • The 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 • The 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 in 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,X2, ---yXq) in the following manner: V = + e x = Ax£ + 6 where e is a vector of errors of measurement in y, 6 is a vector of errors of measurement in x, Ay(p x m) is a matrix of regression coefficients of y on n, Ax(q x n) is a matrix of regression coefficients of x on £. Appendix B. Causal Modeling 133 The 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 in the diagonal and I — B is nonsingular Let $(n x n) be the covariance matrix of £ $(m x m) be the covariance matrix of £ 0£ be the covariance matrix of e 0,5 be the covariance matrix of 8 z — {y',x') be the matrix of all observed variables then it follows (Joreskog, 1985) that " A„(J - BJ-^r' + *)(/- 5')-^ + 0e Ay(7 - B)_1r$A^. [ Ax$r(j - s')-1^ AX$A; + where E is the covariance of z. Elements of the matrices Ay, Ax, B, T, $, 0e 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 Ky and Ax 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. An example shall illustrate the setup of a structural equation model as a LISREL model. Appendix B. Causal Modeling 135 Consider model CMI5 in figure 6, which is actually the final version of model I. The following equations illustrate the location of parameters in the equations. Structural Equation Model 7i 0 V 0 72 ) Measurement Model for y 2/3 2/4 2/5 2/6 Vr \y«J /A1 0^ A2 0 A3 0 A4 0 0 A5 0 A6 0 A7 0 Afi / \ ei £2 £7 V 68 J Measurement Model for x / \ * 1 X2 X3 x$ X6 \X71 A9 •^10 An Al2 0 0 0 0 0 0 0 Al3 AX4 ^15 \ 67 ) Appendix B. Causal Modeling 136 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 LISREL control language several matrix specifications have to be made. LISREL 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 in the Au and Ax 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 in 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 in fixed form, which requires freeing elements corresponding to hypothesized path coefficients, or in free form, which requires fixing all elements corresponding to a path that has not been hypothesized. To assign the unit of measurement in the structural model, one can • fix one free parameter per column in 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. Appendix B. Causal Modeling 137 Before a model can be tested by estimating parameters the model should be identified. B.1.3 Model 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 iden tified there has to be at least as many equations as parameters to be estimated. The identification problem manifests itself in the following way. A given set of values of pa rameters results in 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 in both structures, it is said to be identified. If all parameters are identified the model is identified. The 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. The order condi tion involves a simpler method, but is not a sufficient condition for model identification. Each structural equation is tested separately for the condition that me + ke > m — 1 where me is the number of endogenous manifest variables excluded from the structural equation being tested ke 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 Appendix B. Causal Modeling 138 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. The following estimation procedures are available in 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 min imizes the fitting function F = log{det(Y,)) + tr(SE-1) - log{det{S)) - (p + q) The ULS and ML 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 in case of a perfect fit of the model (i.e. 5 = £). No distributional assumptions have to be made for the ULS function, whereas the ML 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 in model fitting. If it is not met, parameters can be estimated but standard errors are invalid. A positive definite input matrix is required for ML estimation. Other estimation methods such as elliptical and asymptotically distribution free meth ods designed for the treatment of non-normal data and generalized least squares are available in other computer software packages, which are described below. The only constraint on the ML 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 "to use various tricks to force the program to stay within the admissable parameter space" (Joreskog & Sorbom, 1985, p. 1.32). These "tricks" are discussed in section 3.4.2. B.1.5 Assessment of Fit Primary aims in model fitting are the production of valid indices of fit and valid param eter 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 in 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 $, 0e, 0$ of estimated parameters are not positive 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 in the LISREL model is the %-square value as defined by Joreskog (1985) X2 = (n - 1)F 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 x2 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, %2 should be regarded as a criterion to decide whether the fit is adequate or not rather than a test statistic. In general, a lower x2 corresponds to a better fit of the model. However, x2 is sensitive to sample size and departures from multivariate normality of observed variables. Since %2 is linearily de pendent on sample size, it is, for example, practically impossible to get a low %2 value with large samples. Some researchers have suggested to use the ratio of Xzl^f as a relative measure of fit. Although this technique is questionable for comparing the fit of models using different Appendix B. Causal Modeling 141 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. An alternate way of using x2 is to assess the change in fit between two models. If a model is, for example, modified based on the results from an initial test, the improve ment in fit can be assessed by evaluating whether the change in %2 in conjunction with the difference in associated degrees of freedom is significant or not. If it is, a signifi cant 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 in model fit and the original model should therefore be retained. This pro cedure, 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 LISREL is the Goodness of Fit Index (GFI) and the Adjusted Goodness of Fit Index (AGFI), which is adjusted for the degrees of freedom. Both 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 in LISREL 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 LISREL 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 in 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 GFI and low RMR, 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. The following descriptions of various criteria should be regarded in 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 in a matrix of raw residuals, where elements r\j are calcu lated as They represent the difference between the sample covariance and the covariance estimate given by the LISREL model. LISREL 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 in 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 Appendix B. Causal Modeling 143 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 minimum decrease in %2 if that parameter is relaxed and estimated as a free param eter in the model. The highest modification index indicates which (possibly omitted) parameter could improve the overall fit of the model the most if it were included in 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 in 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 psy-chometricians and statisticians. Dillon and Goldstein (1984) conclude that GFI and likelihood-ratio statistic (%2) should be replaced by other statistics. McDonald and Marsh (in press) point out that most available fit assessment methods depend largely on sam ple size or on expressing fit relative to the fit of a chosen nullmodel. The nullmodel is defined as the most restrictive theoretically defensible model for relative fit indices such as the Bentler-Bonett normed fit index (Bentler, 1985). The Tucker-Lewis Index and the Unbiassed Relative Noncentrality Index (McDonald) are suggested as relative fit indices by McDonald 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 MacDonald. 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 COSAN model, which was developed by McDonald. It states that any model can be expressed as £ = F1F2...FkPFi..F!iF[ 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 LISREL-type causal model can easily be defined as a COSAN model of order 2 by applying the RAM system developed by McArdle and McDonald. Bentler developed the EQS computer program for testing structural equation models, which has been embedded in the Biomedical Computer Programs (BMDP) statistical package. 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 SYSTAT, is a very userfriendly and efficient program that allows the user to set up models in a quasi-graphic representation. The program then transforms this input into a COSAN-type model. 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 in addition to various other fit assessment criteria. Confidence intervals for the Goodness of Fit indices are given as well, which allows the researcher to evaluate the fit of the model to the data more appropriately. Appendix B. Causal Modeling 145 B.1.7 Categorical Data Many 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 in 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. Muthen (1985) de veloped and tested the Categorical Variable Method (CVM) as an alternative estimation method and implemented it into the computer program LISCOMP. The program PRELIS was developed by Joreskog as a preprocessor for categorical data. The program produces detailed information about distributional characteristics of the variables. Tables and statistics are calculated for three types of variable pairs: • continuous vs. continuous: The product moment correlation is calculated for all observations with no missing data. • continuous vs. categorical: The mean value of the continuous variable for all sub jects 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 LISREL model. The LISREL computer program has a built-in option to automatically calculate these correlations and estimate the parameters in the model with it. B.1.8 Non-Normal Data One of the major assumptions underlying the distribution of the ML function is multi variate normality. Several other estimation methods have been developed that do not require this assumption. Unweighted Least Squares (ULS) or Generalized Least Squares (GLS) 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 maximum likelihood estimates. Bentler developed elliptical estimation meth ods and Asymptotically Distribution Free (ADF) methods to give more precise solutions for non-normal data. They are available under EQS along with criteria for the assesment of multivariate normality (e.g., Mardia's Kappa Coefficient). Anderson and Gerbing (1988) report that several researchers have tested the robust ness of estimation procedures with respect to violations of the assumption of multivariate normality in 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 in causal modeling is the development of a sound theoretical model with justifiable hypothesized causal relationships. The development of model I and model II, which are the causal models examined in this study, is discussed in 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, in the operationalization of variables, which is discussed in 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. The mathematical definitions of these models have been described in section B.1.2, whereas practical procedures are explained in the following sections. B.2.1 Measurement Model The first step in testing a hypothetical model is a test of the measurement model. The hypothesized factor structure is tested by applying confirmatory factor analysis. Struc tural 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 la tent variables. By testing the measurement model first, the researcher would, in 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 sep arately 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 in the following manner: In a chosen A matrix (it makes no difference whether Ay or Ax 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 hypoth esized 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 con firmatory analysis. Furthermore, off-diagonal elements of the matrix $ are estimated as free parameters in testing the measurement model, which allows for correlated factors. The LISREL program is then run on the covariance or correlation matrix of the observed variables. The estimated parameters in 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 149 B.2.2 Structural Equation Model In the case of an acceptable fit of the measurement model, its structure is directly imple mented 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. All 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 LISREL 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 with out 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 signifi cantly 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 signif icantly without major changes to the structure. Appendix B. Causal Modeling 150 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. The following modifications can be implemented in order to improve the fit of a measurement model in 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 theo retical 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. While 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 YOU OESCRI8E YOUR ACTIVITIES. WE HAVE DESIGNED FOUR QUESTIONS - ONE FOR THOSE YOU DO DAILY, ONE FOR THOSE YOU DO EACH WEEK, ONE FOR THOSE YOU HAVE DONE IN THE LAST MONTH, AND THE FOURTH FOR THOSE ACTIVITIES YOU HAVE DONE IN THE LAST YEAR. 1. DAILY ACTIVITIES For those activities which you do most days of the week (such as work, school and housework), how much time'do you spend. . . AVTMHI of if. oma HxxA 1/4 of 9* arm of tf* fjmt AbQUX 1/4 of tha dm* Airmail* of in* Sitting • • • • Standing • • • • Walking • in • • Walking up •uira • • • • Lifting or carrying heavy objects • • • • 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. Light hooaawork and Kandyworfc w» thing dbjhea. ironing, making beda, mowing lawn, ate Ught Mtxfcjm Hoavy Brno sagr« prrrMn pw» Numtwr of occAttont tan» (M^i Ate** prrean ••eft men fh from nemm Mmtvy PKKKUWA wn« biMfh^f bnMtfwvj J » M A M J J A 1 OMO >MMn I • I . I • II • I . I . II • I • 1 . II • I . I • 1 ULJ • • • Haavy houaawork and handywork wathing and waxing floor*, painting, ate light MnoVim am* Nvmbar of rrrmmrm J f M AMJ J A J ONO l- , , , I . I • I • II . I. I • II . I , I , II • I • I • I ULJ • • • Nama of activity L. , • I OryaWarJ Morr*-»f of occ«My« A^t^. Intarwfv * « •axhrron* am* L-^M M«Sum H«arvt tn • t»*gu« JUM AUj J A % OMO t+t «»w« rm Ho jm No I . I . I. ii • I. I . il . i. i. ii. i . I. I I M , l • • • • • • L7J a a a a a » a a a Nama of activity 1 , , • 1 Hvtvb* of occaun Avtx»ot kmnt »»cn month oma LV11 HAtxSurn HO«VY 0»OAn«Md ComortrtA. J * M A M J JAJ ONO I* *° 'lit. £2. I • I • I. II. I. I. M . l. I, ll, I , I, I I II • I. • • • • UJ a a a a aaa  « Nama of activity I 1 I ' I ' 1 Nurriw of octwora Av»»»»ot kttararly Mch month tima light M«drum Htavt JfM AMJ JAS OMO <*n XW» -I | I II I I II I I II I I I I I I I I I I ' I 1 TM MO r*» 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) 2s Gardening and cultivating *uch as spading, digging, weeding monfri *c*v*etH «p«m on Men occiMn Hnj Mirw U LJ Ligm MMwn • • Shovelling mow OccMton* in tr* tag* Av*r»Q4 ami aciuatv «fH on **chocca*>on Hn) Mr« U LxJ Light lm»nsffy VUOaj^ Vsr^e '«(*• enor • • KMW • Mowing the lawn (pushing a power mower) Av*r»gt WW on OOCA acceaxy Hn Uirw u Light • InunMy M«*u<n • • Name of activity i OccM*om LJ Name of activity Mnj Mina U LJ Light Medium Hww • • • in krvwr, or in • ingm y«* HO • • Cornp«tiOv», YM NO • • LJ Avinjoi orm Hn mm U LJ Light fcUdum HNV« • • • YM No • • YM No • • Nam* of activity in Tm tat LJ Away* Hm Min* U LJ Ugnt M«oVjn K«9vy • • • YM NO • • YM No • • Name of activity Occa**onft in 9* loci Awigi torn* Hn Mint trnaognV LtgM M*dwjr* H*#w U LJ • • • Organoid YM NO • • Comp#vtK>« YM NO • • Name of activity in tf* IMI month Hr» Mina U LJ Vi Howry light Medium Heavy OoJivjexj YM NO Cornp«fjtrv»j YM NO • •••••• 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) MontT* n wft*cn *cwf» ww Gont Walking lor axtxcise Jogging lusing short strides) Running lusing long strides) BicycJing Home exercise (push-upa, sit-upsl Exercise classea Weigtit draining Yoga Gorf (walking and carrying club*) Rscquetbal Squeeh Tennia Basebal Softbea Ice hockey Curling Swimming at a pool Dots country skiing AJpine/Downhill skiing lea tkabng Names of scovrtjea: Nurriow Of OCCJwOOt •n 1M1 J'MAMJJASO*0 'W« ww 10 40 iwXitM loonl on •ocr* occAwon S « Jl II • ••••••••••• LJ''[TLJTJT] • ••••••••••• LJ • • • • • ••••••••••• LJ ••• • • • ••••••••••• LJ • • • • la <0 J L J L • ••••••••lf]DD U"D"D'D*D • ••••••••••• LJ • • • • • •••••••••DO LJ • • • • • ••••••••••• LJ • • • • >* IS 11 il JFMAMJJASOND ww X «0 Bj>navw««]Oww« o •••••••••••a LjTrDTra •••••••••••a LJ • • • • •••••••••••a LJ • • • • •••••••••••a LJ • • • • it i« ii « JFMAMJJAI0N0 ii 5 «0 «»» noMSsiCwwanca « •••••••••••a LJ ••••••••.•••a LJ • • • • ••••••••••••LJ• • • • •••••••••••a LJ • • •• w 10 11 w *3 • ••••••••••• LJ •••••••••••a LJ• • • • •••••••••••a LJ • • • • •••••••••••a LJ • • • • it m J •••••••••••• L^TDTTCrn J•••••••••••• LJ • • • • J•••••••••••• LJ • • • • J•••••••••••• LJ • • • • J •••••••••••• LJ ••• • • M J J in >o "I IS to X j •••••••••••• 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? «npon£nt Of homt •mporunc* Of »n>« *>< fDoonani 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 LLI WMMnai LU so* 8. 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 N[ J lntfu«v*ning »CJ At f 9. Where do you usually do your physical activities? (Indicate one or more) • I—I 1—I ScNxH. or Mom. „l I Wort „i I ufwwwty faolhy • CorrvTwcitf TlolrtV | I O^tuo* utV>g no 10. 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 •ctjvitv t*:h w*«k st I 3 rnonth* n' J juH und* 6 monihi al J juit un0#H J y»J f—\ from 3 y«*r» to '—' r"-~ |—^ From 1 v«*v to fu»t ppendix C Questionnaire of the 1981 Canada Fitness Survey 12. 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* .• Nof»c*it*M naaroy .• Avfteb-* ^otrba* *n tnaOaQuata Iryxy or ha^rjicjQ No fo»r. yysjaibaj Lack of VTt .• Kaourai too nxich ia»*1-di*cip-»** L*c* of rtrrm btOUM Of wort laC*OOt}. .• Lack tT»» rvcatsa/Y rJuttl Lack of Dm* bacauat of otftar a**** acuvioa* .• Coats too fnucn 1 13. 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 .• „• .• 8«Rar or ctoaar t*c*tim frffarant facaftaa Lot ajuwnvv* t*cHhim Mora inforrrtjoon on Uha b*n«ftta of doing pnv**=* actStfy Ernptovw or i***»»on tponaorad acVvttMl *v**4atta Oro*nix*d •port] .tvarfaba) Oryantzad fttnaw .• .• .• Ftoo** taxi wnh p*K»ory»J activity proorwn rvaaafita iHop-a wnti «rhom to partxap*ta Common rttar«i of f»maV Cornrrion rarwi of tri»nrji MoraH 09m Which of the following programs have you heard of? JO CtnarJan Homa Rmaaa Tan .• Sta^darrJo*d Taai of Ftraai JO Canada Gamal ,• Rtn*a» ant) A/nrtaur Sport BO Canada Hirai A«rm»: .• Ftaaa* Cavvada »CH HTlUT .• SD INFORMacoofl .• AD PAXTICIP^rBon ,• Cinad* f^tnaaa facM 15. 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 YOU ever seen this symbol? No - Go to oucroon 17 • Not Sum - Go to xwoon 17 Where have yoj heard of or s««n the PAfiTlCIPacbon symbo* or measag,«? (Indicate ell applicable) On Mkivwon On radio „• In r^wioapari In m*>gu>n*M in ooc*J*ti or p4im©n*** .• Onbirtboarda On pcatam Onbuve* or tuowar* „• On mrk cariona On f thins .• At acnoor At PirriciPaA* In PtP—•: Tha Fae»' -• Sudani notabooAa Oon'l know 17 . Have you previously taken t physical fitnet* test? No - Gotoouwtion IS • Don't know - Go » quonon Ii Whet type of cerdto-vescular laerobkl exercise did this test use? ,D SMOOX« Q • Wl»V Jog/Hun Where did you take this fitness test? »Q YMCA/YWCA Lt3 Q WoitorKNjol Q Commaroai1 ofcjo or t*G*«V • When did you take this teat? jp L J .3 In tf>a avt 4 montfai • front % manrttv) II Inarlgo • OW 1 r«r igo Were you satisfied with the way the tesl was explained and administered? -CD Vvyomf*} CD Saoxflad • Notllduta 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) Nona or Actrrfty Atry did TOU tlop doing thai acOVrty? OffcaUaa m Qtf<m Uaa dix C. Questionnaire of the 1981 Canada Fitness Survey 1 19. 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 ninM in*? Acrvny AcDvrty Wh*n « tf* m*«n outon you n*v* no* y*l itartx] M> Wh*rt * tf** matn r**»on you Kav* not r*i rtartad tm) OtVaOw CKtV* UM LJ 20. How important are each of the following to you in gaining a feeling of well being? Vary Of *ona> 0* Irrda lUMlim tmeorunca Importance Of no Imponanca Adaquatt r**1 and *Xlp • • AoooddWl • • • Low caloria anacls barwaan rrtnU • • • Ma«^t»n*nc* of propar »*iqN • • • rVixapabon in aooai and oufturaf actfvroaa • • • Co*'trod of fvaM • • • Ragoia/ phya>cai actMry A*cn aa *x*rca*. <xjra or gama* • • • U*ng atconof mcOanjtary or oaing • rkor^oVinMr • • • Ba»ng a rwrvamofcar • • • A^oouatv rrwoVa* and dantai car* • • • • • • LIFESTYLE AND YOUR HEALTH What do you usually eat for breakfast? [Usually means at least four days a week.'. that appty. Check all »L) 1 donl MI braairtaai .MO* aO (»gi a D Al Wt • our <m ofm* 1 1 Swyi or <rtfiar moat, IWl or poultry aO Chaoaa s 1 } aVaarJ. daniah or donul „Q Yogurt aO Own . a CD Taa or coflaa X,0 CW»r caraaa) In the last year, have you been eating twaat food* and cindlaa j,[D Mora • Laaa • S*ma • mount as bafora frun and v«o«t»b»aa BCD Mora CD laaa • Sama amount U txfon> Appendix C. Questionnaire of the 1981 Canada Fitness Survey 23. About how often do you usualfy drink alcohol? Gj 4 to 7 «ma> i «r*»M E lata than one* a mont* Gj ! to J oma« « M« Gj looft'iorrt alcohol - Go loovaaaon 24 8 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. • • Ona Two Of Irm Four or flva) ED Saoriwvao [jD C*}M Or fTVOn 24. Which of the following best describes your experience with tobacco. Check all that apply. • • • • • I currant** trnofca: bgaraRa-f occaa«x>»aV an tan 1/5 pack of c*g*v«f-»a 4a*Jy about a pock of doarvnaa oaJy two or mora packs otogavvnaa da»V a pipa. cigar or c»oar*o • • • I Hope-ad amoaJng: dg*v«ttaa rncanAV ciganmaa ovar a v*ar ago a pipa. cigari or aganioa racanOV • ptpa. 69am or cJQaHtaa pvax a yaar ago • pipa. ooar or ciganlo daaV 25. 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 ... On «oo of lha world? Vary fc>rtary or 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 CO*r^rr«e>nL*vJ you on tomatfaing you had oonar* So ra^dnst you COu*dn't »it long in a chaW That tftingj »v*f t goir»g ytw wry? Ottan tom«timai Nov* • • • • • • • Q • • • • • • • • • • Appen dix C Questionnaire of the 1981 Canada Fitness Survey 160 26. About how many hours of sleep do you usually get each day? pLD Sb houri or laaa 0 Nina CU S*««n 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? • I—| Yae. bacauaa of 9 Ho LiJ tamponry «*ajry • Yaa. baouMoTi i—i Yaa. bacaun of a ttamporary aYiaaa LiJ parmanant injury or handicap • Yaa. bacauaa of a crvorac or long-tarm aViaaa 28. 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? • YM. b*c*uM of a j—i YM. tectuM of • ptnnantnt WnpOfWY *f— LiJ injury or ha-"»dca© • YM. bictuM of I chnwwc or long-tarrr. ttrwM 29. In general, how would you describe your state of health? Vary good LiJ »oor CZ1 Good 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 LlJ ItaSan Gl! frvx*. 0 Carman LU Orhar | 32. Is there another language that you are in the habit of using? BQ Nona O Itatan Engbah LU Uk/a*iian endix C. Questionnaire of the 1981 Canada Fitness Survey 10 33. Are you . . . 31 34. How old are you? • r. IF YOU ARE 14 YEARS OF AGE OR YOUNGER, YOU HAVE FINISHED THE QUESTIONNAIRE. THANK YOUI WE WOULD BE GRATEFUL FOR YOUR COMMENTS. A SPACE FOR THIS HAS BEEN LEFT ON THE LAST PAGE. IF YOU ARE 15 YEARS OF AGE OR OLDER, . . . 35. What is your present marital status? Are you presently . . D Uarrwd Widow** CD KnM • Saparatad Q S«ngfctIN#va/ 36. What's the highest level of education you have reached? • at Cmr+niari or am LlJ or canificata • Soma t*cora3*vy |—J Cornrr^unrty coftao* LU or CK£f <*>oma • Secondary £pic*m« f—| Ona or mom UJ LWvarvtv da^aaa • Soma poa TV* C or*Sa*"V 37. Are you . . . ICheck alt that apply) • «*wad • t^Yiptoyad" tut-oma • • Empiovad pa^-orna • • StwJant hj4-0ma • • SiwSam pavvoma Hc«mama* ar/Hc»^aaWa ^ -» Moma^kar/Houaawrfa pani lJna*r»?_oY*d or on nrfca Ornar | 38. 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 What kind of work do you do? leg. posting invoices, selling »hoes. etc.) Please provide as much detail as possible. For whom do you work? (Name of business, government depertment. agency, person, or are you serf employed?! What kind of business, industry or service is this? (eg. paper box manufacturing, retail shoe store, municipal board of education.I 42. Is there an opportunity for physical recreation where you work? G Yaa. atlunct. G No • m Q Yaa. « ooTfaa braas. G Yaa. afar Mart 43. Approximately what was your family's total income last year, before taxes? Q taaa tfwi H.000 Q tZ.OCOtt> t29.Ht a a • 16.000 » 19 9BB LiJ IX.000 lo U6.Q0O Q llO.OOOto l<.99» G uvatWo.OOO Q G Don't know Appendix D SPSS Control Commands for Transformation of IPA Variables 164 Appendix D. SPSS Control Commmands 164 For University of British Columbia License Number 12495 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 Improvemen t s in: MANOVA TABLES 1 ? 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 16 19 20 21 22 23 24 25 26 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 TITLE ' CFS • MALES. 20 TO 40, DESCR STATS ALL OTHERS 4 ALL CORR1 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 7 RECORDS FROM FILE DATA VARIABLE REC START ENO FORMAT WIOTH DEC AGE 1 3 4 F 2 0 DAYS 1 8 8 F 1 0 ADHERENC 1 9 9 F 0 LIMITED 1 10 10 F 1 0 ACTIVSCA 1 11 1 1 F 0 WALKTYPE 2 3 3 F 1 0 WALK INT 2 4 7 F 4 1 WALKYEAR 2 8 to F 3 0 WALKLMON 2 1 1 12 F 2 0 WALK TI ME 2 13 15 F 3 0 JOGGTYPE 2 16 16 F 1 0 JOGGINT 2 17 20 F 4 1 JOGGYEAR 2 21 23 F 3 0 Appendix D. SPSS Control Commmands 165 JOGGLMON 2 24 25 F 2 0 JOGGTIME 2 26 28 F 3 0 RUNNTYPE 2 29 29 F 1 0 RUNNINT 2 30 33 F 4 1 RUNNYEAR 2 34 36 F 3 0 RUNNLMON 2 37 38 F 2 0 RUNNTI ME 2 39 4 1 F 3 0 BICYTYPE 2 42 42 F 1 0 BICY1NT• 2 43 46 F 4 1 BICYYEAR 2 47 49 F 3 0 BICYLMON 2 50 51 F 2 0 BICYTIME 2 52 54 F 3 0 GOLFTYPE 2 ' 55 55 F 1 0 GOLFINT 2 56 59 F 4 1 GOLFYEAR 2 60 62 F 3 0 GOLFLMON 2 63 64 F 2 0 GOLFTIME 2 65 67 F 3 0 RACQTYPE 2 68 68 F 1 0 RACOINT 2 69 72 F 4 1 RACOYEAR 2 73 75 F 3 0 RACOLMON 2 76 77 F 2 0 RACQTIME 2 78 80 F 3 0 TENNTYPE 3 3 3 F 1 0 TENNINT 3 4 7 F 4 1 TENNYEAR 3 8 10 F 3 0 TENNLMON 3 1 1 12 F 2 0 TENNTI ME 3 13 15 F 3 0 BASETYPE 3 16 16 F 1 0 BASEINT 3 17 20 F 4 1 BASEYEAR 3 21 23 F 3 0 BASELMON 3 24 25 F 2 0 BASETIME 3 26 28 F 3 0 ICEHTYPE 3 29 29 F 1 0 ICEHINT 3 30 33 F 4 1 ICEHYEAR 3 34 36 F 3 0 ICEHLMON 3 37 36 F 2 0 ICEHTIME 3 39 41 F 3 0 SOFT TYPE 3 42 42 F 1 0 SOFT INT 3 43 46 F 4 1 SOFTYEAR 3 47 49 F 3 0 SOFTLMON 3 50 51 F 2 0 SOFT TI ME 3 52 54 F 3 0 SWIMTYPE 3 55 55 F 1 0 SWIMINT 3 56 59 F 4 1 SWIMYEAR 3 60 62 F 3 0 SWIMLMON 3 63 64 F 2 0 SWIMTIME 3 65 67 F 3 0 SKI A TYPE 3 68 68 F 1 0 SKI A INT 3 69 72 F 4 1 SKI AYEAR 3 73 75 .F -. 3 0 SKIALMON 3 76 77 F 2 0 SKI ATIME 3 78 80 F 3 0 SKICTYPE 4 3 3 F 1 0 SKICINT 4 4 7 F 4 1 Appendix D. SPSS Control Commmands 166 SKICYEAR 4 8 10 F 3 0 SKICLMON 4 1 1 12 F 2 0 SKICTIME 4 13 15 F 3 0 SKATTYPE 4 16 16 F 1 0 SKAT INT 4 17 20 F 4 1 SKATYEAR 4 21 23 F 3 0 SKATLMON 4 24 25 F 2 0 SKATTIME 4 26 28 F 3 0 ROLL TYPE 4 29 29 F 1 0 ROLL INT 4 30 33 F 4 1 ROLLYEAR 4 34 36 F 3 0 ROLLLMON 4 37 38 F 2 0 ROLLTIME 4 39 41 F 3 0 CALITYPE 4 42 42 F 1 0 CALIINT 4 43 46 F 4 1 CALI YEAR 4 47 49 F 3 0 CALILMON 4 SO 51 F 2 0 CALITIME 4 52 54 F 3 0 EXERTYPE 4 55 55 F 1 0 EXERINT 4 56 59 F 4 1 EXERYEAR 4 60 62 F 3 0 EXERLMON 4 63 64 F 2 0 EXERTIME 4 65 67 F 3 0 WEIGTYPE 4 68 68 F 1 0 WEIGINT 4 69 72 F 4 1 WEIGYEAR 4 73 75 F 3 0 WEIGLMON 4 76 77 F 2 0 WE IGTI ME 4 78 80 F 3 0 BAOMTYPE 5 3 3 F 1 0 BAOMINT 5 4 7 F 4 1 BADMYEAR 5 8 10 F 3 0 BAOMLMON 5 1 1 12 F 2 0 BADMTIME 5 13 15 F 3 0 8ASKTYPE 5 16 16 F - 1 0 BASK INT 5 17 20 F 4 1 BASKYEAR 5 21 23 F 3 0 BASKLMON 5 24 25 F 2 0 BASKTIME 5 26 28 F 3 0 FOOTTYPE 5 29 29 F 1 0 FOOT INT 5 30 33 F 4 1 FOOTYEAR 5 34 36 F 3 0 FOOTLMON 5 37 38 F 2 0 FOOTTIME S 39 4 1 F 3 0 SOCCTYPE 5 42 42 F 1 0 SOCCINT 5 43 46 F 4 1 SOCCYEAR 5 47 49 F 3 0 SOCCLMON 5 50 51 F 2 0 SOCCTIME 5 52 54 F 3 0 VOLL TYPE 5 55 55 F 1 0 VOLLINT 5 56 59 F 4 1 VOLLYEAR 5 60 62 F 3 0 VOLLLMON 5 63 64 F 2 0 VOLLTIME 5 65 67 F 3 0 FR1STYPE 5 68 68 F 1 0 Appendix D. SPSS Control Commmands 167 FRISINT 5 69 72 F 4 1 FRISYEAR 5 73 75 3 0 FRI SIMON 5 76 77 F 0 FRISTIME 5 78 80 0 Rl 6 3 3 F 1 0 R2 6 4 4 1 0 R3 6 5 5 F 1 0 R4 6 6 6 1 0 R5 6 7 7 F 1 0 R6 6 8 8 1 0 R7 6 9 9 F 1 0 R6 6 10 10 1 0 R9 6 1 1 1 1 F l 0 R 10 6 12 12 1 0 MATE 1 6 13 13 F 1 0 MATE? 6 14 14 1 0 MATE 3 6 15 15 F 1 0 MATE 4 6 16 16 1 0 MATES 6 17 17 F 1 0 MATE6 6 18 18 1 0 MATE 7 6 19 19 F 1 0 FITNESS 6 20 20 1 0 BAR 1 6 21 21 F 1 0 BAR2 6 22 22 1 0 BARS 6 23 23 F 1 0 BAR4 6 24 24 \ 0 BARS 6 25 25 F 1 0 BAR6 6 26 26 \ 0 BAR7 6 27 27 F 1 0 BARS 6 28 28 1 0 BAR9 6 29 29 F 1 0 BAR 10 6 30 30 1 0 BAR 1 1 6 31 31 F 1 0 BAR 1 2 6 32 32 1 0 8AR13 6 33 33 \ F 1 0 PARTICIP 6 34 34 F 1 0 LIFE1 6 35 36 1 0 LIFE2 6 36 36 F 1 0 LIFE3 6 37 37 1 0 LIFE4 6 38 38 F 1 0 LlFES 6 39 39 1 0 IIFE6 6 40 40 F 1 0 LIFE7 6 4 1 41 1 0 LIFE8 6 42 42 F 1 0 LIFE9 6 43 43 1 0 LIFE10 6 44 44 F 1 0 LIFE 11 6 45 45 1 0 ALCFREQ 7 3 3 F 1 0 ALCAMOUT 7 4 4 1 0 SMOKETYP 7 5 5 F 1 0 SMOKING 7 6 6 1 0 SMOKSTOP 7 7 7 F 1 0 BRAOPOS 7 8 9 2 0 BRAONEG 7 10 11 F 2 0 BRADSCAL 7 12 13 2 0 SLEEP 7 .14 14 F 1 0 HEALTH 7 15 15 1 0 MARITAL 7 16 16 F 1 0 EDUCAT 7 17 17 1 0 INCOME 7 18 18 F 1 0 SKINFOLD 7 19 22 4 1 AEROBIC 7 23 24 F • 2 0 GRIPSTR 7 25 27 3 0 PUSHUPS 7 28 30 F 3 0 FLEXION 7 31 33 3 0 SITUPS 7 34 36 F 3 0 END OF OATALIST TABLE. Appendix D. SPSS Control Commmands 168 2? 0 MISSING VALUES 28 0 I I MI TED(0) »CTIVSCA(4) ADHERENC(O) R1 TO R10(0) FITNESSIO) 29 0 PART1C1P10) LIFE) TO L1FE1K0) ALCFREO(O) SMOKETYP(O) 30 0 8RADP0S TO BRAOSCAL(OO) SLEEP(O) HEALTH(0l MARITAL(O) EDUCATIO 31 0 INC0MEI0.8) SKINF0LDI999 8) AER0BIC(98) GRIPSTR!995.996 . 998) 32 0 PUSHUPS FLEXION SITUPS(995,996.998) ALCAM0UT(8) 33 0 RE CODE ALCFREQI6=0)(5=1)(4 = 2)< 2 = 4)< 1 = 5) 34 0 00 IF (ALCFREQ EQ 0) 35 1 • COMPUTE ALCAMOUT=0 36 1 • ELSE IF (ALCAMOUT EO 0) 37 1 • RECOOE ALCAM0UT(0=8) 38 1 END IF 39 0 RECOOE 40 0 WALKYEAR JOGGYEAR RUNNYEAR BICYYEAR GOLFYEAR RACOYEAR TENNYEAR 4 1 0 BASE YEAR ICEHYEAR SOFTYEAR SWIMYEAR SKIAYEAR SKICYEAR SK A T Y£ AR 4? 0 ROL L VE AR CALIYEAR EXERYEAR WEIGVEAfi 8ADMYEAR BASKYEAR FOOT YE AR 43 0 S0CCYEAR V0LLYEAR FRISYEAR(998=0) 44 0 RECOOE 45 0 WALKLMON JOGGLUON RUNNLMON 81CYLMON GOLFLMON RACOLMON TENNLMON 46 0 BASELMON ICEHLMON SOFTLMON SWIMLMON SKIALMON SKICLMON SKATLMON 47 0 ROLL LMON CALILMON EXERLMON WE IGLMON BAOMLMON BASKLMON FOOTLMON 48 0 SOCCLMON VOLLLMON FRISLMON(98=0 I 49 0 RECOOE 50 0 WALKT1ME JOGGTIME RUNNTI ME B1CYTIME GOLF TI ME RACOTIME TENNTIME 51 0 BASETIME ICEHTIME SOFT TIME SWIMTIME SKI ATIME SKICTIME SKAT TIME 52 0 ROLL TIME CAL1TIME EXERTIME WE IGTI ME BADMTIME BASKTIME FOOT TIME 53 0 SOCCTIME VOL L TI ME FRISTIME(998=0) 54 0 RECOOE LIMITE0(4=2)(5=3) 55 0 00 IF (WALKTYPE EO 2) 56 1 • COMPUTE WALKFREQ=WALKLMON 57 1 • ELSE 58 1 • COMPUTE WALKFREQ=WALKYEAR/12 59 1 END IF 60 00 IF (JOGGTYPE EQ 2) 6 1 1 • COMPUTE JOGGFREO=JOGGLMON 62 1 • ELSE 63 1 • COMPUTE JOGGFREO=JOGGYEAR/12 64 1 ENO IF 65 DO IF (RUNNTYPE EO 2) 66 1 • COMPUTE RUNNFRE0=RUNNLMON 67 1 • ELSE 68 1 • COMPUTE RUNNFREQ=RUNNYEAR/12 69 1 END IF 70 DO IF (BICYTYPE EO 2) 7 1 1 • COMPUTE 81CYFRE0=BICYLMON 72 1 • ELSE 73 1 • COMPUTE 8ICYFREQ=8ICYYEAR/12 74 1 END IF 75 00 IF (GOLFTYPE EO 2) 76 1 • COMPUTE GOLFFREQ=GOLFLMON 77 1 • ELSE 78 1 • COMPUTE G0LFFREO=GOLFYEAR/12 79 1 END IF 80 DO IF (RACQTYPE EO 2) 81 1 • COMPUTE RACQFRE0=RAC0LMON 82 1 • ELSE 83 1 • COMPUTE RACOFREO=RACOYEAR/12 84 1 END IF 85 DO IF (TENNTYPE EO 2) 86 1 • COMPUTE TENNFREQ=TENNLMON 87 1 • ELSE 88 1 • COMPUTE TENNFREQ=1ENNYEAR/ 12 89 1 END IF 90 DO IF IBASETYPE EO 2) 9 1 1 • COMPUTE BASEFRE0=BASELMON 9? 1 • ELSE 93 1 • COMPUTE BASEFREO-BASEYEAR/12 94 1 END IF 95 DO IF ( ICEHTYPE EQ 2) 96 1 • COMPUTE ICEHFREO=ICEHLMON 97 1 • ELSE 98 1 • COMPUTE ICEHFREO=ICEHYEAR/12 99 1 END IF 100 0 DO IF (SOFTTYPE EQ 2) Appendix D. SPSS Control Commmands 169 101 1 • COMPUTE S0FTFREQ=S0FTLMON 102 1 • ELSE 103 1 • COMPUTE SOFTFREQ=SOFTYEAR/12 104 1 ENO IF 105 0 DO IF (SW1MTYPE EO 2) 106 1 • COMPUTE SWIMFREQ=SWIMLMON 107 1  ELSE 108 1 • COMPUTE SWIMFREO-SWIMYEAR/12 109 1 END IF 110 0 DO IF (SKIATYPE EO 2) 1111 • COMPUTE SKIAF REQ=SKIALMON 112 1  ELSE 113 1 • COMPUTE SKIAFREQ=SKIAYEAR/12 114 1 END IF 115 0 DO IF (SKICTYPE EO 2) 116 T • COMPUTE SKICFREQ=SKICLMON 117 1  ELSE 118 1 • COMPUTE SKICFR£Q=SKICYEAR/12 119 1 END IF 120 0 DO IF (SKATTYPE EO 2) 121 1 • COMPUTE SKA TF REO=SKATLMON 122 1  ELSE 123 1 • COMPUTE SKATFREQ=SKATYEAR/12 124 1 END IF 125 0 00 IF (ROLLTYPE EO 2) 126 1 • COMPUTE ROLLFREQ=ROLLLMON 127 1  ELSE 128 1 • COMPUTE ROLLFREQ=ROLLYEAR/12 129 1 END IF 130 0 DO IF (CALI TYPE EO 2) 131 1 • COMPUTE CALIFREQ=CALILMON 132 1  ELSE 133 1 • COMPUTE CALIFRE0=CALIYEAR/12 134 1 END IF 135 0 00 IF (EXERTYPE EO 2) 136 1 • COMPUTE EXERFREQrEXERLMON 137 1  ELSE 138 1 • COMPUTE EXERFREQ=EXERYEAR/12 139 1 END IF 140 0 00 IF (WEIGTYPE EQ 2) 14 1 1 • COMPUTE WEIGFREQ=W£IGLMON 142 1 • ELSE 143 1 • COMPUTE WEIGFREQ^WEIGYEAR/12 144 1  END IF 145 0 DO IF (BADMTYPE EO 2) 146 1 • COMPUTE BADMFRE0=BADMLMON 147 1  ELSE 148 1 • COMPUTE BADMFREQ=8ADMYEAR/12 149 1  END IF 150 0 00 IF (BASK TYPE EO 2) 151 1 • COMPUTE BASKFRE0=8ASKLMON 152 1  ELSE 153 l • COMPUTE BASKFREQ=BASKYEAR/12 154 1  END IF 155 0 DO IF (FOOT TYPE EQ 2) 156 1 • COMPUTE FOOTFREQ=F0OTLMON 157 1 • ELSE 158 1 • COMPUTE FOOTFREQ=FOOTYEAR/12 159 1 • ENO IF 160 0 DO IF (SOCCTYPE EO 2) 161 1 • COMPUTE S0CCFRE0=S0CCLMON 162 1 • ELSE 163 1 • COMPUTE S0CCFREQ=S0CCYEAR/12 164 1  END IF 165 0 DO IF (VOLLTYPE EO 2) 166 1 • COMPUTE V0LLFREQ=V01LLM0N 167 1  ELSE 168 1 • COMPUTE VOLLFREQ=VOLLYEAR/12 169 1 • END IF 170 0 DO IF (FRISTYPE EQ 2) 17 1 1 • COMPUTE FRISFREQ=FRISLMON 172 1 • ELSE Appendix D. SPSS Control Commmands 170 173 1 • COMPUTE FR1SFREQ=FRISYEAR/12 174 1 • END IF 175 0 COMPUTE YEARPA I R=GOLFFREQ*RACQFREQ+ TENNFREQ + BADMFREQ 176 0 COMPUTE YEARTEAM=BASEFREQ*ICEHFREQ+SOFTFREQ* BASKFREQ•FOOTFREQ',• 177 0 SOCCFREQ• VOLLFREQ 178 0 COMPUTE YEARFIT=JOGGFREQ+RUNNFREQ+BICYFREQ+SWIMFREQ+SK ICFREQ+ 179 0 CAL IFREQ + EXERFREQ-* WE IGFREQ 180 0 COMPUTE YEARL EIS=WALKFREQ*SKIAFREQ* SKATFREQ*ROL LFREQ•FRISFREO 181 0 COMPUTE YEARGAME=YEARPAIR+YEARTEAM 182 0 COMPUTE YEARACTI=YEARFIT+YEARLEIS 183 0 COMPUTE YEARTOT=YEARGAME*YEARACTI 184 0 COMPUTE WALKTME=WALKFREQ'WALK INT'WALKTIME/60 185 0 COMPUTE JOGG TME = JOGGFREO•JOGGINT *JOGGT I ME/60 186 0 COMPUTE RUNNTME=RUNNFREQ'RUNNINT'RUNNTIME/60 187 0 COMPUTE BICYTME=BICYFRE0'BICYINT*BICYTlME/60 188 0 COMPUTE GOLFTME=G0LFFREQ'GOLF INT'GOLFTIME/60 189 0 COMPUTE RAC0TME=RACQFREQ'RACQINT'RACQTIME/60 190 0 COMPUTE TENNTME=TENNFREO*TENNINT'TENNTIME/60 19 1 0 COMPUTE BASETME=BASEFREQ"BASE INT'BASE TIME/60 192 0 COMPUTE ICEHTME=ICEHFREO*ICEHINT* ICEHTIME/60 193 0 COMPUTE SOFTTME=S0FTFREQ*SOFT INT'SOFTTIME/60 194 0 COMPUTE SWIMTME=SWIMFREQ*SWIMINT*SWIMTIME/60 195 0 COMPUTE SKI ATME=SKIAFREO*SKI AINT*SKI ATIME/60 196 0 COMPUTE SKICTME=SKICFREQ*SKICINT*SKICTIME/60 197 0 COMPUTE SKATTME=SKATFREQ*SKAT INT*SKATTIME/60 198 0 COMPUTE ROLL TME=ROL LFREQ'ROLL INT'ROLL TIME/60 199 0 COMPUTE CALITME=CALIFREQ'CALIINT*CALITIME/60 200 0 COMPUTE EXERTME=EXERFREQ*EXERINT*EXERTIME/60 • 201 0 COMPUTE WEIGTME=WEIGFREO'WEIGINT'WE IGTIME/60 202 0 COMPUTE BADMTME=BADMFREO*BADMINT'BADMTIME/60 20 3 0 COMPUTE BASKTME=BASKFREQ*6ASKINT *FJASKT IME/60 204 0 COMPUTE FOOTTME=FOOTFREO*FOOTINT'FOOTTIME/60 205 0 COMPUTE SOCCTME=SOCCFREQ*SOCCINT'SOCCTIME/60 206 0 COMPUTE VOLLTME=VOLLFREO*VOLLINT *VOLLTIME/60 207 0 COMPUTE FRISTME=FRISFREO*FRIS INT'FRISTIME/60 208 0 COMPUTE TMEPA1R=GOLFTME*RACQTME* TENNTME*8ADMTME 209 0 COMPUTE TMETEAM=BASE TME »ICEHTME*SOFTTME•BASKTME•FOOT TME•SOCC TME• 210 0 VOLLTME 21 1 0 COMPUTE TMEF I T = JOGGTME*RUNNTME*BICYTME + SWIMTME*SK ICTME + CALI TME* 212 0 EXERTME'WEIGTME 213 0 COMPUTE TMELEIS=WALKTME*SKIATME*SKATTME+ROLLTME+FRISTME 214 0 COMPUTE TMEGAME=TMEPAIR»TMETEAM 215 0 COMPUTE TMEACTI=TMEFIT*TMELEIS 216 0 COMPUTE TMETOT=TMEGAME*TMEACTI 217 0 COMPUTE RHF=R1«R4»R5*R7 218 0 COMPUTE RSOC=R2-R3 219 0 COMPUTE RSELF=R6*R8 220 0 COMPUTE RADV=R9•R 10 221 0 DO IF (MATE 1 EO 1) 222 1 • COMPUTE MATE=0 223 1 • ELSE IF (MATE2 EO 1) 224 1 • COMPUTE MATE= 1 225 1 • ELSE 226 1 • COMPUTE MATE=2 Appendix D. SPSS Control Commmands 171 227 1 END IF 228 0 COMPUTE BAR=BAR1-»BAR2+BAR3*BAR4*BAR5+BAR6+BAR7*BAR8*BAR9 + BAR10*BAR11 + 229 0 BAR 1 2*BAR13 2 30 0 RECODE PARTICIP(3=2) 231 0 COMPUTE LIFE=LIFE1*LIFE2+LIFE3+LIFE4+LIFE5+LIFE6+LIFE7*LIFE8*LIFE9* 232 0 LIFE 10»LIFE11 233 0 COMPUTE ALC=ALCFREQ"ALCAMOUT 234 0 DO IF (SMOKING EO 1) OR (SMOKING EO 5) OR (SMOKING EQ 7) 235 1 • COMPUTE SM0KE=4 236 1 • ELSE 237 1 • COMPUTE SM0KE=5 238 t END IF 239 0 IF (SMOKSTOP EO 2) OR (SMOKSTOP EQ 4) OR (SMOKSTOP EO 6) SM0KE=2 240 0 IF (SMOKSTOP EQ 1) OR (SMOKSTOP EQ 3) OR (SMOKSTOP EQ 5) SM0KE=3 241 0 IF (SMOKETYP EO 1) SMOKE=1 242 0 RECOOE HEALTH(4=2)(5=3) 243 0 RECODE MARITAL<5=1)< 1 = 2X2=5) 244 0 MISSING VALUES WALKFREQ TO FRISFREQ(60 THRU HIGHEST) 245 0 YEARPAIR TO YEARTOT(90 THRU HIGHEST) 246 0 MATE(O) 247 0 SELECT IF (TMETOT LE 1500) 248 0 FREQUENCIES VARIABLES = DAYS ADHERENC LIMITED ACTIVSCA 249 0 RHF TO RADV MATE BAR LIFE ALC SMOKE 250 0 FITNESS PARTICIP BRADPOS BRADNEG BRADSCAL SLEEP HEALTH MARITAL 251 0 EOUCAT INCOME SKINFOLD TO SITUPS 252 0 /FORMAT ONEPAGE LIMIT(25) 253 0 /HISTOGRAM NORMAL 254 0 /STATISTICS = ALL THERE ARE 31536 BYTES OF MEMORY AVAILABLE. 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