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An environmental level analysis of economic correlates of child abuse in the Lower Mainland May, Paul J. 1990

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AN ENVIRONMENTAL LEVEL ANALYSIS OF ECONOMIC CORRELATES OF CHILD ABUSE IN THE LOWER MAINLAND by PAUL MAY B.S.W. THE UNIVERSITY OF VICTORIA, 1983 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SOCIAL WORK in THE FACULTY OF GRADUATE STUDIES SCHOOL OF SOCIAL WORK We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER 1990 (c) PAUL MAY, 1990 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 The University of British Columbia Vancouver, Canada Date DE-6 (2/88) ABSTRACT The question of the etiology of child abuse has received growing research attention since the early 60's. This attention has moved from a s t r i c t l y individual psychopathology focus to a more systemic, environmental perspective. The determination of significant correlates of chi ld abuse, in view of this dichotomy, holds very important policy and intervention implications. This is because as the importance of environmental factors r ises , so does the "depth" or systemic nature of the intervention required. The environmental model proposes that abusive behaviour is not only a function of an individual's psychological makeup. In addition, factors outside the individual are thought to be c r i t i c a l components in the abuse phenomenon. These factors are a part of the social environment of the individual and thus impinge upon a l l individuals who l ive in that environment. Research into environmental correlates of child abuse is s t i l l at an early phase of development. The works of James Garbarino, Blair and Rita Justice, and Ralph Catalano, David Dooley, et a l . have made progress in identifying possible significant systemic correlates, in tentative connective hypotheses, and in research approaches. Garbarino, and Catalano, Dooley, et a l have focused on various community-level features of economic climate. The Justices' have focused on the importance of high levels of stress in inducing abusive behaviour. However, this work has a l l pertained to the American environment. There are no studies which have started replicating their seminal work in Canada. The present study does precisely th is . This study tests for the existence of an association between selected correlates of the economy's a b i l i t y to provide jobs and the incidence of chi ld abuse. The selected correlates of the economy are the size of the labour force and the unemployment rate in the Greater Vancouver Metropolitan area, and the rate of income assistance receipt by employable persons for a subset of municipalities found within the Greater Vancouver Metropolitan area. These variables are aggregate monthly i i totals . They are correlated with a monthly incidence rate of chi ld abuse reports drawn from the same geographical area as the income assistance s ta t i s t i c s . The a b i l i t y o£ a community to provide jobs is a significant feature of a community's environment, and one which may create general stress. Thus, a significant correlation was expected. The series' were manipulated using the ARIMA method of time series analysis in order to remove regular, patterned behaviour in the series ' . The "prewhitened" series' were then regressed from a twelve month lead through to a twelve month lag interval . This resulted in 300 correlations. The findings were very conservative, with only 13 significant correlations. The interpretation of this was based on patterns of correlation, consistency across lags and between similar variables. There did not appear to be any consistency in the significant findings. However, regression of unprewhitened series' showed very significant correlations. This lead the researcher to the conclusion that the modelling process removed whatever features were producing the correlation. This suggests, due to the nature of the modelling process, that some regular or very subtle pattern occurs within both the economic series' and the chi ld abuse series ' . Further research is needed to determine the nature of this pattern, and the degree of actual correlation i t indicates, as opposed to a simple third variable explanation. i i i TABLE OF CONTENTS Abstract i i L is t Of Tables v Lis t Of Figures v i i Chapter 1: Child Abuse: The Rise And F a l l Of The Medical Model 1 Chapter 2: The Ascendency Of The Environmental Model 22 Chapter 3: A Canadian Test Of The Environmental Model.. . .47 Chapter 4: Research Design And Discussion 66 Chapter 5: Findings, Discussion, And Recommendations 88 Notes: 121 Bibliography: 125 LIST OF APPENDICES APPENDIX A Abuse s tat i s t ics data col lection tool - log sheet from Emergency Services. APPENDIX B Raw, corrected, and residual series' for abuse totals , income assistance totals , regional totals , and labour force and unemployment rate s ta t i s t i c s . APPENDIX C Autocorrelograms, ARIMA model outputs and residual diagnostic values for a l l ser ies ' . iv LIST OF TABLES TABLE I Stat ist ics Of Unmodelled Abuse Series' 93 TABLE II Stat ist ics Of Raw (Unmodelled) Income Assistance, Unemployment Rate, and Labour Force Series' 94 TABLE III Statist ics Of Modelled Abuse Series' 94 TABLE IV Stat ist ics Of Residuals For Modelled Income Assistance, Unemployment Rate, and Labour Force Series' 95 TABLE V Regression Stat ist ics For Abuse Total Series With Income Assistance Totals 97 TABLE VI Regression Stat ist ics For Abuse Total Series With Labour Force Series 98 TABLE VII Regression Stat ist ics For Abuse Total Series With Unemployment Rate Series 99 TABLE VIII Regression Stat ist ics For Region 19 Abuse Series With Region 19 Income Assistance Series 100 TABLE IX Regression Stat ist ics For Region 19 Abuse Series With Labour Force Series 101 v TABLE X Regression Stat ist ics For Region 19 Abuse Series With Unemployment Rate Series 102 TABLE XI Regression Stat ist ics For Region 13 Abuse Series With Region 13 Income Assistance Series 103 TABLE XII Regression Stat ist ics For Region 13 Abuse Series With Labour Force Series 104 TABLE XIII Regression Statist ics For Region 13 Abuse Series With Unemployment Rate Series 105 TABLE XIV Regression Stat ist ics For Region 12 Abuse Series With Region 12 Income Assistance Series 106 TABLE XV Regression Stat ist ics For Region 12 Abuse Series With Labour Force Series 107 TABLE XVI Regression Stat ist ics For Region 12 Abuse Series With Unemployment Rate Series 108 vi LIST OF FIGURES FIGURE 1 Zalba's Six Level Typology of Abusive Parents 14 FIGURE 2 Gelles' Social Psychological Model Of The Causes Of Child Abuse 17 v i i The "history" of child abuse as a recognized social issue is punctuated by several dramatic events. Apart from the outlaw of infanticide, which occurred throughout western civilization as late as the early 1800's, child protection as we know it really begins in 1874 with the famous case regarding Mary Ellen. Due to a lack of legal statutes or precedents regarding the maltreatment of children, this child was rescued from severe neglect and abuse by the Society for the Protection of Cruelty to Animals by virtue of her being a member of the animal kingdom. Hers became a "cause celebre" and prompted the creation of societies for the protection of cruelty to children. Children's rights and the need for protection of children gradually grew, including child labour laws, mandatory education, separate criminal proceedings, and many other protections and special status'. There may well have been many cases as drastic and heart-rending as Mary Ellen's in the next 80 years, however none gained a similar public notoriety. This lack of public attention, in view of the sensational initiation which child protection received, is a little surprising. However during that period, child abuse was poorly understood. Research and intervention was a disorganized undertaking, and it appears that there was considerable reluctance to recognize the state's right 1 CHILD ABUSE: THE RISE AND PALL OF THE MEDICAL MODEL to intervene in a family's home. Children were stil l largely viewed as the property of their parents and abuse of children was not recognized, as far as research is concerned, as a behaviour distinct from other forms of violence or dysfunctional behaviour. However, research and field protection work carried on. Societies for the protection of cruelty to children sprang up, intervention and prosecutions ensued. It is remarkable, therefore, that the "discovery" of child abuse is frequently attributed to Dr. C. Henry Kempe in 1962. It was in this year that Dr. Kempe published an article in the Journal of the American Medical Association entitled "The Battered Child Syndrome" (Kempe et al., 1962). This article is credited with bringing the issue of child abuse to public and professional attention, and indeed it did so. It has often been said that this article had such a notable impact because of the "exalted" profession of the author. No longer was abuse of children the concern of low status social workers. It now had the stamp of legitimacy and importance, given by the medical profession. While it was absolutely crucial that child abuse become an object of concentrated effort, from the perspective of hindsight. 2 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL the manner in which it achieved its prominence had certain drawbacks. It is often stated that Dr. Kempe's article is responsible for creating or promoting the "psychological" model of the etiology of child abuse. This model proposes that abusers of children have some psychological defect which predisposes them to abuse. In simple terms, it views child abusers as strictly responsible for the behaviour and accepts little or no influence of external factors. While this perception is hot entirely fair to Dr. Kempe1- his article was the rallying point for applying a medical model to the whole study of child abuse. This therefore engendered a perspective which viewed the abusing individual as "owning the problem" rather like a disease. Research and models of etiology focused on individual characteristics and looked for evidence of mental illness. By designating child abuse as a syndrome, Dr. Kempe drove researchers to see it as distinct, a phenomenon separate from other violent behaviour. This had the benefit of focusing the research, of giving researchers an entity to study. As Frude. points out "...the uselessness [sic..usefulness?] of the syndrome approach depends on the uniformity of the phenomenon and on the tightness in the clustering of different elements." Research 3 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL therefore concentrated on itemizing common elements in abusive episodes, particularly those elements concerning the psychological status of the participants. -The .importance of developing such a metaphor, the syndrome, was crucial in bringing the necessary attention to this problem. David Gi l 2 aptly details earlier articles which identify and discuss nonaccidental injury to children. In particular, he notes that medical professionals began publishing articles concerning nonaccidental Injury to children in the late 1940's. Elizabeth Elmer, a well known child abuse researcher and author, had drawn attention to the reluctance of society and various professionals to directly address the issue of child abuse. However none of this earlier work had-the dramatic Impact of Dr. Kempe's article. Stephen Antler has noted that the sudden priority which, medical assessment and treatment took in child abuse intervention had rather serious consequences on the contemporary practice. In fact, he intimates that the result was something of a backwards step into knee jerk protective intervention. He points out that at the time, social work intervention tended to centre on more environmental, systemic 4 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL issues. In view of current practice and theory, this was quite progressive. Therefore, while it thrust child abuse into the spotlight, Dr. Kempe's syndrome diverted attention from other etiological factors. Researchers before and after this article was published were querying environmental factors. Indeed, Dr. Kempe himself makes reference to assessing other factors such as a discrepancy between clinical findings and historical account of injury, neglect symptoms (poor hygiene, malnutrition), alcohol use, marital instability. As he states in his article "Psychiatric factors are probably of prime importance in the pathogenesis of the disorder, but our knowledge of these factors is limited. Parents who inflict abuse on their children do not necessarily have psychopathic or sociopathic personalities or come from borderline socioeconomic groups...".. (Kempe et al. 1962, p.60) However for the first several years it appears the psychological model had primacy and indeed to date it is one of the leading etiological models. While the medical model itself promoted an individualistic interpretation of child abuse, there is a further explanation for this early focus on psychopathology as the root cause of child abuse. This has to do with the definition of or accepted 5 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL evidence for child abuse. Dr. Kempe focused primary attention on radiological evidence for making the diagnosis. This pertained to evidence of both current and old fractures. As well, at that time, physicians would have been reluctant to make such a diagnosis without considerable evidence. This all , suggests that cases of bonafide child abuse would be of a rather extreme nature. Regardless of how "far" the research and understanding of child abuse has come, most would agree even now that mental illness must play a part in cases where abuse is that severe. I offer this suggestion primarily as an example of the influence which the accepted definition of child- abuse has had over research and modelling. This definition has changed since 1962 and continues to be a subject of considerable discussion. It certainly cannot be said that there is a universally agreed upon definition. This problem is frequently cited as a confounding factor when comparing data between jurisdiction- or between studies which used different definitions. The sudden research focus on child abuse following the publishing of Dr. Kempe's article was accompanied by legislative and increased service responses. Child protection was becoming, a growth industry. In an effort to consolidate the experience of each jurisdiction and as a timely attempt to assess the degree and nature of this problem on a national scale, David Gil 6 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL carried out a collection of data nationally within the United States for a period of two years (1967 and 1968). This study, reported in a book entitled 'Violence Against Children", has proven to be of immeasurable value. It considerably broadened the focus of child abuse research and propelled a host of studies in a wide range of directions. This was quite a timely consolidation of the study of child abuse because there was beginning to be dissatisfaction with the strictly psychological explanation of child abuse. As Frude points out •'The evidence for clustering has been disappointing to those who have taken the syndrome position, for it seems that injury deliberately inflicted on children by their parents is of many types, and that the personality of the parents themselves, their social background, the circumstances in which the attack takes place and the age and personality of the child involved all vary prodigiously." (Frude, p.6). Gil ties in the debate regarding the psychological model and the need for comprehensive data. He points out that to date studies had relied on samples of abusers drawn from seriously unrepresentative populations: "The findings and interpretations of medical, psychiatric, and social welfare investigators concerning physical abuse of children were 7 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL derived from observations on relatively small and unrepresentative study-samples in specialized settings such as children's hospitals, courts, psychiatric clinics, and children's protective services." (Gil 1970, p.34 - 35). He uses this fact not only to dispute the validity of findings to date, but to justify and promote his national survey. Indeed, with the advent of reporting laws and enhanced vigilance by professionals and the public in general, the amount and quality of data increased enormously after 1962. Some essential features of Gil's study were his discussion and conclusions regarding the definition of child abuse, his estimation of the importance of a cultural value condoning physical punishment of children, and finally his general findings in the data. Gil emphasized the importance of a clear, comprehensive, widely accepted definition of child abuse. He eschewed the contemporary approach which defined abuse in terms of its observable effects- the injuries sustained. This, approach suffered from both types of errors- false positives, in the form of accidental injuries wrongly presumed to be the result of abuse, and low "power" to identify abuse where, by chance, no injury occurred. 8 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL Rather, Gil identified the motivation or intent of the abuser as the crucial feature in diagnosing child abuse. As he states, "twe must identify].elements of intentionality, which, by definition, constitute a sine qua non of child abuse..." (Gil 1970, p.6). He offers the following definition, and refers to it throughout the book: "Physical abuse of children is the intentional, nonaccidental use of physical force, or intentional, nonaccidental acts of omission, on the part of a parent or other caretaker interacting with a child in his care, aimed at hurting, injuring, or destroying that child." (Gil 1970, p.7) Gil recognizes that this definition poses a number of problems for the researcher having to operationalize his concepts (he is hasty to note, however, that the difficulty is strictly operational and not conceptual, which is to say the concept is accurate regardless of the difficulty in measuring it). His definition has essentially stood up over time and in practical terms fairly accurately describes the definition currently used by field workers. It certainly broadened the range of behaviour which may be considered abusive. It is perhaps a sad note on progress in this field that as recently as 1984 problems in comparing data continued due to the 9 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL differences in definitions used by each researcher or data collection agent (Smith 1984, p.338). Gil expanded the contemporary definition to such an extent in order to overcome what he felt was a cultural bias towards accepting violence towards children. One very central point which Gil made was that child abuse flourishes in a culture which condones the use of physical punishment. He very cogently argues that even if we are to accept the psychodynamic explanation of abuse "the content of neurotic and psychotic fantasies and symptoms in any given society, tend to be influenced by the sociocultural context in which they develop.[and) ...what a society considers sick and deviant in human behavior is not necessarily qualitatively different from what it considers healthy and normal. The difference may be quantitative only." (Gil 1970, p.12). This certainly brings the concern to the front door of every parent, that abuse is simply a matter of degree. Gil's suggestion of a cultural acceptance of violence against children is clearly true in Canada. Section 46 of the Canadian Criminal Code permits the use of physical force "by way of correction" provided such force is "reasonable". 10 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL There is little doubt that Gil's conceptualization opened the door for an entirely new outlook on child abuse. In a very eloquent way, he sidestepped the confrontation between psychological and environmental models of abuse and nested the one within the other. In a manner as convincingly as Dr. Kempe, Gil intensified the study of child abuse by offering a compelling new description of the problem. His data was not so much directed at developing a model as proposing some concrete groundwork for a more systematic study of abuse and offering grist for the research mill. Gil's data covered a wide range of demographic and statistical ground. One of his most significant findings was that "...physical abuse of children is not a uniform phenomenon with one set of causal factors, but a multi-dimensional phenomenon." (Gil 1970, p.125) and "..the phenomenon, while uniform in symptoms, is nevertheless likely to be diverse in causation." (Gil 1970, p.126). This finding undoubtedly spurred on research into a wide range of areas, legitimated a broader examination of the child abuse phenomenon. Another significant finding, insofar as this study is concerned is his "discovery" of the influence (in statistical terms) of low socioeconomic status and the prevalence of life 11 CHILD ABUSE: THE RISE AND PALL OF THE MEDICAL MODEL stress in abusive incidents. He found that a significant number of families where abuse occurred had low incomes, and a disproportionate number of families were or had been on financial assistance. In his own words: "The present series of studies revealed also a significant association between growing up in poverty and being subjected to acts of individual violence and abuse." (Gil 1970, p.15). This - finding helped signal the official move away from a more strictly psychological perspective. Gil is often cited in the literature with having propounded the proposition which suggests that there is a "subculture of violence" , found within lower socioeconomic class. He contends that "...families of low socioeconomic and educational status tend to use corporal punishment to a far greater extent than do middle-class families." (Gil 1970 , p. 134). He also suggests that "It has also been observed that the uninhibited acting out of aggressive impulses is more likely to occur in poor and working-class families than in middle-class families." (Gil 1970, p.127). In a substudy within the national survey, Gil requested that reporting parties (e.g. investigating social worker) l ist what they considered important factors in each abusive event. In flfty-^nine percent of all- incidents, "mounting stress on 12 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL perpetrator due to life events" was Indicated. Gil includes poverty in this category and sums his findings up nicely when he states "...environmental stress and strain are considerably more serious for persons living in poverty than for those enjoying affluence." (Gil 1970, p.144). These words have echoed throughout the research ever since. Gil's data may not have accurately described the status of child abuse in the United States at the time, and almost certainly did not measure the extent of abuse as he defines it. This is because reporting laws had only just been instituted in the last 5 years and the prevailing definition of abuse, that which propelled reporting, required far more serious incidents. However Gil's review and distillation of the contemporary literature, his insightful conceptualizations, and the extensive nature of the study were landmarks in the study of child abuse and inspired a new, energetic direction. There is a wealth of literature and scholarship after Gil, much of which rests on Gil's foundation. Remarkably, however, despite Gil's rigourous treatment of the field, little headway has been made of an empirical nature since that time. As well, until recently there has been no study of a similarly extensive 13 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL nature. Researchers relied heavily on Gil's data and his theoretical discussions. As well, to that point in time, there had been few models of child abuse dynamics. Naturally the prevalent perspective, the medical or pathopsychological model, essentially represented a simple, "one-trick pony'' explanation. Models to that point were simplistic and revolved around use of this explanation as the primary focus. Zalba's six level typology (see Fig. 1) is a fair example of this. Fig.l Classification of Abusive Parents Parent's Ability to Control Abuse Locus of Problem Not Able to Control Able to Control Personality 1. Psychotic parent. System 2. Pervasive angry and abusive parent. 3. Depressive, passive-aggressive parent. 4.Cold, compulsive Family System 5. Impulsive but generally adequate parent with marital conflict. Person-Environment or Family-Environment System 6. Parent with identity/role crisis. 14 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL This typology, while it hints at some sense of the importance of environmental factors, st i l l clearly adheres to the medical model and places responsibility squarely, almost solely, on the abusive parent. Even the section which specifically addresses environmental features focuses on a very individual interpretation of that relationship. The next major breakthrough, and an example of this reliance on Gil's study, was that made by R. Gelles. In 1973 Richard J. Gelles published an article in the American Journal of Orthopsychiatry. This article was a reworking of a presentation given by Gelles to the American Sociological Association in August 1972. In the article, entitled "Child Abuse As Psychopathology: A Sociological Critique and Reformulation?', Gelles goes beyond the reconciliatory nature of Gil's proposals by directly refuting the psychopathological model. This article clearly was of significance, judging from the extent to which it is cited in the subsequent literature. This significance derives from two fundamental features in the article. Not only did Gelles persuasively (if not empirically) dispute the psychopathological model; he proposed a model in its place which included much of Gil's findings and suggestions regarding causal factors. Of Gelles' critique of the 15 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL psychopathological model I will speak in a later chapter. However, his proposed model is of significance to the current discussion. In his article, Gelles proposed a model which addressed the multi-causal nature of child abuse as suggested by Gil. This feature represents the first recognized model of the new, "environmental" outlook on child abuse. It begins the conceptual organization of the multitude of factors thought to play a part in abuse. The model attempts to order these factors in some etiological picture or hierarchy. Gelles' model is clearly more environmentally based than Zalba's model. On the other hand, it is clearly more complex and comprehensive as well. It may indeed describe the nature of the child abuse phenomenon but such a complete explanation has some drawbacks. When a model requires such an extensive series of contingencies and factors, it approaches that evil of which Gelles himself spoke: "This type of analysis does not distinguish the behavior in question from the explanation."3. (Gelles 1973, p.614). In other words, a model which includes all possible factors gets very close to a simple description of the behaviour as opposed narrowing the options so as to offer predictive value. 16 Fig. 2 A SOCIAL PSYCHOLOGICAL MODEL OF THE CAUSES OF CHILD ABUSE SOCIAL EIPBRIBBCB OF PASBIT Age Sex S o c i o e c o n o i i c s t a t u s CLASS & COHKUIITI Values i n o r i s regarding v i o l e n c e 'Subculture of v i o l e n c e * SOCIALIZATION EXPE&IBMCE Abase Bole Model of v i o l e n c e Aggression SITUATIONAL STRESS A. R e l a t i o n s between parents 1. I n t e r - i a r r i a g e 2. M a r i t a l d i s p u t e s B. S t r u c t u r a l S t r e s s 1. Excess c h i l d r e n 2. Unemployment 3. S o c i a l i s o l a t i o n L Threats to p a r e n t a l a u t h o r i t y , v a l u e s , s e l f - e s t e e i C. C h i l d Produced S t r e s s 1. Unwanted c h i l d • P r o b l e i c h i l d * a. c o l i c k y b. i n c o n t i n e n t c. d i s c i p l i n e problea d. i l l e. p h y s i c a l l y d e f o n e d f . retarded 2. IMMEDIATE PRECIPITATING SITUATIONS C h i l d l i s -behaves Argoient E t c . PSICBOPATBIC STATE P e r s o n a l i t y t r a i t s Character t r a i t s Poor c o n t r o l N e u r o l o g i c a l d i s o r d e r s CBILO ABUSE 1. S i n g l e p h y s i c a l . a s s a u l t 2. Repeated a s s a u l t s 3. •Psycho-l o g i c a l v i o l e n c e F r o i 8.J.Gelles (1)73) 17 CHILD ABUSE: THE RISE AND FALL OF THE MEDICAL MODEL The other drawback is that considerable empirical research is necessary to verify the importance of each category, indeed of each subcategory. Such research has been proceeding, albeit slowly. This model continues to encompass the current beliefs regarding abuse. Research and theory have explored various aspects of the domains represented. Models (perhaps better described as sub-models) have been propounded which address or acknowledge only portions of Gelles' proposed factors. To date, none has compiled a more or even equally complete description of this phenomenon. This is both a compliment to Gelles' thoroughness and a comment on the state of research into child abuse. The dominant theme in child abuse research continues to be the ascendancy of environmental influence. I will detail the more current research in the following chapter. 18 THE ASCENDENCY OP THE ENVIRONMENTAL MODEL This chapter provides a more specific theoretical framework upon which to hang the current study. As will be seen, the work of Rita and Blair Justice, of James Garbarino, and of Dooley, Catalano, et al. are a l l central to the hypothesis being tested herein. As we saw in the last chapter, Dr. Kempe brought child abuse to the attention of the United States if not the world. Along with the attention, he brought a model which placed almost entire responsibility for abuse on the abuser and ignored or denied the influence of external factors. However, the individual psychology model 4 was viewed as inadequate by a number of researchers and since the mid-sixties, a new model, the environmental model, has gained prominence. We have reviewed some of the dominant themes which developed in child abuse understanding and research since the early 1960's. The two main theoretical players were, as indicated above, the individual psychology model and the 19 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL environmental model. This is an important debate because of the far-ranging implications which each model entails. If one subscribes to the "disease" model, as Stephen Antler calls it, intervention may stop at individual therapy along with possible removal of the child for that period of time. The investigation and intervention is likely to be more authoritarian. Stephen Antler alludes to this when he writes "[the disease model contributes] to a general public sentiment that child abuse is caused by essentially vicious and depraved parents who should not be permitted to raise children." (Antler 1981, p.46). On the other hand, if one holds to the environmental model, an examination of the family's social context would be advocated, and changes of a broader, more systemic nature may be prescribed. Naturally, this option involves much more political action and denotes a philosophy along the lines of C. Wright Mills' famous "private troubles are public issues" proposition. Stephen Antler (1975, p.50) succinctly states the case: "Solving the problem of child abuse and neglect requires not simply reporting and treating physical emergencies, but a fundamental realignment of public priorities, one that accepts the necessity of attacking the social, economic, and cultural 20 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL conditions associated with abuse and neglect. These conditions - among them poverty, unemployment, and inadequate housing -are disproportionately represented among the ranks of abusing parents." Some believe that the depth of change which the environmental model would advocate and the simplicity of the disease model are strong reasons for the tenacity of the disease model. In spite of developments and research regarding the environmental model there continues to be vigorous debate over the two dominant models. Susan Smith notes that the individual psychology model currently remains as one of three dominant research themes. She writes: "These categories tof current research activity! include sociological/environmental factors in abuse; the role of the child in abuse; and psychological/personality factors of the abusive parent. Individual studies have tended to address only one of these factors and to accentuate the significance of this single factor in explaining the occurrence of abuse. This single factor research in child abuse is approaching the proportions of the historical nature-nurture controversy." (Smith, 1984, p.338). 21 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL As I pointed out in chapter 1, the disease model was fairly adequate for its time since the definition of abuse used at that time allowed only the most serious cases to be diagnosed as battered child syndrome. However, when David Gil expanded the definition, it included behaviour of a less severe nature and thus psychopatholgy was not necessarily a factor. Gil offered the cultural context and the sanctioning of physical discipline as a general, systemic explanation. This was the beginnings of the move away from the disease model. Richard Gelles1 1973 article contained several criticisms of the psychopatholgy model. Among them, he pointed out that there is no agreement among the professionals as to which personality characteristics were concomitant with abuse: "Of nineteen traits listed by the authors, there was agreement by two or more authors on only four traits. Each remaining trait was mentioned by only a single author. Thus, there is little agreement, as to the make-up of the psychopathy."• (Gelles 1973, p.614). Clearly the model, at that stage of development, had little predictive value and appears to have relied on very subjective measures. Another criticism Gelles had of this model was that the evidence seemed to be rather tautological. He suggested that this was because many of the studies had been ex post facto. 22 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL As he pointed out, "For instance, authors state that abusive parents have poor emotional control, or that they react with poorly controlled aggression. Analyzed after the fact, it seems obvious that a parent who beats his child almost to the point of death has poor emotional control and reacts with uncontrolled aggression. This type of analysis does not distinguish the behavior in question from the explanation." (Gelles 197 3, p.614). In other words, as Parke and Collmer (1975, p.520) note, "Re-labelling is not a substitute for adequate explanation.". Gelles also found the contemporary discussions regarding child abuse using the disease model were "inconsistent and contradictory". To quote Gelles (1975, pp.613 - 614): "Some authors contradict themselves by first stating that the abusing parent is a psychopath and then stating that the child abuser is no different from the rest of society. Steele and Pollack state that their first patient was a 'gold mine of psychopathology/ and then later state that their patients were a 'random cross-section of the general .population' who 'would not seem much different than a group of people picked by stopping the first several dozen people one would meet on a downtown street.*". This last point alludes to a major criticism levelled at the individual psychology model by many researchers. Since the sole focus of the individual psychology model is on personality traits 23 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL of the abusers, this model eschews the importance of external factors. Gelles (1975, p.615) himself points this out directly: "It should be noted that authors advancing the psychopathological model make a special effort to point out that social variables do not enter into the causal scheme of child abuse. Steele and Pollack, for instance, state that social, economic, and demographic factors are irrelevant (emphasis mine) to the actual act of child beating. Other researchers also argue that their cases of child abuse make up a cross-section of socioeconomic status, ethnicity, age, and education." This debate has been the central battleground between the • individual psychology model and the environmental model. Parton (1985, p.153) adequately sums up the argument used by those promoting the individual psychology model: "While a l l available s tat i s t ics (emphasis mine) lead to the conclusion that the lower socio-economic classes are disproportionately represented among cases known to the public agencies, it is usually suggested that the social processes whereby cases are identified is biased against the poor, for 'poor people are more available to public scrutiny, and likely to be known to social agencies and law enforcement agencies, whose workers, have had the opportunity to enter their households'." Thus, it is admitted by disease model adherents that a certain "class'' of person is statistically- over-represented In the abusive population. However this is not accepted as being 24 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL an empirical fact or as indicating the importance of factors beyond the individual psychology of those particular persons. Rather, they view this as being an artifact, a sampling effect. Pelton rejects this assumption and offers three arguments against it. Firstly he notes that increased public awareness regarding abuse has not resulted in a concomitant increase in reports of abuse from middle and upper class families. Thus, the proportions of abuse cases from each socioeconomic class have remained the same over time. One would expect that as awareness grows, a greater percentage of cases would be reported from the previously "untapped", unreported abuse from higher classes. Pelton (1978, p.27) cogently points out that there is a logical fallacy in the sampling bias argument: "While the premises are valid - poor people are more subject to public scrutiny -the conclusions do not follow logically from them. We have no grounds for proclaiming that if middle-class and upper-class households were more open to public scrutiny, we would find proportionately as many abuse and neglect cases among them. Undiscovered evidence is no evidence at all." 25 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL Pelton also cites statistics which show that incidence is correlated with degrees of poverty. In other words, abuse shows an intra-class correlation with poverty: there is more abuse found in the poorer families within the lower class. In Parton's words "...the highest incidence of the problem occurs in families experiencing the most extreme poverty." (Parton 1985, p.153). Lastly, Pelton found that severity of abuse was similarly correlated within the lower class. He cites several, studies which primarily concern child deaths. Socioeconomic class was highly correlated (negatively) with severity of trauma and he quotes from one which found "...with few exceptions, most came from 'homes of extremely low socioeconomic level,' and none came from upper-middle or upper-class families." (Pelton 1978, p.29). Pelton quotes a finding from Gil's national survey which indicates "that injuries were more likely to be fatal or serious among families whose annual- income was below $3,500." (Pelton 1978, p.2 8) Gil's study reported an over-representation of lower class parents in the cases of reported abuse. Pelton sums up Gil's 26 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL findings: "...Gil (1970) found that nearly 60% of the families involved in the abuse incidents had been on welfare during or before the study year of 1967, and that 37.2% of the abusive families had been receiving public assistance at the time of the incident. Furthermore, 48.8% of the reported families had incomes below $5,000 in 1967, compared with 25.3% of all American families who had such low incomes....On the other side of the coin, only 3% of the families (reported for abuse] had incomes of $10,000 or more (compared with 34.4% of all American families for the same year)..." (Pelton 1978, pp.24 - 25). Susan Smith reported a study by Kadushin and Martin (1981) which found that of an 830 case sample of abuse cases over a two year period, 61% were from the lowest social class (Smith 1984, p.339). Indeed, Smith goes so far as to state unequivocally "The assumption that child abuse is broadly distributed throughout society and unrelated to socioeconomic class is a myth." (Smith 1984, p.338). Studies from the early seventies, into the present report finding a negative correlation between income and rate of violence. In 1976, Garbarino found a correlation of -.27 (p<.05) between abuse and "Median income of all families (used in study]" and a correlation of -.40 (p<.01) between abuse and "Median income of families [used in study] with female head" (Garbarino 1976, p.181). 27 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL A number of other indicators of lower class standing have also been found to be over-represented in child abusers. Occupational status and years of education have been found to be correlated with abuse to some degree. Another commonly reported characteristic is employment status. This factor has received a fair amount of attention in the research. Gil reported that "Only 52.5% of the fathers of sample cohort children were employed throughout the year." and that "...11.8 percent of the fathers were actually unemployed, a rate about three times as high as the nationwide unemployment, rate." (Gil 1970, p.lll). Gil also found that "...nearly 4 in 10 families were on public assistance." (Gil 1970, p.112). Being on public assistance almost certainly means both unemployment and very low income. Ditson and Shay (1984) found that 63% of a sample of 184 substantiated abuse cases (gathered over a period of one year) were on public assistance. One report found that "Cases of substantiated abuse by a male were almost six times as l ike ly [emphasis mine] to be reported for unemployment as in unsubstantiated cases." (Hawkins and Duncan 1985, p.408). In a simple time series analysis of physical abuse cases correlated with unemployment statistics, Krugman et al (1986) found a correlation of r=.81 (r2=.66, p<.001) between the two series. 28 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL Finally, in 1988, a study compared rates of maltreatment (where there was at least "reason to believe" maltreatment had occurred) with a number of demographic characteristics for a number of neighbourhoods in El Paso, Texas. The researchers found that "An overwhelming proportion (87.4%) of alleged perpetrators are in families with yearly incomes under $18,000." and that "Maltreatment by males, however, is particularly related to the general socioeconomic stress that is attendant to high unemployment." (Young and Gately 1988, p.251). The response of the disease model to the foregoing research would be that none of the above rules out strictly individual factors. It may be that the individual psychological factors which promote child-abusive behaviour also promote or result in membership in the lower class (i.e. inability to maintain employment, transience, poor money management). While none of the research has effectively countered this argument, there is strong face validity to the argument that given the clearly frequent correlation between economic stress and lower class standing and child abuse, there is also something about the social context, outside the individual, which promotes abusive behaviour. The environmental model does not entirely discount the importance of individual factors. However, it tries to 29 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL develop and test hypotheses regarding likely external factors which also account for some of the correlation. Putting aside the "kind of person" proposition, what other hypotheses or mechanisms can account for the frequent association between poverty and child abuse. Put another way, if we reject the individual psychology model as totally explanatory, we must assume that the position of being poor carries with it, outside the individual, some characteristics or forces which are associated in some way with child-abusive behaviour. Most researchers have identified stress as one intermediary. An excellent example of the use to which stress as an explanatory factor is put is the research of Blair and Rita Justice. Their work is premised on the seminal stress research of Hans Selye and more recent works by Holmes and Rahe. The Justices denounced the primary importance of economic stress and postulated the importance of "life stress" in general. Essentially the theory states that stress arises from "readjustment" challenges from the environment. Such things as marriage, a move, changing jobs, pregnancy and birth, death in the family, regardless of the value (good or bad) they may hold, require new or enhanced responses from individuals. Enough of 30 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL these changes in a short period of time results in or verges on an inability to cope, to keep up with the changes, to generate, enough effective responses (what Selye calls the "exhaustion phase). Justice and Justice matched a sample of 35 abusing families with non-abusing families (matched- -for age, education, and income), and assessed each for life stress using the "social readjustment rating scale" of Holmes and Rahe. They found that a significant percentage (JP = 25.69, p < .001) of the abusing families had greater stress quotients than non-abusing families. It is their theory that the number and timing of crises is the primary factor which predisposes parents to abuse. As they state "The number and magnitude of the changes they [the abusing parents] had to adjust to constituted a 'life crisis', which preceded the onset of abuse." (Justice and Justice 1976, p.26). The psychological theorization regarding stress and its impact on health and' quality of life in general is fairly well established9.. Therefore Justice and Justice's work is premised on solid ground. However, as regards child abuse, they refute the importance of economic and environmental factors (in particular those environmental factors which relate to 31 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL socioeconomic class). They sum their argument up neatly: "...child abuse also occurs among the affluent. If economic stress were the overriding factor, no abuse would occur among middle- and upper-income families, and most, if not all, poor people would abuse their children. This is clearly not the case." (Justice and Justice 1796, p.26). These are commonly posed arguments and can generally be refuted by admitting that abuse does occur at all socioeconomic levels but not equivalent to their representation in the population as a whole...abuse is sti l l found to be over-represented in the lower class. In addition, Richard Barth, in a critique of several models correlating stress with child abuse, notes that "Further questions are raised by findings that the life-event scaling technique does not explain nonabusive parents with significant life events. In a prospective study of new mothers6, life change scores for the adequate child caring group were lower than scores for the inadequate group. Fewer than 25 percent of the mothers with high levels of life change, however, appeared in the inadequate care group." (Barth and- Blythe 1983, p.481). In other words, increased life stress does not always result in child abuse, there is not a direct, clear relationship. 32 THE ASCENDENCY OP THE ENVIRONMENTAL MODEL As well, while middle- and upper-income families do not experience direct economic stress to the degree that lower income families do, some have suggested that anticipated economic stress may affect all within the population. Steinberg, Catalano, and Dooley (1981), studying the correlation between unemployment rate and child abuse rate, hypothesized that not only the experience of unemployment but also the anticipation of possible unemployment (when and because rates are high) induces stress which increases the likelihood of child-abusive behaviour. It could be argued that while to date the middle- and upper-class appears to be under-represented in child abuse statistics overall, there have been no studies which have looked at their representation over time. Child abuse statistics usually come in time aggregates (e.g. monthly or quarterly incidence rates). Overall their representation may be low but it is possible that their representation increases and decreases for some duration within the aggregation period. The nature of the statistics and the type of study to date would, if this were the case, be unable to detect and track forces which, drive or are associated with such fluctuations. The other side of the environmental coin may be represented by the research of James Garbarino and his 33 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL "ecological" approach. Garbarino strongly endorses the premise that poverty or low socioeconomic status is associated with child abuse. He also supports the importance of stress as the mediating factor. However he takes a strictly systemic approach and proposes that 'low socioeconomic class" is a position within society which carries with it, independent of the individual  occupying that position, certain characteristics. Barth and Blythe (1983, p.482) capture the essence very well: "...diminished social or ecological resources accompany poverty and increase child maltreatment among the poor." Garbarino further asserts that society does little to recognize or ameliorate the situation. In the words of Garbarino (1976, pp. 178 - 179): "...child abuse occurs as a function of the degree to which the human ecology enhances or undermines parenting. Where the total human ecology provides adequate support, child abuse is minimized; where support is inadequate and stress great, the ^personality" and "cultural" factors cited by Gil are manifested in child abuse." Garbarino's theorization is not , so much that low socioeconomic status or economic stress in general causes child abuse, but that it does nothing to ameliorate the living conditions and stresses on parents and is thus associated with higher incidence of child abuse. His ecological model places the 34 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL responsibility squarely in the hands of the social context to provide at least a minimum of supports for parenting. For the most part, the contextual factors which most promote abusive behaviour are concentrated in the position of "lower class" because they are economic factors and because this group experiences economic stress more continuously. As he states: "...the ecological model- suggests that attention be focused on the degree to which the immediate setting nurtures the parent-child interaction....the degree to which socioeconomic forces support or conspire against the family as a setting for parent-child relationships is hypothesized to be a critical factor in the etiology of child abuse/maltreatment." (Garbarino 1976, p.179). The conclusion one draws from this proposition is that when certain characteristics are extant in a social context, families coming into contact with that context will be at greater risk of child abuse. One of the prime contextual factors which is associated with child abuse is economic stress. One question which flows from this is "how does one define context". One may hastily assume that context in this discussion means socioeconomic class, however it may also refer to a community. Indeed, Garbarino used as his unit of analysis the "neighbourhood". In his initial study in 1976, he correlated 35 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL the incidence of child abuse by county in New York State with several demographic characteristics of each county. What he was looking for was a correlation between high child abuse rates and the presence of indicators of "social impoverishment". In particular, he used five variables - transience, economic development, educational development, rural - urban split, and socioeconomic situation of mothers. He found a significant correlation -of R = .6. He went on to note that "...it is the factors in the human ecology most directly reflecting the socioeconomic support system for mothers that.account for the bulk of the variance in rates of child abuse." (Garbarino 1976, p.181). In a separate multiple regression analysis of economic factors alone, he found an R of .40 which thus accounts for 16% of the variance found in the child maltreatment rates between counties. Garbarino's model may be summed up as follows: in general, various environmental factors are associated with all kinds of behaviour but the environmental factor which seems most associated with child-abusive behaviour is economic stress. He then offers the following hypothesis for this connection: insofar as the social and support structure or environment of a neighbourhood does not support and enhance parenting it becomes more likely that abuse will be the outlet of choice for those 36 THE ASCENDENCY OP THE ENVIRONMENTAL MODEL living in those "impoverished" neighbourhoods. Neighbourhoods which are characterized by poor socioeconomic opportunities seem to be those in which supports are least in evidence. This responds to the concerns posed by Justice and Justice regarding the influence of socioeconomic status. It suggests that if upper- and middle-class families resided in a high-risk neighbourhood or otherwise were exposed to economic stress, they too would be at greater risk of abusing their children. This highlights the underlying hypothesis of the environmental model, that extant social structures, as reflected by such things as high unemployment, low median family income (which are manifestations of the social structure) impinge on a l l members of society living within the jurisdiction where these conditions exist. This takes the responsibility away from the individual and places it in the hands of society. One criticism of Garbarino's research (or any that so far has addressed the ecological perspective) may be the lack of complementary research and data. Without examining the relationship over time and/or complementing it with individual level data, the distinct possibility exists of a third variable explaining the variation in the indicators without any true influential relationship. For instance, a study could be done 37 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL tracking individuals who move into a neighbourhood which is statistically high in "neighbourhood impoverishment" indicators. The rate of abuse in these families would have to be checked before and after to ascertain the extent of the effect (if any). Naturally, such a study sounds fraught with ethical and some logistical dilemmas, which may explain why there are no studies of this nature. Indeed, the nature of the data available and the strictures of the research method limits what can and should be done. In spite of these qualifications, there continues to be a need for complementary studies. Another group of researchers who have approached this question somewhat more practically or "operationally" is the team of Dooley, Catalano, et al. They are certainly among the foremost researchers of this topic in the field today. Dooley and Catalano have been publishing their studies on the connection between the economy and various aspects of mental health and behaviour since the late 70's. Theirs is a synthesis of Justice & Justice's life stress model and Garbarino's ecological model. Apart from empirical research, they present thoughtful hypotheses and discussion regarding possible ways in which economic forces are translated into economic stresses which impact members of society. In addition, many of their studies have used individual level survey data, which thus can 38 THE ASCENDENCY OP THE ENVIRONMENTAL MODEL come to stronger conclusions regarding the influence of economic factors on behaviour. In contrast to Garbarino, Dooley, Catalano, et al. (as well as the bulk of researchers of this topic) believe that employment is the key indicator of economic trends and stress which is correlated with abuse. Employment in this case can mean- both an individual's employment status and history and the relative ability of the economy to provide jobs for the population as a whole. The form used depends upon the nature of the method of testing, of the data used. It should be noted that their research is not primarily directed towards the phenomenon of child abuse. While they have studied the link between child abuse and economic trends, they usually have a more general focus involving employment patterns and use of mental health services or self-reported surveys concerning individual subjective experience. In fact, they are following a growing tradition of researchers who study the effect of the economy on behaviour and mental and physical health (again, with child abuse not being one of the social indicators studied). There is a slowly growing body of literature to draw upon for general principles and findings regarding the relationship between economic fluctuations and various social problems (see Brenner 1973, Adams 1981). One common theme which links this research with the earlier 39 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL discussion is the recurring proposition that stress is the influential factor in translating the economic environment into behaviour. From the literature, and in particular from Dooley, Catalano, et al., there are several hypotheses which seek to explain the relationship between economic conditions and behaviour (both in terms of what are the functional indicators of economic stress and why they are functional). For the most part, past researchers as well as Dooley, Catalano, et al. have identified employment characteristics as strong candidates as measures of economic stress to be used for correlation with numerous social ills. Dooley, Catalano, and Brownell state that theorists are divided into two camps on why economic stress should be correlated with social problems. One camp supports the "uncovering" explanation while the other advocates the "provocation" argument. In the words of Dooley, Catalano, and Brownell (1986, p.103) the uncovering hypothesis proposes that "aggregate use of mental health facilities, is correlated with economic indicators because shifts in the economy affect the decision to seek professional help for the chronically or marginally disordered." In other words, economic stress does not 40 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL bring on or increase the incidence of mental health or life stress but rather it encourages the use of mental health facilities or help seeking by those who otherwise would have needed the facilities anyway but who, in times of economic expansion (and thus lack of economic stress), would not have sought help. If this proposition were applied to child abuse, it would suggest one of two things (or a combination thereof): that the level of abuse does not change over time (in spite of economic trends) but rather that reporting goes up at times of economic contraction or, that it is the same families whose abusive behaviour is fluctuating with economic conditions. This second alternative is suggested by the finding that "Time series analysis of admissions to mental health facilities showed that readmissions rather than new admissions were correlated with unemployment rates." (Dooley, Catalano, and Brownell 1986, p.114). The other hypothesis, the provocation argument, is the natural other side of the coin: economic trends, particularly downturns, dp, create ,induce, or at least increase the risk of instability in individuals. Dooley, Catalano, and Brownell note that if this hypothesis is true, there are three possible modes of action or ways in which the economy is related to individual behaviour. 41 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL The first is the obvious proposition that in times of economic hardship, many people lose their jobs, have to relocate, take pay cuts, work harder to avoid being fired, and so on. In this case, there are several reasons to anticipate an increase in child abuse. For one thing, this would directly increase their level of stress (due to new financial constraints, loss of status, loss of significant work relationships, worrying). As well, a previously working parent is now spending considerably more time with their child which increases the opportunity for conflict. This proposition would suggest that only those directly and immediately affected by job threat or stress are at risk of mental health problems. The second alternative they call the "interactive" explanation. Using this framework, they suggest it may be that economic conditions exacerbate (or at least do not ameliorate) stress which arises out of any of the numerous situations which induce stress, whether or not they are financial or job related. They report findings that "help-seeking for mental health problems was higher for unemployed persons who lived in areas of low unemployment than for those in areas of high unemployment...[suggesting]...an individual who is experiencing undesirable economic events in an area or time of low unemployment may attribute his or her problems to personal 42 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL inadequacies; thereby the likelihood of reporting mental health problems is increased" (Dooley, Catalano, and Brownell 1987, p.104). As they point out, this hypothesis requires that individuals be aware of the economic climate for it to have this sort of impact. The third hypothesis is the "anticipation'1 alternative. In their own words, "It is possible that economic instability disrupts the physical and social environments of communities, which makes it more difficult for individuals who are experiencing stressful life events to adapt successfully, whether or not the events are financial or job related." (Dooley, Catalano, and Brownell 1987, p.104). The type of disruption is widely variable and includes such things as reduced funding for daycare centres or recreational centres and activities, reduced transportation services, closing of usual secondary support services (e.g. laundromats, food stores, department stores), and a general dwindling of industrial and social community base. As they point out, this form of influence does not require that individuals in the community be aware of the economy's status. Such a mechanism would also support the ecological proposition that all individuals within the community experiencing this economic stress are affected. Simply put, economic stress is a community characteristic. This is very similar to Garbarino's propositions 43 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL and is a plausible explanation for the apparent association between economic stress and child abuse. Steinberg, Catalano, and Dooley also offer a fourth alternative, something of a synthesis of the last two propositions, in their article on the relationship between economic trends and child-abusive behaviour. They propose a-working hypothesis that the anticipation of possible job loss may induce stress in most or all individuals in a community, not just those who have lost their jobs. Essentially, an unstable economic environment creates anxiety over one's own tenure. As they state, "Economic change supposedly reduces the predictability of the social and physical environments and can lead individuals to anticipate difficulties in coping." (Dooley, Catalano, and Serxner 1987, p.109). Of course, this hypothesis requires that individuals be aware of the economic climate in order for it to Influence their stress level. In fact, they reported significant levels of correlation between child abuse incidence and the size of the work force*7 in the two communities they studied. Change in the size of the work force explained 5% of the variation in child abuse rates (at the 5% confidence level) although no relationship was found between change in unemployment rate and child abuse rate. This study used 44 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL aggregate data and thus could not be used to posit a causal hypothesis on individual experience. In another study they entitle this hypothesis the "contagion" model: "A second form of contagion assumes social comparison and other cognitive processes rather than direct involvement with persons who have been adversely affected by the economy may affect one's risk of experiencing other undesirable events. Plausible arguments could be made that this information will increase or decrease the risk. Awareness of an economic threat to the community may heighten anxiety and increase nonadaptive coping behaviors, such as use of alcohol, that affect the risk of experiencing undesirable stressors. People may, on the other hand, act more cautiously when concerned about economic security." (Catalano, Dooley, and Rook 1987, pp.634 - 636). Research reported in their paper was not, however, able to find a significant relationship to support this contagion theory. Indeed, their own research has been unable to find significant correlations to support the interaction and anticipation hypotheses (see Dooley, Catalano, and Brownell 1986). This left the uncovering and the direct provocation explanations as the more likely hypotheses. Of course, failing to disprove the null 45 THE ASCENDENCY OF THE ENVIRONMENTAL MODEL hypothesis does not prove the null hypothesis. Thus the anticipation and Interactive hypotheses cannot be thought of as discounted. In fact, they note that the communities tested experienced "modest economic swings". They call for the need to test the hypothesis in communities experiencing more dramatic economic downturns. They also note that "the interaction hypothesis should be replicated in longitudinal studies in higher unemployment communities." (Dooley, Catalano, and Brownell 1986, p.114). This indeed may be the case with the contagion hypothesis as well. While the above theorizations do not all speak directly or solely to the child abuse question, the connection is clear. The hypothesis regarding child abuse is that environmental factors Induce stress which in turn results in child-abusive behaviour. We have also found there is reason to suspect that economic conditions of a community impact the residents of that community either directly or through some intermediate mechanism. Dooley and Catalano (et al) then propose several possible the means of influence. 46 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL The preceding chapters may be summed up in the following way. There is an over-representation of low socioeconomic class families in child abuse data. There are numerous theories which try to explain the relationship and they may be divided generally into two categories: individual psychology theories and environmental theories. Neither should be thought of as trying to account for the whole of the phenomenon of child abuse. In fact , they undoubtedly interact. The environmental models are s t i l l in the stage of development and testing, however some description is possible. The primary characterist ic of these models is that they assert the importance of factors outside the individual. They also generally propose that factors from the social ecology influence most or a l l individuals in the society, more or less independent of their personal psychology. Particular to child abuse, using the environmental perspective leads us to the following speculation: since there is a correlation between low socioeconomic status (an individual measure) and abuse, and since we suspect the environment exerts influence "across the board", is there a detectable correlation 47 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL between environmental level indicators of economic conditions and child abuse? The search for a simple correlation is just the first step towards a complete explanation. Once a correlation is discovered, theories may be propounded and tested which seek to explain the relationship. The research reported in the second chapter went on to outline some of the environmental level indicators which have been tested for correlation. The researchers included justification for selection of their indicators, in the form of likely causal connections. Simply put, the hypotheses may be thought of as stating "these are the indicators which I believe represent the essence of economic stress or at least the facet of economic stress which is most correlated with child abuse, and these are the reasons why I believe this". Thus, in one sense the causal hypotheses need be thought of only as justification for the selection of indicators, particularly when the study is seeking simply to detect a correlation. Dooley et al. have proposed and researched the correlation between employment statistics and various health and social problems, including child abuse. They have used both individual level data and aggregate data. In spite of their numerous research efforts, they have established no clear association 48 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL between child abuse and this aspect of economic stress. They have called for further studies into this area. This study is a response to this call. It will assess the correlation between selected employment statistics and child abuse. Because of the desire to examine the environmental level of this phenomenon, and because of the association between economic conditions and abuse, I will be testing the relationship between community-level indicators of abuse and economic conditions. I expect a significant correlation between the two. The proposition of interest here is the contagion theory of Dooley et al. It, I believe, most closely expresses the essence of the environmental theory. As stated in the previous chapter, this theory holds that as jobs are lost in a community, abuse will go up in that community. It also proposes that the abuse will arise not just in homes where family members have lost jobs. Rather, the effect will be generalized to the population of the community, as we would expect from an environmental-level theory. Dooley et al. suggest that a number of possibilities exist for why this generalization should occur: knowledge of job loss by others creates insecurity over one's own tenure (stress leads to child abuse, as Justice and Justice found); awareness of high unemployment rate as a general indicator of economic climate again creates insecurity over one's 49 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL own position; high unemployment is indicative of a slow economy, which effects not only employment but the provision of services and amenities, and it is this reduction in services which fails to ameliorate stress and thus child abuse increases. The foregoing should not be thought of as a causal proposition which is being tested in this study. It is merely offered to explain why community-level measures of job loss are to be the indicators used and why a relationship is expected. There are admittedly other plausible explanations for a relationship between job loss and child abuse. For instance, abusive behaviour may indicate stress at home which could result in job loss, or discovery of child abuse in a home could lead to the parent leaving, being incarcerated, or otherwise losing his job, or a rise in child abuse rates signals some other stress inducing feature in the community which also results in net job loss (e.g. Seasonal Affective Disorder, as is mentioned, later in this chapter). Thus, the search for a correlation between job loss and child abuse is simply the first step towards a more complete understanding of the phenomenon. Discovery of a correlation could then lead to an examination of the "mechanism" by which 50 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL they are correlated. This research is, in fact, st i l l in this discovery phase, particularly in Canada. This is particularly relevant in Canada because there is an almost complete absence of studies of the Canadian context. The studies of James Garbarino, Dooley et al., and Justice and Justice were all done in and were about the United States. O.B. Adams carried out a study similar to some of Dooley et al.'s work, comparing unemployment with mortality in Canada. This study used longitudinal data, time series analysis, and multiple regression analysis. He noted that "...there have been surprisingly few Canadian studies...[and]...[a] serious effort to test these findings [correlating economic indicators with various mental and physical health problems] in the Canadian context today is urgently required." (Adams 1981, p.7). Indeed, I was unable to discover a single case of research in Canada using Garbarino's model or the strategies of Dooley, Catalano, et al. There is good reason to test this relationship within Canada, to suspect there may be a different result from the American studies. Of course, the reasons Why a Canadian study may find a different result depends upon the nature of the connection between economic stress and child abuse. Regardless, however, it must be conceded that the Canadian social context is 51 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL not identical to the American social context (to which all previous studies have pertained). The biggest single difference which could result in a less significant correlation- is the more extensive socialization within Canada. Because of the availability of subsidized medical insurance, subsidized, low cost housing, unemployment insurance and welfare benefits, economic downturns may have less of an impact on Canadians. The common understanding seems to be that Canada-offers more social support for the needy; the society is based less on individualism, capitalism, and private enterprise. There is likely less stigma attached to receiving social benefits in Canada. Therefore there may be less stress on individuals who are either unemployed or who believe their jobs to be in jeopardy. This possibility exists regardless of which hypothesis one uses of those we have seen so far. The prospect of losing one's job is less dramatic with two levels of "safety net" (unemployment insurance and income assistance); community supports tend to be publicly funded and thus more widely available in all areas thus reducing the likelihood of neighbourhood impoverishment or the closing of support services (admittedly this happens even in government subsidized programs); 52 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL in the same way, if economic stress is thought of as a community characteristic, the existence of government paid services makes most communities equal or at least equipped with the same minimum standard supports; reduced stigma would reduce the impact of negative attribution for job loss or for using support services. Of course, if this is the case, it does not overturn the hypothesis that the economy influences peoples' health and behaviour. Indeed, it-may support the hypothesis because it may be interpreted that steps taken to alleviate stress due to economic hardship (i.e. unemployment, insurance, welfare benefits, low cost housing, etc.) are effective and therefore the economy does impact individuals. In other words, if the target, economic hardship/stress, were not the appropriate one (compared to, say, individual mental health), then such programs would not influence the level of mental health or, in the present case, child-abusive behaviour in times of recession. This would, of course, be only conjecture or an alternate explanation in the case of negative results and could not be "proven" because of such a result. Because of the need for further studies of the type conducted by Garbarino and by Steinberg, Catalano, and Dooley, and because of the dearth of Canadian studies, the current 53 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL study may be seen as a vital start. This study is in many ways a replication of that done by Steinberg, Catalano, and Dooley (1981). It will use longitudinal data> time series and cross-correlation of these series', and it will compare data from different municipalities. Two of the three economic series'- in this study are those used by Steinberg, Catalano, and Dooley (unemployment rate and labour force). As well, the child abuse statistics are drawn, as in their study, from the child welfare agencies in the areas studied. The use of longitudinal aggregate data is based on the need to examine child abuse as an environmental problem rather than an individual one. As stated earlier, this requires Indicators which- represent community-level experience. Since aggregate data is a summation of the prevalence of a phenomenon in a community,^  changes in this data can represent changes at the community level. In other words, it does not measure and assess the differential response and experience of each individual to a condition in the community. The aggregate data in this study are measures of the prevalence of unemployment, employment, and income assistance receipt. If the environmental model is valid, changes in these indicators should show some association with changes in the dependent community level variable, in this case child abuse. 54 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL Apart from the importance of longitudinal studies for testing the environmental models, Steinberg, Catalano, and Dooley (1981, p.976) strongly endorse this method on other grounds as well: "First, the definition of child abuse varies across geographic units such that reported differences between communities may be artifacts of definitional and reporting practices. But in the longitudinal approach, little or no variation in definition and reporting is expected in a community over relatively short periods of time....Second, the social class reporting bias mentioned above is removed when a community is used as its own control, as in time-series analysis. Assuming the proportion of low-social-status families is unchanging or only very slowly changing, any variation in abuse rates must be attributed to dynamic factors impinging on the whole community rather than to reporting bias. Third, several third-variable counter-explanations are made less plausible by the longitudinal aggregate technique. Individual personality or family factors of which both child maltreatment and economic difficulty may be effects are practically invariant over short periods of time in a large community." (Steinberg, Catalano, and Dooley 1981, p.976). They also suggest that the measurement of change in a variable in comparison with equivalent change in another variable strengthens the relationship found. Finally, they state that longitudinal studies are rare in the extreme in child maltreatment research. 55 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL Howing et al. (1989, p.4) also calls for longitudinal studies of child maltreatment, stating that such an approach can offer a "deeper understanding of the etiology and effects of child maltreatment." While the data will be explained in greater detail in the next chapter, a quick explanation will help the reader understand the ensuing discussion. The first series will be all reported abuse cases coming from several lower mainland B.C. municipalities covering the period from January 1981 to December 1987, aggregated monthly. These will be only those cases reported between the hours of 16:30 and 08:30 (after hours social services). The economic indicators will be monthly tallies of: all employable income assistance recipients from the same municipalities as the abuse data comes from, the number of employed persons in the greater Vancouver Metropolitan area, and the unemployment rate also for the Greater Vancouver Metropolitan area. The data will span 84 months. These series' will be compared using time series analysis (to remove regular trends) and cross-correlation (see later in this chapter for a description) to discover any relationship. It is anticipated that: as the number of employable people on welfare increases, as the 56 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL unemployment rate increases, and- as the number of employed persons decreases, the number of incidents of child abuse will rise. As stated above, the series' will be "treated" using time series analysis. This method compiles and prepares a series of "snapshots" at, in this case, monthly intervals with which to perform regression analysis. It thus offers as many correlation points as there are intervals in the time series. This method offers the advantage of tracking and assessing change over time and can assess time-lagged relationships. There are several issues which must be discussed regarding the data and the method of statistical analysis. First there is the guestion as to the adequacy of the three economic measures as valid indicators of economic fluctuations. In other words, do the indicators used measure-what the hypothesis suggests should be measured? The hypothesis suggests that the ability of the economy to provide jobs is the critical factor in whether stress is experienced. Steinberg, Catalano, and Dooley argue that labour force data is a very accurate measure of the ability of the economy to provide jobs and certainly this proposition has strong face validity. The labour force data used in this study is a monthly tally of a l l employed persons in the Greater 57 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL Vancouver Metropolitan area. This must be a fairly accurate portrayal of job numbers and the change over time. They also used unemployment rate data but qualified its use by noting it does not measure strictly the jobless but rather it measures only those who are actively seeking work. Thus It misses those who, for a number of reasons, have given up trying. In addition, it does not include those people who did not work enough weeks in the previous year to qualify for benefits or those who are st i l l unemployed but whose claim for benefits has run out. Thus, while on face value "unemployment rate" would seem a sure indicator, i t has some qualifications. However, as will be explained later, it is valuable. The next issue is that the present study uses income assistance data in addition to unemployment data and labour force (as was used by Steinberg, Catalano, and Dooley). One reason for this is simple pragmatics. Unemployment and labour force data is not available at the aggregation level of municipality. Therefore the abuse statistics will be correlated with unemployment data for all of Greater Vancouver Metropolitan area (the smallest aggregation level available). Naturally, this could be a source of error insofar as each municipality experiences and responds to economic stress differently. On the plus side, the Greater Metropolitan Vancouver area includes all 58 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL those municipalities serviced by New Westminster Emergency Services. However, it cannot be disaggregated for direct regional correspondence, and there is a possible source of Inaccuracy. In contrast, income assistance data is available at the municipality level and therefore a perfect match may be had. Even so, for the most part, their economies are intimately intertwined. Therefore the economic data pertaining to Greater Vancouver should be highly representative of the picture in the individual municipalities. As well, I believe income assistance may be more sensitive than unemployment figures in some ways. Income assistance is the last resort for financial support. Only those who, as described above, either have not worked enough weeks in the previous year to qualify for unemployment benefits or whose unemployment entitlement has run out are eligible for welfare. Figures indicate that a very high percentage of welfare recipients meet the criteria and thus are "deserving". Therefore, it may be assumed that apart from those unable to work, recipients have been unable to obtain work. Thus, if the number of employable income assistance recipients goes up, it may be fairly assumed that the economy is extremely "tight" and less able to provide employment opportunities to the public in general. 59 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL Also, fluctuations in income assistance receipt may be thought of as indicating relatively more extreme economic trends than unemployment rate shows because of its being the last resort. Thus, bumps in the income assistance series may indicate periods of prolonged economic constriction. The use of data on only "employable" recipients also adds power to this data as an indicator of the economic situation. This responds to the call from Dooley, Catalano, and Brownell (1986) for testing the relationship in communities experiencing more extreme economic hardship. Steinberg, Catalano, and Dooley (1981) argued that unemployment data was also useful, however, because it is a statistic with which the public is generally familiar. . They assert that because of this familiarity people use unemployment rate in a rough way to gauge the state of the economy. Therefore, when unemployment is high, even the employed people experience stress because they know that unemployment is high therefore they feel that their position is more tenuous. Assuming this to be true, by virtue of this quality alone and regardless of its ability to indicate accurate economic or job opportunity trends, our hypothesis (the anticipation/contagion hypothesis) predicts a positive association between unemployment rate and child abuse rate. 60 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL I will best for correlation between-the economic indicators as well. This can add strength to the study because if a relationship is found between the indicators, both should be associated with the child abuse series similarly as well. As Steinberg, Catalano, and Dooley (1981, p.976) note "To the extent that [these indicators] are not related, their differential association with abuse should reflect differences in their underlying constructs." While the theory would tend to support my hypothesis, to predict a positive outcome, there are several factors which may mitigate a positive finding. To begin with, there-may in fact be no relationship at all. Either the environmental proposition is not significantly influential (and it is strictly an individual psychological phenomenon which is not amenable to detection through, aggregate methods) or the wrong indicators of economic conditions have been used. As in all research, it will not be possible to state unequivocally that a failure to disprove the null hypothesis is a proof of the null hypothesis. Such a finding would simply suggest further research. 61 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL Another possibility would be that the effect is too small to detect with this* method. The temporally random "noise" may be too great to tease out the relationship sought. The use of -"de trending" through time series analysis offers a very conservative method of correlation and the process of removing trends may remove valid correlation. The correlation could be contained within or entirely represented by a regular pattern. Since such regular patterns are removed through detrending, this valid correlation would be lost. The argument used against this, however, is that one is unable, through this method, to differentiate between a true, direct relationship and the covariation due to a common third variable. This third variable problem is perhaps the biggest potential confounding factor and is a common one in time series analyses. Another variable not accounted for in the theory may be influencing both child abusive behaviour and income assistance application/receipt. For instance, the weather may affect both mood and job-seeking behaviour. It may, for instance, be that people experience Seasonal Affective Disorder which may make them prone to both abusive behaviour and make them less likely to look for/find work (because S.A.D. occurs in winter which has conditions which are not as conducive to job-seeking as summer conditions). Thus, welfare receipt or employment status and 62 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL child abuse could fluctuate coincidentally without any real connection. As Steinberg, Catalano, and Dooley (1981) point out, the detrending and deseasonalizing functions used in time series analysis remove any such third variable problems which have a regularly recurring period. However, third variable effects which are random or are "too subtly patterned" remain. They also point out that cross-sectional studies have a greater problem with the "third variable" explanation and are unable to look at separation of variables in time. As they state "...several third-variable counter-explanations are made less plausible by the longitudinal aggregate technique.[...]For example, the proportion of dispositionally violent or conflicting parents in a metropolitan population probably does not vary from month to month." (Steinberg, Catalano & Dooley 1981, p.976). This, too, then recommends the use of longitudinal data and time series analysis. Finally, some potential third variables may simply be discounted on face value. For instance, a drop in softwood lumber prices will affect unemployment but the suggestion of a concomitant influence on the rate of child abuse is stretching 63 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL the bounds o£ credibility. The unfortunate truth, however, is that third variable explanations simply cannot be entirely ruled out. Once again relying on Dooley, Catalano, and Brownell (1986, p.H6), there is a potential attenuation of the effect of economic stress or at least a variable response throughout the public because, as they note: "Normal adults with established work identities may be able to weather moderate, short-term, economic turbulence through tangible (e.g., unemployment insurance [or such things as savings, borrowing from extended family]) and cognitive compensatory mechanisms." Essentially,, there may be a variety of both thresholds and responses to economic stress. In other words, the hypothesis that stress is induced generally throughout the working population may be incorrect; those with jobs do not experience significant stress, and it is only those directly affected, those who lose jobs, who experience stress. Naturally, this study, by its design, cannot measure or interpret to such a sub-group. It must be recognized that child abuse is a multi-faceted phenomenon. It is not expected that economic stress is the sole correlate of child abuse, nor that it will account for a major proportion of the variation in abuse reports. Indeed, Steinberg, 64 A CANADIAN TEST OF THE ENVIRONMENTAL MODEL Catalano, and Dooley (1981, p.981) found that "Change in the work force adds 4% and %5 to explained variation lin abuse report incidence!." Garbarino (1976) was able to find an R* of only 16% for the ability of economic variations to account for variance in the abuse rate. There are admittedly a number of likely correlates, many which are not economic in nature. As well, as has been mentioned before, economic variables may play no causal role in abuse, but rather are interactive factors or co-vary due to a common third variable. Another qualification which must be made is that the data is, of necessity, in two different forms. Child abuse data represents incidence, meaning each month's total is strictly of new cases or reports. The other series' are prevalence measures. Thus, each month may (and undoubtedly does) include cases carried over from previous months. In fact, they will certainly include cases which carry over for up to a year or more. However, if we accept them as measures of the ability of the economy to provide jobs and assuming all or most of those represented by the statistics are seeking work, they can do what we are asking of them. 65 RESEARCH DESIGN AND DISCUSSION This study will involve a time-series analysis of ten series' and a correlation between series' after some s ta t i s t i ca l modification. The f i r s t set of series' is drawn from a monthly compilation of child abuse reports collected by one office of the Ministry of Social Services and Housing. This ministry is responsible in Bri t i sh Columbia for investigating a l l reports of child maltreatment. The data on child abuse comes from the Emergency Services office of the MSSH (Ministry of Social Services and Housing), located in New Westminster. A second set of series' is a collection of regional s tat i s t ics on number of employable "families" receiving welfare. I decided to use number of "cases" involving an employable family member rather than the number of people receiving benefits. I felt that number of cases is a more accurate indication of the economy because not a l l members of a family which is classified employable are actually seeking work (e.g. the children in these families). The income assistance s tat i s t ics are drawn from 17 d i s tr ic t offices of MSSH. These 17 d i s tr ic t offices are those responsible for the ongoing, daily disbursement of income 66 RESEARCH DESIGN AND DISCUSSION assistance to the same catchment area as Emergency Services covers. In other words, the income assistance data and the child abuse data pertain to the same geographic region and therefore the same population. The 17 district offices represent all the offices from 3 MSSH regions: regions 12, 13, and 19. It should be noted that each data set will not be a random sample but rather I will be using the entire population, e.g. "all cases of income assistance receipt by an employable individual or family in Burnaby and New Westminster" (Region 13), or "all reported cases of child abuse [for the same area]". The data will be aggregated into their respective regions and these regions will be the unit of analysis. The regions contain municipalities as follows: Region 19 - Coguitlam, Port Moody, Port Coquitlam, Pitt Meadows, Maple Ridge; Region 13 - Burnaby, New Westminster; Region 12 - Richmond, Delta (including Tsawwassen and Ladner). Therefore, there will be 4 child abuse and 4 income assistance series'; one for each of the above regions, and one comprised of the sum from all the regions. 67 RESEARCH DESIGN AND DISCUSSION The final two series' are the unemployment rate and the number of employed persons (labour force), for the Greater Vancouver Metropolitan area. As indicated in the previous chapter, the Greater Vancouver Metropolitan area includes (though it is not comprised solely of) all the municipalities covered by New Westminster Emergency Services. These series were available in monthly intervals from Statistics Canada. Emergency Services investigates reports of child physical and sexual abuse and neglect, and administers emergency income assistance. The office is open seven days a week (from 16:30 hrs to 08:30 hrs on weekdays and from Friday at 16:30 hrs through until 08:30 hrs Monday morning). The office responds to calls concerning all the above-listed municipalities. The catchment population is roughly 500,000 people. Calls come from other agencies as well as the general public. The range of possible callers includes school personnel, daycare workers, other social workers, doctors and hospital staff, private citizens'*, the child him/herself. Each social worker (4 per day on weekdays, 6 per day Saturdays and Sundays) records the intakes they are responsible for on log sheets and includes certain descriptive information, such as whether the call reported physical or sexual abuse of a 68 RESEARCH DESIGN AND DISCUSSION child, district office servicing the area in which the child lives, and whether the child was taken into custody by apprehension (see Appendix A for a reduced photocopy of a blank log sheet). These statistics are collated monthly and go back to early 1981 in an uninterrupted series. The compiled statistics may be found in Appendix B. The total number of abuse calls is the sum of calls from the three constituent regions. This may not seem strange but it is in fact something of an artifact, because not all calls had a district office coded on the log sheet. Therefore, actual number of abuse calls dealt with by New Westminster Emergency Services is in fact well above what is used in this study. The manner of compilation was as follows: statistics came from the Ministry Of Social Services and Housing's computer division (known as the "Systems" branch). It is to this branch that log sheets are sent, where they are entered into a computer. Every case where abuse was designated was included in the statistics which they provided me. Since log sheets are done daily, the original form of this data was in daily totals. I aggregated the data into monthly totals. I then removed all calls where either a district office was coded that was not within the catchment area of New Westminster Emergency Services (children may call New West E/S from an appropriate district although the child lives in a 69 RESEARCH DESIGN AND DISCUSSION district covered by another after hours office), or where there was no district office coded. Statistics from 1981 illuminate the degree to which this compressed the data: they went from 4858 total calls as recorded on all log sheets, to 1299 calls for which either there was no district office coded or for which there was a district office coded from within the proper catchment area, to 700 for only those calls where a district office was coded and the office was within the proper area. In fact, while there were many calls recorded for October '87, not a single one had either an appropriate district office coded or a district office indicated at all. This has given the unlikely result in the data of no calls in October '87. While there is an element of "throwing out the baby with the bathwater", this process ensures as much as possible that the series includes abuse reports only from the appropriate areas. An important issue regarding these statistics is that they are records of abuse reports and do not necessarily represent actual incidents of abuse. Those calls which allege abuse are designated "abuse" on the log sheets, whether or not subsequent investigation substantiated the allegation. Steinberg, Catalano, and Dooley (1981, p.977) used similar data and reported "Both Los Angeles County and the Orange County agencies investigate all abuse and neglect reports; over 90% of the reports made to 70 RESEARCH DESIGN AND DISCUSSION each agency are verified as actual cases of maltreatment as defined under present California state law." Other reports show a more conservative substantiation rate. For instance, the Illinois Department of Children and Family Services found a substantiation rate of 40.71% for all calls received between July 1, 1980 and June 30, 1981 (US Department of Health And Human Services 1984, Table II). The same publication cites a substantiation rate of 34.2% for calls received by the Pennsylvania equivalent of Emergency Services. A random analysis of calls- designated as "abuse'' on the log sheets was done in order to establish the rate of substantiation for this data set. A random selection of 40 log sheets was made -from one of several boxes (the 1987 log sheet box was picked at random). These log sheets recorded a total of 73 abuse reports. Because the log sheets also record name of child/family about whom the report is made, and since in virtually all cases where abuse is alleged there is a written case report, it was possible to determine through these reports (called "memos") the disposition of each call. In many cases, the report was a repeated entry on the same log sheet. In several other cases, the call actually concerned sexual abuse, for which there is a 71 RESEARCH DESIGN AND DISCUSSION separate designation on the log sheets (which was not used in these cases). Also, in a-few cases there was no memo written. Only those cases where no memo was written were excluded from the analysis, and this resulted in a possible 62 cases. It should be noted that the definition applied in order to determine substantiation was essentially that of David Gil's, as reported In chapter-1 of this study. This Is because this is essentially the operational definition used by Ministry personnel. The Inter-Ministry Child Abuse Handbook put out by the Province of British Columbia for the purpose of detailing each ministry's responsibility in addressing child abuse defines physical abuse as "...any physical force or action which results in or may potentially result In a non-accidental injury to a child and which exceeds that which could be considered reasonable discipline." (Province of British Columbia 1988, p.10). This is the definition used by ministry social workers of necessity because ministry policy itself does not clarify or delineate its own standards9 (other than to refer its social workers to the above-mentioned handbook). In all 62 cases, the--memos were examined. The criteria used to assess substantiation were: - admission of abuse by perpetrator, and/or; - clear physical evidence, and/or; - current incident accompanied by history of similar 72 RESEARCH DESIGN AND DISCUSSION incidents, and/or; — - an allegation by the child of hitting, pushing, slapping, hair-pulling, and so on, with some reason to believe the child's story (independent corroboration, consistency of detail, amount of detail). The type of information which warranted a designation of founded abuse in the memos ranged from occasional use of slapping to dangling a child out a window. Of the 62 eligible cases, 56.45% were substantiated, with 11.29% representing repeat calls and 32.26% being either unsubstantiated on investigation or incorrectly designated as abuse (e.g. were actually sexual abuse cases). This substantiation rate is entirely in line with that reported by Hawkins & Duncan (1985, p.408) where they found a 54.34% rate. The foregoing analysis of abuse-designated reports speaks to one aspect of the validity of the data; that they do indeed represent incidents of abuse (at a rate of 56.45% of the reports). However, there are several other questions regarding this data. It must be admitted that the statistics represent, in -the first instance, reporting behaviour as opposed to abuse behaviour directly. Having established a substantiation rate for reports, the question arises as to the stability of this rate 73 RESEARCH DESIGN AND DISCUSSION over time. Naturally this is an important issue because this study is of a series of data points over time. The simple response is that there is no reason to assume that an increase in reporting of abuse is the result of simply an increase in reporting behaviour; that the percentage of reports to actual incidence changes significantly. Therefore, increases in recorded abuse intakes will be assumed to imply Increased abusive behaviour. This assumption may be made because of the length of time which not only Emergency Services, but child welfare services in general have been in existence in British Columbia. As Parke and Cbllmer (1975, p.514) noted, there were dramatic increases in the rate of reporting of abuse following the inception of reporting legislation and the development of a system to respond to reports. In fact, they note that between 1966 (when reporting legislation was first enacted) and 1975, New York experienced a 549% increase in reporting. However, logically, the increase would be sharpest in the early years of the reporting requirement and its ensuing public endorsement. At some point, reporting behaviour will become, if not entrenched, at least more or less fixed at some rate. Krugman et al (1986, p.415) make this assumption when they note we are out of the "discovery" 74 RESEARCH DESIGN AND DISCUSSION phase of physical abuse. This variable is influenced by the ongoing prominence (visibility) of the problem and the agency and the time in existence. In the case of MSSH, in British Columbia child welfare services have been available since at least the early sixties, and Emergency Services in particular has existed since 1976, five years before the first data point in the abuse series. Occasional advertising campaigns have punctuated their history, but overall, given the length of time in service, I assume that because of this factor alone, reporting behaviour on the average has been stable since the beginning of the series. Therefore, fluctuations in the data are assumed to represent fluctuations in the incidence of abuse, not in reporting behaviour. Admittedly, the theories of Dooley, Catalano, et al. reported in chapter 2 mentioned the possibility that economic stressors influence reporting or "uncovering?' of behaviour rather than the behaviour being reported. In view of the current design, this must remain an unanswered qualification. Another issue regarding this data is the adequacy with which it represents the true incidence of abuse. It is manifestly improbable that 100% of abuse is reported. Therefore the question arises "What percent of abuse is reported and is 75 RESEARCH DESIGN AND DISCUSSION this proportion stable?". Garbarino (1976, p.179) confronted this issue as well and noted: "It is assumed that the 1973 reports recorded by the state-wide Central Registry are a reasonably valid index of child abuse/maltreatment. While no claim is made that all incidents (or even a very high percentage of them) are reflected in the data, it is assumed that there is a high correlation between actual incidence and the registered reports and that the discrepancy between actual incidence and registered reports is constant across counties." Garbarino relied on post-1973 reports because of the "improved" validity which had been generated through the installation of a toll-free telephone reporting line (such as the one from which my data is taken) and the enactment of mandatory reporting legislation. Such validity-improving (in Garbarino's estimation) measures were in place several years before the first data points in the time series used in this study. I will therefore make the same assumptions as Garbarino, based on the same criteria. Of course, given the virtual impossibility of determining the true incidence of abuse, assumptions of data constancy must be made. Finally, there is the concern regarding reporting bias, or as Ho wing et. al. (1989, p.5). describe it, the tendency to "confustej factors that lead to identification of families as maltreating, with factors that actually are related to 76 RESEARCH DESIGN AND DISCUSSION maltreatment." Again I must first rely on James Garbarino for comparison. In his 1976 study, he simply makes the assumption that his data is relatively free of bias. He bases this assumption partly on a report by J. Gray which found "...report data prior to 1973 (when there was no mandatory reporting laws or toll-free telephone reporting lines] were unreliable and biased in the direction of having progressive and rich counties report more abuse/maltreatment. Much of this appears to have changed since enactment of the 1973 law." (Garbarino 1976, p.179). Once again, the fact that Emergency Services has been in place since well before the first data points supports an assumption of at least improved reliability. As well public ad campaigns have kept the public periodically reminded of this service. Also, the ad campaigns emphasize the availability of Emergency Services to the children themselves, and they are encouraged to call on their own behalf. This feature also helps improve the reliability of the data. Finally, because of its location outside the municipalities it serves (other than New Westminster) and because it is not generally associated (by the public) with "the welfare" as readily as daytime district offices (due to different hours of work, no routine disbursement of income assistance), Emergency Services also has less of a class-linked public image. All these factors, I believe^ improve the reliability of the data. 77 RESEARCH DESIGN AND DISCUSSION As I will discuss below, the statistical procedures used herein also are designed, where possible, to remove this sort of bias. As indicated earlier, one of the other series' used as an independent variable involves monthly totals of the number of employable income assistance cases for the same period (Jan. '81 to Dec. '8 7) and for the same municipalities. This data is collected in a form which allows separation into separate municipalities or aggregation into the constituent regions. It is an extremely accurate, up-to-date - measure of the numbers of cases of welfare receipt for these areas. A wide range of breakdowns is kept on this data, so it was possible to select out only those employable cases. This selecting out was done manually, transcribing computer-generated reports for each month for each district office. All of the series' being modelled, or more precisely, the models developed, are examples of discrete statistical series'; discrete because each measurement is taken following a constant intervening time interval. They are statistical in that they are not defined or generated by a mathematical function (although the purpose of time series analysis is to develop an approximate mathematical model). That is, future measurements can only be described in probabilistic terms. This is, as Box and Jenkins 78 RESEARCH DESIGN AND DISCUSSION (1976 p.24) note, a stochastic process, which they define as "A statistical phenomenon that evolves in time according to probabilistic laws...". Each series will be first analyzed using the Box-Jenkins model of time-series analysis. All time series analysis methods attempt to generate a mathematical formula which best accounts for the points in the known time series. -The purpose of constructing such a formula is usually to use it to forecast what the future values are likely to be. One method used to forecast future values in many statistical applications is using the mean of the known values. When the set of data is normally distributed and random, this is an adequate method. However, in time series', the set of data may fluctuate sporadically, over time, may increase steadily (be non-stationary), and be non-random. For instance, population data usually increases steadily over time and thus shows not only nonstationarity but each value is very dependent upon and can be calculated from the previous value or values once one knows the mathematical function describing the growth. Thus if it was found population rose by .01% every year, a formula such as P * = P * - i + 01%(Pt-a) would presumably accurately forecast future population figures. 79 RESEARCH DESIGN AND DISCUSSION The Box-Jenkins model of time series analysis is used in this study to assess all series' used. For a complete treatment of this model, see Hoff (1983). In brief, however, we may start with a completely determined series, such as a straight line, whose behaviour is predictable and invariable (such as the population example). Now, a time series (in "real life") may be thought of as just such a line- which undergoes "shocks" at each time point. That is, there are external influences which create variance from the line. These shocks, in the Box-Jenkins model of time series, are thought of as arising from 4 processes or sources. Three are regular, predictable, and one is random and unpredictable. Hoff (1983, p.45) illustrates this concept in the formula: X_ — Ft: + E_t t = 1,2,3,... He explains that "Jft represents the original time series, Ft: represents the pattern component of the series, and E. represents the random error component of the series. The objective, then, is to find some mathematical -formula that can reproduce the pattern component in the series....INJote that since the random error component, by definition, cannot be forecasted, a forecast consists only of an extension of the pattern component. This fact implies that a forecast is always expected to be in error.n 80 RESEARCH DESIGN AND DISCUSSION The value of the Box-Jenkins model is that it seeks to explain, within the bounds of parsimony, as much of the series as possible in terms of the patterned component. The three predictable influences, patterned components, are autoregression, moving average, and trend (seasonal or secular). Autoregression is the influence of past values of the series on the present value. This may be represented by the formula: Xt: ~ AlXti—3. + Et: where X* is the value at time •fr', E* is the random error term at time 't\ and AiX*-i is the value of the series at •fr-I* multiplied by some factor Ax. Moving average also concerns the influence of past values but it accounts for the present value only in terms of past and present error terms. The formulaic representation is: Xt: — ~BxE^—i + 2?* This formula indicates that the current value of X is directly proportional only to the random error E*-n from some previous interval plus the current random error Et:. It is noted that the negative sign in front of the moving average parameter B is only convention and has no significance otherwise. 81 RESEARCH DESIGN AND DISCUSSION Trend is the tendency to move in a general direction away from a specific mean (e.g. constantly increasing, as in the case of population given above). It is specified in a time series formula as a constant (see below). The Box-Jenkins model is a specific example of a type of procedure known as "ARIMA" modelling (AutoRegressive integrated M_oving Average). In other words, it integrates within the formula all the patterned components, trend, autoregression, and moving average factors (where appropriate). Thus, a Box-Jenkins generated formula takes the generic form: Xt: — Bo + AlXt: — n — BxEtz—n + Ei: Bo is the constant accounting for the overall trend. The Box-Jenkins model . is simply a mathematical procedure for determining which parameters are present and their degree of influence. While this set of procedures is primarily used for forecasting (i.e. in business) it also serves as a method of "detrending", or as it is also known in the literature, "prewhitening". Essentially this means once the patterned components are determined, they are removed from the series, and regression analysis is done on the remaining error terms, 82 RESEARCH DESIGN AND DISCUSSION known as the residuals. This process has received a great deal of attention. Some believe that removing basic characteristics of a series takes away valuable data and seems too open for opportunistic manipulation. Perhaps Kasl (1979, p.786) sums up the controversy best in his criticism of Harvey Brenner's study on infant mortality rates: "In the report of infant and maternal mortality the raw Infant Mortality Rate data looks quite straightforward...The unemployment data from the same period shows a pattern which bears no relationship to the Infant Mortality data. However through the image of de trending, the high rates in 1920 now become low rates and the slight elevation around 1960 becomes a high rate. Then with a little lag thrown in and some manipulations, the link with the unemployment cycle is beginning to emerge. It is of course hard to know what it all means." Adams, too, points out the discrepancies when he writes "...the adoption of more conservative methods of time-series analysis [results in contradictory findings]..." (Adams 1981, p.9). The process of model specification is admittedly not iron-clad and involves some judgement on the part of the statistician as to which parameters should be included. 83 RESEARCH DESIGN AND DISCUSSION The argument for prewhitening is that, by definition, a time series which incorporates patterned parameters (not all series' requires all or any of these terms) is correlated with itself -the values are contingent on previous values in the series. An adequate model accounts for all of this autocorrelation and trend through the parameters. The residuals, therefore, are independent of each other. It is this feature which recommends prewhitening to time series data. Because autocorrelation in one series can result in spurious correlations with another series, prewhitening is recommended for each series prior to regression analysis. This procedure results in an extremely conservative estimate for correlation but it reduces the possibility of third variable explanations (e.g. an apparent correlation because of coincident seasonal variation due to some other factor). This process was used in many of the previous studies involving analysis of time series' (Brenner 1973), (Adams 1981). While Kasl's argument is persuasive that parsimony is served by the "least intrusive" treatment of the data, I believe Melvin Mark's (1978, p.335) argument must take precedence: "The cross-correlation of prewhitened series was seen to overcome most [spurious correlation] problems under at least some conditions and further meets the criterion that X should be 84 RESEARCH DESIGN AND DISCUSSION considered a possible cause of Y only if it adds to the predictability of Y over and above the predictability arising from l"s own orderly behaviour." The procedure for analyzing the residuals is known as cross-correlation. As described by Catalano and Dooley (1979, p.183) "...cross-correlation refers to computing and displaying as many lead correlations (i.e., the dependent variable temporally ordered before the assumed independent variable) as lagged correlations. The resulting array should ideally show random, insignificant coefficients for the lead correlations with a shift to significant, Increasing and subsequently declining correlations for synchronous and lagged configurations." While this procedure is very useful when a causal hypothesis is being tested, there is sti l l good reason to use this analysis in this study. Simply put, there is no reason to presume a greater likelihood of synchronous correlation than correlation at any other staggered interval. Indeed, in many cases a correlation of synchronous data points is not anticipated. Thus we may avoid making a causal inference while sti l l requiring the assessment of correlation at staggered time intervals. Though interpretation would have to await further research, the finding of a pattern in the lead/lag process is at least indicative of a potentially significant relationship. 85 RESEARCH DESIGN AND DISCUSSION Regression analysis is applied to the residuals from the modelled series' using a simple least-squares method in order to determine the coefficient of correlation in each case. Design Specification: Each series will be prewhitened according to its own ARIMA model10. A regression analysis of ordinary least squares method will be performed using the following criteria: Independent Variables prewhitened income assistance series' prewhitened labour force series prewhitened unemployment rate series Dependent Variable prewhitened abuse intakes series' There are actually 4 series' from the abuse statistics, and 4 series' from the income assistance statistics. They are the aggregated statistics for each of the three regions and the total of the three regions. After prewhitening, each abuse series will be regressed against the income assistance series from the corresponding region and the labour force and 86 RESEARCH DESIGN AND DISCUSSION unemployment rate series'. They will also be "lagged and leaded" through 12 months on either side. Along with the synchronous correlation, this will give 25 correlation coefficients for each pair of series'. For each lag/lead R, /?*, a two-tailed significance level, the Durbin-Watson statistic for the residuals of the dependent variable, and the number of observations N will be reported. The Durbin-Watson statistic simply measures autocorrelation between the residuals of the regression equation. It is a further check to reduce the chance of spurious correlation. All analyses will be conducted using the SYSTAT statistical computer software package. Appendix C shows the SYSTAT output of the Box-Jenkins identification and estimation steps for each series. 87 FINDINGS, DISCUSSION, AND RECOMMENDATIONS Prior to modelling the series', there was one missing data point. This is crucial when using the SYSTAT time series program because the next value is used as a replacement for the missing value, and this process continues to the end of the series. In other words, the series is out of sync by one value for each missing data point, starting at the first missing data point. The missing data was the income assistance value from Region 12 for December 1983. The value for November '83 is 1212, the value for January '84 is 1243. The trend from well before December '8 3 is clearly rising and it continues to rise after this date. In addition, it is unlikely in the extreme that there would be no income assistance receipt by employables for this one month alone. I therefore substituted the value for November '83 into December '8 3. I felt this was an adequately conservative approach given the above qualifications. This value was then used in the calculation for total employable income assistance value for December '8 3 (using Regions 19 and 13 alone resulted in a value of 4739; using the substituted Region 12 value as well, the new total was 5951). 88 FINDINGS, DISCUSSION, AND RECOMMENDATIONS Before reporting the actual results, there are several points which must be made regarding the modelling and the resultant series'. To begin with, the reader will note in the tables reporting the lead and lag regression results that N varies from 83 to 59. This is due to two factors. First, all the independent variable series' required one regular differencing due to nonstationarity. This process involves subtracting the previous value from the present value for every data point. Since there is no previous value for the first point, it must be excluded from the resulting series (the reader will see this in the listed residuals from ARIMA modelled series' in Appendix B). This of course then required that the first data point in the abuse series' be excluded from regression analyses. As well, for the Region 19 income assistance series, one seasonal difference was necessary. This process is identical to regular differencing except that the value 'n' time intervals previous is removed, where »n' is the season used. In the case of Region 19, the season was 12 months, therefore an additional 12 data points were removed, resulting in a total of only 71 values for this series. Second, the lead/lag procedure results in missing values at one or the other end of the series. Since the lead and lag 89 FINDINGS, DISCUSSION, AND RECOMMENDATIONS went to 12 months, there was a maximum loss of 12 data points on each end. Thus the number of data points for lead 12 (-12 on the regression table) and lag 12 is 71, or in the case of Region 19 income assistance, 59 points of correlation at lag 12. As the reader will note from the autocorrelograms (plots of autocorrelation) of residuals contained in Appendix C, some of the ARIMA models were unable to remove all the significant autocorrelations in the residuals (one of the goals and tests of adequacy for an ARIMA model). The process of ARIMA modelling usually results in several possible models using various parameters and procedures (e.g. differencing), each of which shows different degrees of autocorrelation in the residuals. The choice of the most appropriate model is something of a matter of judgement, based on the "100^ of the original series, the correlation between the parameters (if there are more than one), how close the mean is to zero (a perfectly modelled stationary series would have a mean of zero with the residuals equally distributed on both sides) and if the mean is significantly non-zero, and various characteristics of the residuals such as mean percent error. The models for several series required a choice between many possible parameter combinations. One of the guiding 90 FINDINGS, DISCUSSION, AND RECOMMENDATIONS principles I used to choose was that of parsimony. In other words, the model with the fewest and simplest parameters was chosen (given acceptable diagnostics in other areas as mentioned above). An example of this issue would be the income assistance series' for Regions 19 and for total income assistance. After trying innumerable combinations of parameters, with autocorrelation continuing to be evident in virtually all of them (or completely unacceptable parameter diagnostics), a choice had to be made of which set of parameters resulted in a balance between the least remaining autocorrelation and the best parameter diagnostics with the principle of parsimony kept in mind. The Durbin-Watson statistics make this an acceptable risk in that they check for autocorrelation in the residuals of the regression model. The Durbin-Watson statistics are reported in the next section. There were indications of some autocorrelation (at various lags, e.g. at lag 14 for the partial autocorrelation function of the Region 19 income assistance series) in the modelled Regions 19 and 13 and total income assistance series', the labour force series, and the Region 13 abuse series. The confidence level for the AR parameter for one series, the abuse totals series, brackets a value of 1. This can be diagnostic because a value of exactly one in an autoregressive 91 FINDINGS, DISCUSSION, AND RECOMMENDATIONS parameter (of order 1) is identical to one regular difference (see Hoff p.131 for a simple proof). I therefore generated two models, one starting with a regular differencing and one not involving regular differencing. The model involving no regular differencing stil l achieved no significant autocorrelation in the residuals with the fewest parameters. I therefore chose to use the undifferenced models. As stated in the chapter on methodology, I correlated each independent variable residual series with the other - income assistance total with labour force and. unemployment rate and labour force with unemployment rate. The only significant finding was the -correlation between labour force and unemployment rate, which had a coefficient of .554 (p < .001). The other correlations were insignificant. It should be expected that findings for these two series' would be similar. In addition, I correlated the abuse totals and income assistance totals series' with their 3 constituent regional series', and the regional series' with each other (e.g. Region 19 abuse residuals with Region 13 abuse residuals). All the regional counterparts were correlated with their respective total series at better than the .001 level. Their correlation with other regional series, however, was less consistently 92 FINDINGS, DISCUSSION, AND RECOMMENDATIONS significant (Region 19 abuse residual series was significantly correlated with Region 13 abuse residual series but not with Region 12 abuse residual series). The series' themselves may be seen in Appendix B (raw series', corrected series', and modelled or residuals series'). However, the following is a summary of the corrected and residuals series' statistics: TABLE I STATISTICS ON UNMODELLED ABUSE SERIES' TOTAL REGION REGION REGION ABUSE 19 13 12 1 OF CASES 81 84 84 84 HIBIMUH 0.000 0.000 0.000 0.000 NAIIHUH 31.048 11.85$ 18.064 7.339 BARGE 31.048 11.855 18.064 7.339 NEAR 11.801 4.133 4.476 3.192 VABIAICB 29.890 7.096 6.241 3.590 STANDARD DEV S.46T 2.664 2.498 1.895 STD. ERROR 0.597 0.291 0.273 0.207 SUN 991.262 347.168 375.957 268.138 93 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE II STATISTICS OF RAW (UNMODELLED) INCOME ASSISTANCE, UNEMPLOYMENT RATE, AND LABOUR FORCE SERIES' 1.1. RBGIOI RBGIOI RBGIOI UIC LABOUR TOTAL 19 13 12 RATB FORCE CUBS 14 04 84 84 84 84 HIIIHUH 3677.0 1391.0 1506.0 740.0 4.3 581000 HillHUH 6454.0 2535.0 2625.0 1365.0 15.1 704000 RAIGB 2777.0 1144.0 1119.0 625.0 10.8 123000 HSU S477.S48 2132.440 2217.881 1127.226 10.868 632428.6 VARIAIC8 998063.721 163422.346 157689.552 42936.700 9.159 102736BM STD. DEV 993.031 404.2S5 397.101 207.212 3.026 32052.399 STD..ERROR ,109.003 44.100 43.327 22.609 0.330 3497.203 SDN 460114.0 179125.0 186302.0 94687.0 912.9 5.31240B+7 TABLE III STATISTICS OF MODELLED ABUSE SERIES' TOTAL RBGIOI RBGIOI RBGIOI ABUSE 19 13 12 8 OP CASES 84 84 84 83 HIIIHUM -10.776 0.000 0.080 -3.375 HAH MOM 18.649 11.855 18.064 4.293 RAIGB 29.425 11.855 18.064 7.668 H8AR 0.544 4.133 4.476 -0.254 VASIAICS 29.549 7.096 6.241 2.553 STAIDARD DEV 5.436 2.664 2.498 1.598 STD. ERROR 0.593 0.291 0.273 0.175 SOI 45.698 347.168 375.957 -21.041 94 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE IV STATISTICS OF RESIDUALS FOR MODELLED INCOME ASSISTANCE, UNEMPLOYMENT, AND LABOUR FORCE SERIES' L A . REGION REGION REGION ONEHPLOIHENT LABOUR TOTAL 19 13 12 FORCE 1 OF CASES 83 71 83 63 83 83 HIIIMUH -181.751 -64.348 -84.175 -187.000 -2.600 -25000.000 HAXIHUH 236.892 99.881 88.567 167.000 2.700 24000.000 -RANGE 118.6(3 164.229 172.742 374.000 5.300 49000.000 MEAN 14.314 0.676 6.275 3.277 0.059 638.554 VARIANCE 6803.420 1324.978 1219.937 1738.373 0.962 1.24209Bf09 STUDIED DEV 82.483 36.400 34.928 41.694 0.981 11144.919 STD. ERROR 9.054 4.328 3.834 4.576 0.108 1223.314 SON 1188.085 47.971 520.827 272.000 4.900 53000.000: For autocorrelation to be assumed in the regression residuals, the Durbin-Watson s ta t i s t i c should f a l l between roughly 1.59 and 2.41 (the actual value depends upon the number of data points - the values represent the most conservative l imi t s ) . The Durbin-Watson s tat i s t ics indicate there is no autocorrelation in the regression residuals for a l l but 17 regressions. The residuals for the three regression sets using the abuse totals series between synchronous and lag +6 show for the most part uncertainty as to autocorrelation (see Tables 5 - 8). Four of the 17 actually show autocorrelation in the residuals, with the remaining 13 being in the uncertainty range. FINDINGS, DISCUSSION, AND RECOMMENDATIONS Since all of the 17 are found in regressions involving the abuse totals series, this is suggestive of some artifact in that series. As explained above, this series was modelled using an autoregressive parameter in place of regular differencing. I subsequently modelled the series using a regular difference and redid all the regressions for the lags in question. The Durbin-Watson statistics all fell with the acceptable limit for no autocorrelation in the regression residuals. In addition this modelling, of course, changed the correlation coefficients for these lags such that the one significant finding at lag +5 for labour force as the independent variable was reduced to insignificance (/? = -.034). No correlation was increased to a significant level and the direction of change was not consistent. Naturally, such an recursive approach to statistics is not acceptable and the above remodelling of the one series is merely diagnostic. Those places where the Durbin-Watson statistic did indicate uncertainty or autocorrelation in the regressions using, the abuse totals series did not correspond except in one case, with significant correlation coefficients. Therefore the discussion is somewhat moot. 96 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE V REGRESSION STATISTICS FOR ABUSE TOTAL  SERIES WITH INCOME ASSISTANCE TOTALS LAG R R* P D-W N -12 -.066 .004 .580 2.004 72 -11 -.058 .003 .625 1.966 73 -10 .132 .017 .264 1.990 74 -9 .144 .021 .218 2.102 75 -8 -.334 .112 .003 1.902 76 -7 .191 .036 .096 1.926 77 -6, .117 .014 .308 2.037 78 -5 .014 .000 .903 2.035 79 -4 .105 .011 .356 1.905 80 -3 -.231 .053 .038 2.119 81 -2 -.109 .012 .330 10963 82 -1 .140 .020 .208 2.043 83 SYNC -.077 .006 .490 2.407 83 + 1 -.033 .001 .766 2.443* 82 + 2 .016 .000 .890 2.442" 81 + 3 -.047 .002 .677 2.456" 80 + 4 .004 .000 .974 2.480"" 79 + 5 .017 .000 .883 2.461* 78 + 6 .051 .003 .658 2.461" 77 + 7 .029 .001 .802 2.289 76 + 8 .058 .003 .624 2.351 75 +9 .116 .013 .327 2.374 74 + 10 .074 .005 .535 2.276 73 + 11 -.105 .011 .380 2.371 72 + 12 -.058 .003 .633 2.399 71 * uncertain autocorrelation ** autocorrelation TABLE VI FINDINGS, DISCUSSION, AND RECOMMENDATIONS REGRESSION STATISTICS FOR ABUSE  TOTAL SERIES WITH LABOUR FORCE SERIES LAG R R* p D-W N -12 .022 .000 .857 2.002 72 -11 -.032 .001 .787 1.994 73 -10 .007 .000 .952 2.029 74 -9 .120 .014 .307 1.971 75 -8 -.149 .022 .199 1.947 76 -7 -.056 .003 .626 2.053 77 -6 -.169 .029 .138 2.016 78 -5 .027 .001 .817 2.049 79 -4 .113 .013 .316 1.936 80 -3 .026 .001 .815 2.090 81 -2 -.194 .038 .081 1.977 82 -1 .001 .000 .995 2.117 83 SYNC .176 .031 .112 2.390 83 + 1 .078 .006 .485 2.453" 82 + 2 -.066 .004 .557 2.424" 81 + 3 ... 078 .006 .489 2.435" 80 + 4 -.062 .004 .588 2.517"" 79 + 5 -.289 .084 .010 2.457" 78 +6 .119 .014 .302 2.343 77 + 7 -.116 .014 .317 2.28 3 76 + 8 -.063 .004 .588 2.344 75 +9 .016 .000 .889 2.334 74 + 10 -.067 .005 .571 2.268 73 + 11 .081 .006 .501 2.389 72 + 12 .124 .015 .302 2.425 71 * uncertain autocorrelation ** autocorrelation FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE VII REGRESSION STATISTICS FOR ABUSE TOTAL  SERIES WITH UNEMPLOYMENT RATE SERIES LAG R /?* P D-W N -12 .101 .010 .399 2.007 72 -11 .012 .000 .918 1.994 73 -10 .072 .005 .540 2.019 74 -9 .046 .002 .696 2.019 75 -8 -.021 .000 .859 1.964 76 -7 .129 .017 .264 2.064 77 -6 .105 .011 .362 2.018 78 -5 .002 .000 .985 2.041 79 -4 -.124 .015 .272 1.958 80 -3 .-.130 .017 .248 2.122 81 -2 .125 .016 .263 1.931 82 -1 .034 .001 .762 2.098 83 SYNC -.120 .014 .278 2.397 83 + 1 .028 .001 .806 2.437" 82 + 2 .133 .018 .238 2.478"" 81 + 3 .060 .004 .594 2.472"" 80 + 4 -.023 .001 .838 2.478" 79 •.5 .048 .002 .674 2.455* 78 +6 -.014 .000 .906 2.422" 77 + 7 . 145 .021 .211 2.307 76 + 8 -.025 .001 .833 2.333 75 +9 -.148 .022 .208 2.335 74 + 10 .085 .007 .475 2.241 73 + 11 -.112 .013 .348 2.353 72 + 12 .030 .001 .802 2.391 71 * uncertain autocorrelation ** autocorrelation FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE VIII REGRESSION STATISTICS FOR REGION 19 ABUSE  SERIES WITH REGION 19 INCOME ASSISTANCE SERIES LAG R R* P D-W N -12 ^.091 .008 .448 2.097 71 -11 -.102 .010 .398 2.042 71 -10 -.042 .002 .729 1.938 71 -9 .108 .012 .371 1.870 71 -8 -.246 .060 .039 1.834 71 -7 -.033 .001 .786 1.865 71 -6 .022 .000 .855 1.858 71 -5 -.091 .008 .451 1.696 71 -4 .073 .005 .544 1.626 71 -3 .208 .043 .082 1.779 71 -2 .056 .003 .640 1.623 71 -1 .031 .001 .795 1.651 71 SYNC .061 .004 .612 1.675 71 + 1 .086 .007 .479 1.684 70 + 2 -.002 .000 .986 1.652 69 + 3 .042 .002 .734 1.683 68 + 4 .260 .068 .034 1.738 67 + 5 .057 .003 .650 1.725 66 +6 .185 .034 .141 1.698 65 + 7 -.004 .000 .977 1.703 64 + 8 .262 .069 .038 1.717 63 +9 .100 .010 .438 1.865 62 + 10 .278 .077 .030 1.784 61 + 11 .041 .002 .756 1.779 60 + 12 .083 .007 .532 1.715 59 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE IX REGRESSION STATISTICS FOR REGION 19  ABUSE SERIES WITH LABOUR FORCE SERIES LAG R fl2 p D-W N -12 -.071 .005 .551 1.989 72 -11 -.078 .006 .514 1.976 73 -10 -.078 .006 .510 1.912 74 -9 . 129 .017 .271 1.861 75 -8 . 004 .000 .969 1.842 76 -7 -.007 .000 .952 1.862 77 -6 -.155 .024 .176 1.840 78 -5 -.039 .002 .733 1.792 79 -4 .076 .006 .505 1.696 80 -3 -.019 .000 .865 1.770 81 -2 -.194 .038 .080 1.741 82 -1 -.100 .010 .366 1.792 83 SYNC .013 .000 .909 1.848 83 + 1 .040 .002 .721 1.802 82 • 2 -.087 .008 .4 39 1.762 81 + 3 .097 .009 .394 1.774 80 + 4 -.058 .003 .614 1.814 79 + 5 -.162 .026 .155 1.773 78 •6 -.010 .000 .930 1.766 77 + 7 -.130 .017 .264 1.734 76 + 8 -.045 .002 .702 1.737 75 +9 -.062 .004 .597 1.780 74 + 10 -.057 .003 .633 1.640 73 + 11 -.118 .014 .322 1.650 72 + 12 1.013 .000 .915 1.673 71 TABLE X FINDINGS, DISCUSSION, AND RECOMMENDATIONS REGRESSION STATISTICS FOR REGION 19  ABUSE SERIES WITH UNEMPLOYMENT RATE SERIES LAG R /?a p D-W N -12 .092 .008 .444 1.982 72 -11 -.008 .000 .944 1.946 73 -10 .171 .029 .145 1.938 74 -9 .074 .005 .528 1.900 75 -8 -.116 .013 .319 1.803 76 -7 .091 .008 .434 1.879 77 -6 .168 .028 .143 1.889 78 -5 .069 .005 .544 1.794 79 -4 -.056 .003 .624 1.709 80 -3 -.050 .002 .660 1.774 81 -2 .126 .016 .259 1.689 82 -1 .020 .000 .860 1.737 83 SYNC .019 .000 .866 1.858 83 + 1 -.002 .000 .983 1.808 82 + 2 .146 .021 .19 4 1.823 81 + 3 .139 .019 .219 1.844 80 + 4 -.017 .000 .879 1.797 79 + 5 .107 .011 .351 1.741 78 +6 -.020 .000 .860 1.753 77 +7 .216 .047 .061 1.741 76 +8 .083 .007 .482 1.756 75 +9 .055 .003 .641 1.780 74 + 10 .075 .006 .527 1.625 73 + 11 -.014 .000 .905 1.648 72 + 12 .024 .001 .845 1.665 71 TABLE XI FINDINGS, DISCUSSION, AND RECOMMENDATIONS REGRESSION STATISTICS FOR REGION 13 ABUSE  SERIES WITH REGION 13 INCOME ASSISTANCE SERIES LAG R R* p D-W N -12 .229 .053 .053 2.007 72 -11 .137 .019 .247 1.-88.9 73 -10 .067 .004 .573 1.842 74 -9 -.044 .002 .708 1.-818 75 -8 -.011 .000 .925 1.807 76 -7 .059 .003 .611 1.826 77 -6 .057 .003 .619 1.795 78 -5 .130 .017 .255 1.784 79 -4 -.076 .006 .503 1.741 80 -3 -.079 .006 .486 1.856 81 -2 -.233 .054 .036 1.736 82 -1 .070 .005 .531 1.795 83 SYNC -.052 .003 .642 1.845 83 + 1 .131 .017 .242 1.729 82 + 2 -.136 .019 .225 1.766 81 + 3 .004 .000 .970 1.793 80 + 4 -.035 .001 .756 1.893 79 + 5 -.093 .009 .420 1.814 78 +6 -.010 .000 .933 2.028 77 +7 .064 .004 .583 1.793 76 + 8 .014 .000 .907 1.791 75 +9 .154 .024 .189 1.839 74 + 10 .026 .001 .827 1.855 73 + 11 .162 .026 .175 1.835 72 + 12 .171 .029 .154 1.952 71 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE XII REGRESSION STATISTICS FOR REGION. 13  ABUSE SERIES WITH LABOUR FORCE SERIES LAG R R* p D-W N -12 .044 .002 .715 1.852 72 -11 .110 .012 .353 1.825 73 -10 .061 .004 .608 1.848 74 -9 .041 .002 .726 1.805 75 -8 -.206 .043 .074 1.800 76 -7 -.080 .006 .491 1.862 77 -6 -.134 .018 .242 1.823 78 -5 -.121 .015 .287 1.824 79 -4 -.017 .000 .883 1.754 80 -3 -.110 .012 .328 1.814 81 -2 -.051 .003 .650 1.772 82 -1 -.072 .005 .519 1.827 83 SYNC .151 .023 .172 1.852 83 + 1 .060 .004 .555 1.798 82 + 2 .041 .002 .714 1.811 81 + 3 .015 .000 .895 1.794 80 + 4 -.091 .008 .426 1.957 79 + 5 -.304 .093 .007 1.820 78 +6 .065 .004 .572 1.967 77 + 7 -.043 .002 .710 1.792 76 +8 -.108 .012 .356 1.807 75 +9 .010 .000 .930 1.819 74 + 10 -.103 .011 .388 1.777 73 + 11 .178 .032 .135 1.768 72 + 12 .098 .010 .415 1.795 71 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE XIII REGRESSION STATISTICS FOR REGION 13  ABUSE SERIES WITH UNEMPLOYMENT SERIES LAG R /?2 p D-W N -12 .097 .009 .418 1.821 72 -11 .074 .005 .536 1.837 73 -10 .078 .006 .510 1.862 74 -9 .159 .025 .173 1.876 75 -8 .083 .007 .477 1.861 76 -7 .176 .031 .125 1.906 77 -6 .169 .029 .139 1.885 78 -5 .144 .021 .205 1.821 79 -4 -.078 .006 .489 1.719 80 -3 .010 .000 .929 1.819 81 -2 .081 .007 .470 1.764 82 -1 .081 .007 .465 1.831 83 SYNC -.103 .011 .353 1.844 83 + 1 .089 .008 .427 1.752 82 • 2 .001 .000 .994 1.807 81 + 3 .041 .002 .717 1.796 80 +4 .056 .003 .622 1.891 79 + 5 .000 .000 .999 1.817 78 +6 .131 .017 .256 2.027 77 +7 .098 .010 .401 1.818 76 + 8 -.015 .000 .898 1.816 75 +9 -.310 .096 .007 1.751 74 + 10 .157 .025 .186 1.673 73 + 11 -.156 .024 .192 1.734 72 + 12 .055 .003 .651 1.756 71 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE XIV REGRESSION STATISTICS FOR REGION 12 ABUSE  SERIES WITH REGION 12 INCOME ASSISTANCE SERIES LAG R R* p D-W N -12 .121 .015 .313 1.978 71 -11 .242 .058 .041 1.972 72 -10 .066 .004 .581 2.047 73 -9 .114 .013 .334 2.019 74 -8 -.211 .045 .069 1.955 75 -7 .217 .047 .060 1.980 76 -6 -.007 .000 .955 2.088 77 -5 -.036 .001 .755 2.054 78 -4 .266 .071 .018 2.167 79 -3 .108 .012 .340 2.128 80 -2 .076 .006 .500 2.102 81 -1 .. . .04 3 .002 .704 2.099 82 SYNC -.039 .002 .728 2.098 83 + 1 - .105 .011 .349 2.126 82 + 2 .083 .007 .460 2.100 81 + 3 .042 .002 .714 2.130 80 + 4 -.027 .001 .816 2.169 79 + 5 -.026 .001 .818 2.100 78 +6 -.093 .009 .420 2.108 77 + 7 .066 - .004 .571 2.136 76 + 8 .050 .003 .669 2.077 75 +9 .064 .004 .559 2.091 74 + 10 -.031 .001 .793 2.107 73 + 11 -.176 .031 .139 2.213 72 + 12 -.055 .003 .649 2.088 71 TABLE XV FINDINGS, DISCUSSION, AND RECOMMENDATIONS REGRESSION STATISTICS FOR REGION 12  ABUSE SERIES WITH LABOUR FORCE SERIES LAG R fla p D-W N -12 .058 .003 .628 2.068 71 -11 -.021 .000 .860 2.048 72 -10 .142 .020 .232 2.091 73 -9 .147 .022 .211 2.127 74 -8 .089 .008 .450 2.097 75 -7 .034 .001 .770 2.076 76 -6 -.108 .012 .348 2.084 77 -5 .019 .000 .872 2.040 78 -4 .092 .009 .418 2.053 79 -3 .095 . 009 .403 2.010 80 -2 -.186 .035 .096 2.010 81 -1 .075 .006 .505 2.075 82 SYNC .085 .007 .445 2.118 83 + 1 .048 .002 .667 2.130 82 + 2 -.102 .010 .365 2.083 81 + 3 .040 .002 .725 2.124 80 + 4 .091 .008 .425 2.140 79 + 5 -.186 .035 .103 2.052 78 +6 -.021 .000 .854 2.136 77 +7 -.205 .042 .076 2.195 76 +8 -.118 .014 .314 2.107 75 +9 -.007 .000 .956 2.089 74 • 10 -.047 .002 .690 2.098 73 + 11 .087 .008 .469 2.184 72 + 12 .121 .015 .314 2.107 71 107 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE XVI REGRESSION STATISTICS FOR REGION 12  ABUSE SERIES WITH UNEMPLOYMENT SERIES LAG R R* p D-W N -12 -.086 .007 .474 2.088 71 -11 -.069 .005 .564 2.091 72 -10 -.133 .018 .261 2.106 73 -9 -.088 .008 .457 2.072 74 -8 .123 .015 .292 2.070 75 -7 073 .005 .532 2.090 76 -6 -.011 .000 .927 2.094 77 -5 .006 .000 .959 2.045 78 -4 .083 .007 .467 2.050 79 -3 -.190 .036 .092 1.979 80 -2 .156 .024 .164 2.046 81 -1 .083 .007 .460 2.106 82 SYNC -.114 .013 .306 2.106 83 +1 -.020 .000 .861 2.131 82 + 2 .223 .050 .046 2.126 81 + 3 .015 .000 .892 2.135 80 + 4 .032 .001 .783 2.169 79 + 5 .055 .003 .632 2.096 78 +6 -.052 .003 .652 2.101 77 +7 .100 .010 .390 2.135 76 + 8 .021 .000 .858 2.068 75 +9 .008 .000 .944 2.086 74 +10 - .090 .008 .449 2.110 73 +11 -.041 .002 .734 2.169 72 + 12 .004 .000 .976 2.061 71 108 FINDINGS, DISCUSSION, AND RECOMMENDATIONS There are thirteen correlations which are significant at the p < .05 level. They are: TABLE XVII SERIES Abuse Total with Income: Assistance Total Abuse Total with: Labour Force Region 19 Abuse with Region: 19 Income Assistance Region 13 Abuse with Region : 13 Income Assistance Region 13 Abuse with: Labour Force Region 13 Abuse with: Unemployment Rate Region 12 Abuse with Region: 12 Income Assistance Region 12 Abuse with: Unemployment Rate LAG R p lag -8 -.334 .003 lag -3 -.231 .038 lag +5 -.289 .010 lag -8 -.246 .039 lag +4 .260 .034 lag +8 .262 .038 lag +10 .278 .030 lag -2 -.233 .036 lag +5 -.304 .007 lag +9 -.310 .007 lag -11 .242 .041 lag -4 .266 .018 lag +2 — .223 .046 Given that there are 300 separate regressions in this study, this is a rather modest finding (4.3% of the regressions were significant). In fact, a simple perusal of the regression tables shows that very few were even close to significance at 109 FINDINGS, DISCUSSION, AND RECOMMENDATIONS the .05 level (using a cut-off of p < .075 results in the addition of only 5 more significant correlations). Most of the remaining correlations seem to be generally quite high, and there appears to be no pattern in terms of sign (going from negative to positive as you proceed down the tables) or size (for instance going from very small R to larger and larger R's). Therefore no speculative interpretation may be made of the trend in the correlations other than that they appear to be quite random. To the extent that these results can be interpreted, the following discussion suggests some consistency in the findings. Of the thirteen significant correlations, nine are due to regression with income assistance series' as the independent variable. In addition, the income assistance series' showed significant correlation at some lag with all abuse series'. The fact that the abuse series' are intercorrelated, as are the income assistance series' reduces the noteworthiness of this finding. In fact, given the degree of intercorrelation (R - .689 for the correlation between the Abuse Total residual series and Region 19 abuse residuals series), it is a little surprising there are not more significant findings which correspond across series'. 110 FINDINGS, DISCUSSION, AND RECOMMENDATIONS Six of the nine significant correlations with the income assistance series were in the "child abuse leading income assistance" direction. There seems to be a cluster around the -3 lag (one at each of lags -2, -3, and -4). However, two of these are negative in sign and one is positive, removing any potentially significant Interpretation due to this clustering. The three significant findings in the lag direction at lags + 4, +8, and +10 are all positive in sign. They are also all from the Region 19 abuse residuals series regressed on the Region 19 income assistance series. This alone is a hopeful finding, with the interpretation that a rise in income assistance receipt by "employable" families in the present is associated with a rise in child abuse in the future (at a 4, 8 and/or 10 month lag). However, with such a strong intercorrelation with the Abuse Totals residuals series, and no similar finding in the correlations of that or any other regional abuse series, the validity of this finding must be viewed with considerable skepticism. In most of the regression calculations there were both outliers and values exerting "leverage", undue influence (outliers are due to the dependent variable, leverage comes from the independent variable). There is debate in the statistical 111 FINDINGS, DISCUSSION, AND RECOMMENDATIONS community as to the appropriate way of handling such values. Hamburg (1983, p.437) suggests that if a case can be made that the outliers are from a "different conceptual universe" (e.g. "...all of the points except the extreme observation pertain to women and the outlier was an observation for a man..."), there is a logical argument to exclude that case. This would be a prodigious task with this data set (it would require disaggregation). However, to test the influence of outliers and leverage points on the outcome, I redid several of the regressions where outliers and points of undue leverage were found, removing first just the leverage points, then both the leverage points and the outliers. This of course changed the nature of the series somewhat and in many cases resulted in new leverage points and outliers. There was little consistency in the resulting regression outcomes. Some outcomes were better, some were less significant. My conclusion is that this is not a productive or logically arguable procedure in this case. Another interpretation of the presence of outliers and leverage points is that the ARIMA modelling is -inadequate. As indicated in the previous chapter, a good model accounts for as much of each value as possible. The residuals are the error terms which cannot be modelled, which are random. This may be an argument for including a regular difference in the abuse 112 FINDINGS, DISCUSSION, AND RECOMMENDATIONS series' models (where the outliers came from). This would not, however, alter the leverage points. Also, there is little validity in "wrestling a series to the ground" through overspecification - modelling a series to the point where it is a straight line. This smacks of the black magic which Kasl warns against when using time series analysis. I also checked for heteroscedasticity in several of the regression models' residuals randomly. Using the "eyeball" test, there was not the typical fan-shaped pattern indicating heteroscedasticity, and I believe that generally this alternative (heteroscedasticity in the residuals) can be ruled out. A more conservative interpretation of these findings would be that they are random incidents of significant correlations and the study has failed to find any true association between the dependent and the Independent variables. As suggested in chapter 3, there- could be many reasons for such a finding. There may indeed be no relationship between these variables. Indeed, as stated above, one would expect that in 300 regressions, chance alone could produce 13 significant findings. The use of employment statistics as indicators of economic stress may be inaccurate. The contagion hypothesis may be 113 FINDINGS, DISCUSSION, AND RECOMMENDATIONS incorrect and it may be that only those who directly experience unemployment are at risk of abusing. Alternately, the association may be so subtle that it was undetectable (perhaps even removed through the action of ARIMA modelling). To assess the influence of modelling, I regressed all the unmodelled series' (using only synchronous correlation). The findings offer some very interesting clues (see Table XVIII). A glimpse at the autocorrelation function plots of the unmodelled series' in Appendix C shows the degree of autocorrelation in the labour force, unemployment rate, and the income assistance rate. Using these series' as independent variables should presumably result in autocorrelation in the residuals of the regression. The surprises in the results here are not just in the very-significant correlations but also in the Durbin-Watson statistics which show no autocorrelation in the residuals of the regressions. In fact, the only dependent variable series which showed autocorrelation in the residuals was the Region 12 abuse series. This was the series which my time series analysis showed to absolutely require regular differencing. Since all the independent variables also required regular differencing, this is 114 FINDINGS, DISCUSSION, AND RECOMMENDATIONS TABLE XVIII SUMMARY OF REGRESSION STATISTICS FOR UNMODELLED SERIES' R Rs p D-W Abuse Total with: Income Assistance Total -.416 .173 .000 1 .662 Labour Force -.369 .137 .001 1 .669 Unemployment Rate -.194 .038 .077 1 .423 Region 19 Abuse series with: Income Assistance Total -.297 .088 .006 1 .889 Region 19 Income Assistance -.315 .009 .003 1 .905 Labour Force -.309 .095 .004 1 .944 Unemployment Rate -.100 .010 .367 1 .741 tea ion 13 Abuse series with: Income Assistance Total -.296 .087 .006 1 .965 Region 13 Income Assistance -.272 .074 .012 1 .947 Labour Force -.130 .017 .239 1 .859 Unemployment Rate -.250 .063 .022 1 .901 leaion 12 Abuse series with: Income Assistance Total -.393 .154 .000 1 .352 Region 12 Income Assistance -.304 .092 .005 1 .259 Labour Force -.460 .212 .000 1 .496 Unemployment Rate .089 .008 .419 1 .148 115 FINDINGS, DISCUSSION, AND RECOMMENDATIONS likely the basis for the autocorrelation in the regression residuals. The sign of the coefficients is negative in all but one case, suggesting a rise in child abuse is concomitant with a drop in labour force, but paradoxically (to this first finding) also with a drop in income assistance receipt by employable families and with unemployment rate. Of course, since the current study did not discuss nor direct itself towards correlating unmodelled series, the above findings cannot be interpreted in and of themselves. However, they certainly offer some insight when compared with the results of this study, as well as possible direction for future research. Clearly, the difference in findings is due to the modelling process. As we know, ARIMA modelling takes out detectible regular events in a series. If the independent variable series is both regular and associated with the dependent variable, removal of this regularity will remove the detectible correlation. However, there is no way when using aggregate data alone to determine whether the two unmodelled variables are causally linked or whether they are covarying due to the common influence of a third variable. Thus significant correlation 116 FINDINGS, DISCUSSION, AND RECOMMENDATIONS between unmodelled series' is rather less startling or telling than a significant finding might indicate. It does, however, suggest the need for further study of the series' in question. One particular third variable which alone could account for a great deal of correlation is population growth. Supposing that the ratio of abuse per 1000 families and of employable income assistance recipients per 1000 families remains constant overall, both will increase equivalently as the population increases. This would then show a significant correlation in regression, the extent of which may overshadow a more subtle but theoretically more important association. The population in the New Westminster Emergency Services catchment area went from 4817 30 to 531588 between 1981 and 1986. This is an increase of 10.35%. A greater increase would be expected for the entire period of this study. Such a steady increase would certainly show up in the autocorrelation functions of a time series analysis and should have been dealt with through regular differencing. Since this factor was not removed in the unmodelled trial above, one suggestion for future research would be to correct the series' for population growth alone. Performance of lead/lag 117 FINDINGS, DISCUSSION, AND RECOMMENDATIONS analysis should be included to detect any temporal trends. Such a study could determine whether the significant findings in Table 10 are solely due to population growth or if they include other aspects of the relationship. There is a risk, of course, of now shopping for a model which will give significant results and justifying its use afterward. On the other hand, if there are sound methodological arguments for correction or modelling of a series such as is given in the above case, such a trial is defensible. The discovery of significant results in unmodelled series' definitely advocates for a further assessment of these series. Another option for future research would be to compile the abuse series' using statistics from the daytime district offices. The dynamics of child abuse reporting may be different during the night - i t may require a more serious (and therefore less frequent) event. It is likely true that people would be more Inclined to wait until the morning to report less dramatic or concerning incidents. As well, in spite of the length of time Emergency Services has been in existence, district offices have a daily presence in their communities and are involved frequently with schools, hospitals, daycares, and so on. Certainly it is more likely that a school would report their 118 FINDINGS, DISCUSSION, AND RECOMMENDATIONS concerns during the day, while they have the child in question in their custody. However, as with so much research using archival data, the retrieval and compilation of the above data could be extremely difficult, if it exists at all. An alternate study using material again from New Westminster Emergency Services would provide individual level analysis. Since memos are written about virtually all abuse cases, a random sample of memos could be read for qualitative assessment regarding the socioeconomic status (as well as other characteristics) of the alleged abuser. Unfortunately, in many cases, collateral data or confirmation would be necessary from the alleged abuser. This procedure would stand very little chance of -approval by the Ministry of Social Services and Housing due to issues of confidentiality and ethics. Unfortunately, no policy direction can be taken from the insignificant findings in this study. However, as I have stated previously, the question of environmental level relationships has potentially huge consequences for the provision of social services in terms of cost, efficient allocation of resources, and effective intervention targets. Lack of significant results in this study must not be taken as showing an actual lack of relationship. Since the study of the Canadian context is so 119 FINDINGS, DISCUSSION, AND RECOMMENDATIONS marginal, there is a great deal of work to be done. Perhaps the best injunction to policy makers would be for better data collection or at least directed data collection with a view to studying macro-level relationships. The maintenance of daytime district office statistics and an emphasis on collecting various demographic data would improve research in the future. Naturally, the results of this study cannot disprove an association between economic stress and child abuse. There is certainly no evidence herein to support a hypothesis of relationship between child abuse and job-providing capability of a community. Perhaps more important than simple job-provision capability is the mean family income. Intuitively, the provision of a low paying job much less adequately reduces economic stress than providing a high paying job. Garbarino (1976) used mean family income as one independent variable, which he found to have a significant correlation (R = .27) at the community level with child abuse incidence. In fact, I would advocate for further studies of the type Garbarino has done, assessing Indicators or high risk neighbourhoods. 120 FINDINGS, DISCUSSION, AND RECOMMENDATIONS 1. For instance, Dr. Kempe writes "Beating of children however, is not confined to people with a psychopathic personality or of borderline socioeconomic status. It also occurs among people with good education and stable financial and social background." (Kempe et al. 1962, p.51) He does go on to qualify this: "However, from the scant data that are available, it would appear that in these cases, too, there is a defect in character structure which allows aggressive impulses to be expressed too freely." (p.51). I do not read this as an inflexible or narrow view to other possibilities. He appears quite prepared to defer to the data. 2. See Gil 1970, 18 - 20 for details. 3. This quote admittedly does not, in Gelles' article, refer to a model being overspecific or too extensive. I used the quote because in this context it is appropriate regardless. Gelles made this statement in regard to ex post facto analysis, as he indicates in this quote: "Analyzed after the fact, it seems obvious that a parent who beats his child almost to the point of death has poor emotional control and reacts with uncontrolled aggression." (Gelles 1973, p.614). 121 FINDINGS, DISCUSSION, AND RECOMMENDATIONS 4. I use a number of terms interchangeably throughout this paper: individual psychology model, disease model, psychopathology model. 5. Linsky and Straus (1986) report that "Literally scores of studies have now replicated the relationship between accumulation of stressful events and illness. To be sure, correlations are low, but the basic relationship is stable (emphasis mine), and at least some of the studies use a prospective design." (p.9). 6. This refers to the study noted in the bibliography by Egeland, Breitenbucher, and Rosenberg. 7. They used both unemployment data and statistics on the size of the work force. For reasons explained in the article, they felt size of work force to be a more accurate measure of economic trends. 8. The relationship of caller to alleged abuser is as diverse as the callers are themselves. They may be a separated parent of the child in question, otherwise related (aunt, 122 FINDINGS, DISCUSSION, AND RECOMMENDATIONS grandparent, steparent), neighbour, previous neighbour, friend, cellmate, passerby. 9. The Family and Child Services Act, which is the empowering act for the Ministry of Social Service and Housing, states that a child may be removed to a place of safety by a social worker if the child is deemed to be "in need of protection*1. Section 1 (a) through (e) define what criteria must be met for such a designation as follows: (a) abused or neglected so that his safety or well being is endangered; (b) abandoned; (c) deprived of necessary care through the death, absence or disability of his parent; (d) deprived of necessary medical attention; (e) absent from his home in circumstances that endanger his safety or well being. In addition, the policy manual for social workers states "In determining the need for immediate intervention, the social worker must consider: (a) the age and vulnerability of the child; (b) the extent and severity of the injuries, or the 123 FINDINGS, DISCUSSION, AND RECOMMENDATIONS neglect; (c) previous incidents reported of unexplained injuries, or chronic or serious neglect; (d) the parents' willingness to admit responsibility and use appropritae supports and services; (e) the ability of the non-abusing parent to take appropriate steps to protect the child from an abusive person; (f) the availability of extended family\close friends to provide support through a crisis period. These are admittedly good domains to examine but there is nowhere a functional definition of child abuse other than in the Interministerial Handbook. 10. 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July 1971 675 - 678. Smith, Susan L. "Significant Research Findings In the Etiology of Child Abuse", Social Casework. June '84, 337 - 346. Steinberg, L.D., Catalano, R., and Dooley, D. "Economic Antecedents of Child Abuse and Neglect". Child Development. 52 (3) Sept. 1981: 975 - 985. Stewart, Cyrus, et al. "Family Violence in Stable Middle-Class Homes". Social Work. November-December 1987, 529 - 531. Strauss, Murray A., Gelles, Richard, and Steinmetz, Suzanne. Behind Closed Doors: Violence In The American Family. Garden Ctly, New York: Anchor Press, 1980. 134 BIBLIOGRAPHY U.S Department of Health and Human Services. Review Of Child  Abuse And Neglect Research Addendum,. 1984. U.S., Washington, DC: Department of Health and Human Services, 1984. Wilkinson, Leland. SYSTAT: The System for Stat is t ics . Evanston, IL: SYSTAT, Inc. 1988 Young, Gay, and Tamra Gately. "Neighbourhood Impoverishment and Child Maltreatment", Journal Of Family Issues. Vol.9 No.2, June 1988, 240 - 254. Zuravin, Susan J . , and Taylor, Ronald. "The Ecology of Child Maltreatment: Identifying and Characterizing High-Risk Neighbourhoods", Child Welfare. Volume LXVI, Number 6, November-December 1987, 497 - 506. 135 APPENDIX A EMERGENCY SERVICES LOG SHEET 136 RAW ABUSE SERIES VALUES MONTH TOTAL REGION Jan81 17.500 6.210 Feb81 24.274 11.855 Mar 81 10.726 5.081 Apr 81 14.113 2.823 May 81 15.242 6.774 Jun81 18.064 5.081 Jul81 12.419 1.694 Aug 81 31.048 9.032 Sep81 10.161 3.952 Oct81 14.677 4.516 Nov81 19.193 8.468 Dec81 9.032 0.565 Jan82 6.210 2.258 Feb82 12.419 3.387 Mar 8 2 11.290 4.516 Apr 8 2 10.161 2.823 May 8 2 16.371 3.952 Jun82 21.451 7.903 Jul82 12.419 4.516 Aug 8 2 15.806 6.210 Sep82 14.113 4.516 Oct82 14.677 6.774 Nov82 18.629 7.339 Dec82 8.468 3.387 Jan83 15.806 9.032 Feb83 14.113 6.210 Mar 8 3 12.984 7.339 Apr 8 3 6.210 1.129 May 8 3 16.371 6.210 Jun83 14.677 5.645 Jul83 14.113 1.694 Aug 8 3 16.935 11.855 Sep83 12.419 3.387 Oct83 17.500 5.081 Nov83 3.952 0.565 Dec83 8.468 2.823 Jan84 16.371 5.645 Feb84 15.242 6.774 Mar 8 4 15.242 6.210 Apr 8 4 11.855 4.516 REGION 13 REGION 12 5.081 6.210 7.903 4.516 2.258 3.387 6.210 5.081 5.081 3.387 10.726 2.258 5.081 5.645 18.064 3.952 4.516 1.694 5.081 5.081 5.645 5.081 5.645 2.823 3.387 0.565 4.516 4.516 3.387 3.387 3.952 3.387 5.081 7.339 7.339 6.210 2.823 5.081 5.081 4.516 2.258 7.339 3.387 4.516 5.081 6.210 2.823 2.258 3.952 2.823 3.387 4.516 0.565 5.081 3.387 1.694 7.903 2.258 7.903 1.129 5.645 6.774 3.387 1.694 6.774 2.258 5.081 7.339 1.129 2.258 2.823 2.823 8.468 2.258 5.645 2.823 5.081 3.952 3.952 3.387 137 APPENDIX B MONTH May 8 4 Jun84 Jul84 Aug 8 4 Sep84 Oct84 Nov84 Dec84 Jan85 Feb85 Mar 8 5 Apr 8 5 May 8 5 Jun85 Jul85 Aug 8 5 Sep85 Oct85 Nov85 Dec85 Jan86 Feb86 Mar 8 6 Apr 8 6 May 8 6 Jun86 Jul 8 6 Aug 8 6 Sep86 Oct86 Nov86 Dec86 Jan87 Feb87 Mar 8 7 Apr 8 7 May 8 7 Jun87 Jul87 Aug 8 7 Sep87 Oct87 Nov87 Dec87 TOTAL 13.548 25.403 20.887 11.855 11.855 10.726 11.855 10.161 10.161 10.161 12.419 10.726 20.887 7.903 12.984 10.726 19.758 7.339 8.468 6.774 14.113 9.597 6.774 8.468 7.339 9.597 6.210 6 .774 11.290 3.952 5.081 7.339 5.645 6.774 5.645 5.081 7.339 3.387 6.210 3.387 10.726 0.000 10.726 4.516 REGION 19 2.823 8.468 8.468 5.081 3.387 1.694 1.694 3.952 3.387 2.823 3.387 3.952 9.032 1.694 4.516 3.387 9.597 3.952 3.387 2.823 6.210 1.129 2.258 2.258 1.694 2.258 3.387 2.258 4.516 0.565 2.258 1.694 1.694 1.129 1.694 1.694 2.823 0.565 0.565 1.129 3.952 0.000 4.516 1.694 REGION 4.516 10.161 6.774 2.823 3.952 3.952 5.645 3.952 5.081 3.387 4.516 2.823 7.339 3.387 6.210 5.081 5.081 2.258 1.694 1.694 5.081 5.645 2.258 5.081 4.516 3.952 1.694 3.387 3.952 2.823 1.694 3.952 3.387 5.081 2.823 2.823 3.387 1.694 3.387 1.694 5.081 0.000 5.645 1.129 REGION 12 6.210 6.774 5.645 3.952 4.516 5.081 4.516 2.258 1.694 3.952 4.516 3.952 4.516 2.823 2.258 2.258 5.081 1.129 3.387 2.258 2.823 2.823 2.258 1.129 1.129 3.387 1.129 1.129 2.823 0.565 1.129 1.694 0.565 0.565 1.129 0.565 1.129 1.129 2.258 0.565 1.694 0.000 0.565 1.694 138 APPENDIX B UNMODELLED INCOME ASSISTANCE. UNEMPLOYMENT  RATE. AND LABOUR FORCE DATA MONTH I .A. REGION REGION REGION UI LABOUR TOTAL 19 13 12 RATE FORCE Jan81 3966 1482 1710 774 4.3 641000 Feb81 3985 1499 1707 779 4.7 653000 Mar 81 3900 1476 1661 763 4.9 628000 Apr 81 3840 1461 1614 765 4.5 626000 May 81 3786 1411 1626 749 4.9 635000 Jun81 3736 1391 1605 740 4.5 652000 JU181 3815 1438 1623 754 4.6 654000 Aug 81 3810 1447 1616 747 4.9 655000 Sep81 3879 1461 1640 778 5.4 639000 Oct 81 3732 1402 1574 756 5.5 644000 Nov81 3677 1407 1525 745 5.6 646000 Dec81 3706 1445 1506 755 5.7 639000 Jan82 3696 1441 1506 749 6.3 625000 Feb82 3716 1431 1507 778 7.3 618000 Mar 8 2 3787 1482 1516 789 7.4 631000 Apr 8 2 3781 1484 1518 779 8.7 608000 May 8 2 3851 1491 1548 812 9.1 619000 Jun82 4060 1575 1602 883 10.3 619000 Jul82 4179 1638 1651 890 11.7 621000 Aug 8 2 4315 1685 1721 909 11.5 620000 Sep82 4583 1783 1812 988 11.1 605000 Oct 8 2 4635 1786 1827 1022 11.1 611000 Nov82 4776 1862 1868 1046 11.4 611000 Dec82 5019 1972 1939 1108 12.0 614000 Jan83 5071 1955 1978 1138 13.9 600000 Feb83 5189 2009 2008 1172 12.2 605000 Mar 8 3 5273 2050 2042 1181 13.1 605000 Apr 8 3 5259 2067 2045 1147 12.0 609000 May 8 3 5312 2079 2098 1135 12.4 605000 Jun83 5428 2104 2154 1170 11.9 622000 Jul83 5480 2145 2168 1167 11.4 621000 Aug83 5575 2191 2187 1197 12.4 608000 Sep83 5642 2212 2244 1186 11.8 602000 Oct83 5694 2215 2265 1214 11.3 594000 Nov83 5746 2249 2285 1212 12.0 587000 Dec83 5951 2348 2391 1212 12.8 588000 Jan84 5873 2277 2353 1243 12.7 5436000 Feb84 6054 2333 2412 1309 13.0 582000 Mar 8 4 6057 2341 2404 1312 14.2 582000 Apr 8 4 5946 2295 2369 1282 13.6 581000 139 APPENDIX B MONTH I .A. REGION REGION REGION Ul LABOUR TOTAL 19 13 12 RATE FORCE May 8 4 6000 2301 2430 1269 14.1 588000 Jun84 5802 2276 2444 1082 14.7 593000 Jul84 6060 2322 2469 1269 13.9 602000 Aug 8 4 6122 2365 2467 1290 13.1 611000 Sep84 6099 2332 2489 1278 13.8 601000 Oct 8 4 6112 2339 2476 1297 13.6 606000 Nov84 6178 2393 2495 1290 12.9 610000 Dec84 6315 2445 2531 1339 13.5 605000 Jan85 6390 2472 2562 1356 14.9 601000 Feb85 6431 2490 2576 1365 14.8 610000 Mar 8 5 6439 2492 2591 1356 14.5 613000 Apr 8 5 6385 2484 2559 1342 15.0 615000 May 8 5 6392 2473 2600 1319 12.4 639000 Jun85 6320 2453 2553 1314 14.0 632000 Jul85 6362 2459 2573 1330 13.2 648000 Aug 8 5 6348 2489 2551 1308 11.9 649000 Sep85 6286 2470 2499 1317 10.6 638000 Oct85 6258 2425 2534 1299 12.5 636000 Nov85 6276 2460 2529 1287 13.7 618000 Dec85 6352 2500 2548 1304 11.5 636000 Jan86 6454 2496 2625 1333 11.0 646000 Feb86 6444 2528 2625 1291 11.2 646000 Mar 8 6 6421 2535 2596 1290 11.2 652000 Apr 8 6 6318 2456 2580 1282 10.6 657000 May 8 6 6261 2446 2546 1269 9.6 679000 Jun 8 6 6235 2445 2559 1231 9.3 699000 Jul86 6240 2449 2559 1232 9.9 700000 Aug 8 6 6183 2430 2534 1219 10.2 704000 Sep86 6153 2430 2502 1221 9.6 686000 Oct86 6143 2409 2517 1217 10.3 675000 Nov86 6133 2421 2526 1186 13.0 652000 Dec86 6210 2463 2523 1224 12.9 642000 Jan87 6237 2454 2540 1243 15.1 620000 Feb87 6257 2455 2553 1249 14.3 627000 Mar87 6208 2454 2497 1257 14.0 646000 Apr 8 7 6215 2464 2508 1243 12.6 659000 May87 6146 2437 2508 1201 10.4 680000 Jun87 6213 2449 2538 1226 10.5 695000 Jul87 6240 2452 2553 1235 12.0 688000 Aug 8 7 6248 2422 2603 1223 10.3 688000 Sep87 6202 2439 2528 1235 9.9 685000 Oct87 6148 2433 2517 1198 9.6 686000 Nov87 6091 2418 2483 1190 9.5 676000 Dec87 6007 2480 2481 1046 9.2 694000 140 APPENDIX B STATISTICS FOR RESIDUAL OF MODELLED ABUSE SERIES' MONTH ABUSE TOTAL REGION 19 REGION 13 REGION Jan81 17.500 6.210 5.081 • Feb81 18.649 11.855 7.903 -1.694 Mar 81 -0.840 5.081 2.258 -2.409 Apr 81 2.926 2.823 6.210 -0.128 May 81 3.221 6.774 5.081 -1.790 Jun81 5.122 5.081 10.726 -2.482 Jul81 -2.047 1.694 5.081 1.511 Aug 81 17.376 9 .032 18.064 -0.552 Sep81 -8.966 3.952 4.516 -2.675 Oct81 -1.387 4.516 5.081 1.365 Nov81 3.727 8.468 5.645 1.032 Dec81 -7.486 0.565 5.645 -1.478 Jan82 -7.746 2.258 3.387 -3.375 Feb82 1.085 3.387 4.516 1.400 Mar 8 2 -0.286 4.516 3.387 -0.071 Apr 8 2 -1.213 2.823 3.952 -0.053 May 8 2 5.494 3.952 5.081 3.911 Jun82 8.911 7.903 7.339 1.828 Jul82 -2.866 4.516 2.823 0.253 Aug 8 2 1.587 6.210 5.081 -0.374 Sep82 -0.482 4.516 2.258 2.540 Oct 8 2 0.375 6.774 3.387 -0.902 Nov82 4.341 7.339 5.081 1.011 Dec82 -7.080 3.387 2.823 -3.187 Jan83 2.681 9.032 3.952 -1.845 Feb83 0.250 6.210 3.387 0.299 Mar 8 3 -0.828 7.339 0.565 0.791 Apr 8 3 -7.205 1.129 3.387 -2.789 May 8 3 5.398 6.210 7.903 -1.544 Jun83 2.074 5.645 7.903 -2.296 Jul83 0.962 1.694 5.645 3.909 Aug 8 3 3.600 11.855 3.387 -2.125 Sep83 -1.947 3.387 6.774 -1.042 Oct83 3.895 5.081 5.081 4.293 Nov83 -10.776 0.565 1.129 -1.835 Dec83 -2.657 2.823 2.823 -0.823 Jan84 6.205 5.645 8.468 -1.187 Feb84 3.178 6.774 5.645 -0.333 Mar 8 4 2.270 6.210 5.081 0.878 Apr 8 4 -1.724 4.516 3.952 0.099 May84 0.652 2.823 4.516 2.897 Jun84 12.419 8.468 10.161 2.755 Jul84 4.034 8.468 6.774 0.953 12 141 APPENDIX B MONTH ABUSE TOTAL REGION Aug 8 4 -6.135 5.081 Sep84 -3.993 3.387 Oct84 -3.689 1.694 Nov84 -1.238 1.694 Dec84 -2.410 3.952 Jan85 -1.516 3.387 Feb85 -0.918 2.823 Mar 8 5 1.740 3.387 Apr 8 5 -0.412 3.952 May8 5 9 .987 9.032 Jun85 -6.104 1.694 Jul85 1.071 4.516 Aug 8 5 -1.418 3.387 Sep85 8.184 9 .597 Oct 8 5 -6.756 3.952 Nov85 -3.322 3.387 Dec 8 5 -3.836 2.823 Jan86 4.836 6.210 Feb86 -1.147 1.129 Mar86 -3.499 2.258 Apr 86 -0.584 2.258 May 8 6 -1.440 1.694 Jun86 1.364 2.258 Jul86 -2.383 3.387 Aug 8 6 -0.972 2.258 Sep86 ~ 3.930 4.516 Oct86 -4.602 0.565 Nov86 -1.913 2.258 Dec86 1.026 1.694 Jan87 -0.938 1.694 Feb87 0.555 1.129 Mar87 -0.694 1.694 Apr 8 7 -0.975 1.694 May 8 7 1.654 2.823 Jun87 -2.776 0.565 Jul87 0.997 0.565 Aug87 -2.096 1.129 Sep87 5.968 3.952 Oct87 -6.631 0.000 Nov87 6.289 4.516 Dec87 -1.900 1.694 REGION 13 REGION 12 2.823 -0.973 3.952 -0.171 3.952 0.435 5.645 -0.235 3.952 -2.436 5.081 -2.406 3.387 0.439 4.516 0.897 2.823 0.113 7.339 0.650 3.387 -1.202 6.210 -1.473 5.081 -1.114 5.081 1.981 2.258 -2.454 1.694 0.403 1.694 -0.825 5.081 -0.059 5.645 -0.044 2.258 -0.598 5.081 -1.581 4.516 -1.195 3.952 1.354 1.694 -1.234 3.387 -0.933 3.952 0.988 2.823 -1.511 1.694 -0.578 3.952 0.128 3.387 -1.032 5.081 -0.780 2.823 -0.025 2.823 -0.584 3.387 0.123 1.694 0.093 3.387 1.199 1.694 -0.787 5.081 0.534 0.000 -1.290 5.645 -0.410 1.129 0.819 142 APPENDIX B RESIDUAL FROM MODELLED INCOME ASSISTANCE. UNEMPLOYMENT. AND LABOUR FORCE SERIES i MONTH I .A. REGION REGION REGION Ul LABOUR TOTAL 19 13 12 RATE FORCE Jan81 • Feb81 19.000 « -3.000 5 0.400 12000 Mar 81 -85.000 • -46.000 -16 0.200 -25000 Apr 81 -67.427 • -47.000 -2 -0.400 -2000 May 81 -20.775 # 12.918 -16 0.400 9000 Jun81 -26.547 -6.932 -9 -0.400 17000 Jul81 100.108 • 32.374 14 0.100 2000 Aug 81 14.544 • -10.670 -7 0.300 1000 Sep81 38.120 30.423 31 0.500 -16000 Oct81 -145.046 -71.505 -22 0.100 5000 Nov81 -81.971 -46.859 -11 0.100 2000 Dec81 86.460 -26.340 10 0.100 -7000 Jan82 11.499 20.185 -6 0.600 -14000 Feb82 8.664 -27.000 15.986 29 1.000 -7000 Mar 8 2 74.909 74.000 14.811 11 0.100 13000 Apr 8 2 -13.818 17.000 2.000 -10 1.300 -23000 May 8 2 42.247 68.122 29.694 33 0.400 11000 Jun82 211.345 73.518 51.247 71 1.200 0 Jul82 91.638 8.997 48.388 7 1.400 2000 Aug 8 2 54.305 9.939 60.825 19 -0.200 -1000 Sep82 221.484 53.717 74.485 79 -0.400 -15000 Oct82 -1.161 58.294 0.014 34 0.000 6000 Nov82 36.242 66.906 19.592 24 0.300 0 Dec82 222.674 49.873 43.169 62 0.600 3000 Jan83 -3.115 -37.012 34.412 30 1.900 -14000 Feb83 23.014 36.440 17.461 34 -1.700 5000 Mar 8 3 63.674 -30.544 12.286 9 0.900 0 Apr 8 3 -60.125 30.246 -8.928 -34 -1.100 4000 May 8 3 20.166 -10.010 43.825 -12 0.400 -4000 Jun83 121.472 -46.418 45.602 35 -0.500 17000 Jul83 31.283 -34.459 13.082 -3 -0.500 -1000 Aug 8 3 49.657 3.123 2.791 30 1.000 -13000 Sep83 46.674 -57.879 39.873 -11 -0.600 -6000 Oct 8 3 14.866 14.194 16.718 28 -0.500 -8000 Nov83 25.811 -43.287 14.189 -2 0.700 -7000 Dec83 184.674 12.842 88.567 0 0.800 1000 Jan84 -98.326 -59.847 -44.423 31 -0.100 -2000 Feb84 100.868 19.831 52.883 66 0.300 -4000 Mar 8 4 33.489 -38.290 -40.418 3 1.200 0 Apr 8 4 -181.751 -38.348 -23.378 -30 -0.600 -1000 May 8 4 52.827 -14.169 42.956 -13 0.500 7000 143 APPENDIX B MONTH I .A. REGION REGION REGION UI LABOUR TOTAL 19 13 12 RATE FORCE Jun84 -154.612 -34.228 16.447 -187 0.600 5000 Jul84 236.892 20.796 35.704 187 -0.800 9000 Aug 8 4 139.396 2.836 -20.656 21 -0.800 9000 Sep84 -123.849 -39.901 17.718 -12 0.700 -10000 Oct84 -11.235 -4.566 -20.646 19 -0.200 5000 Nov84 74.990 18.832 19.612 -7 -0.700 4000 Dec84 131.918 -30.564 29.272 49 0.600 -5000 Jan85 49.201 99.881 34.976 17 1.400 -4000 Feb85 -12.552 -45.757 8.189 9 -0.100 9000 Mar 8 5 -21.317 6.590 3.990 -9 -0.300 3000 Apr 8 5 -70.026 -3.143 -41.481 -14 0.500 2000 May85 3.873 1.848 36.718 -23 -2.600 24000 Jun85 -50.892 2.285 -51.588 -5 1.600 -7000 Jul85 39.264 -38.705 29.787 16 -0.800 16000 Aug 8 5 14.144 -13.761 -34.539 -22 -1.300 1000 Sep85 -78.417 13.059 -37.626 9 -1.300 -11000 Oct85 -22.528 -36.056 28.883 -18 1.900 -2000 Nov85 42.235 -13.331 1.728 -12 1.200 -18000 Dec85 86.945 -17.379 34.903 17 -2.200 18000 Jan86 94.964 -16.148 66.296 29 -0.500 10000 Feb86 -39.707 19.491 1.529 -42 0.200 0 Mar 8 6 -62.870 12.159 -34.811 -1 0.000 6000 Apr 8 6 -99.091 -64.348 -39.549 -8 -0.600 5000 May 8 6 -48.010 -7.029 -34.000 -13 -1.000 22000 Jun86 14.261 13.992 21.869 -38 -0.300 20000 Jul86 27.281 24.506 4.893 1 0.600 1000 Aug 8 6 -46.837 -46.105 -14.602 -13 0.300 4000 Sep86 -31.954 13.237 -35.976 2 -0.600 -18000 Oct86 12.281 13.905 15.000 -4 0.700 -11000 Nov86 1.727 -4.009 16.646 -31 2.700 -23000 Dec86 80.909 -3.452 6.787 38 -0.100 -10000 Jan87 30.909 -10.728 12.412 19 2.200 -22000 Feb87 -10.098 -29.349 10.247 6 -0.800 7000 Mar 8 7 -59.554 -6.578 -55.082 8 -0.300 19000 Apr 8 7 -0.818 93.419 5.801 -14 -1.400 13000 May 8 7 -49.847 -4.911 -3.976 -42 -2.200 21000 Jun87 64.264 15.710 47.127 25 0.100 15000 Jul87 53.971 -39.481 11.636 9 1.500 -7000 Aug 8 7 -18.189 -8.977 50.000 -12 -1.700 0 Sep87 -56.554 10.529 -84.175 12 -0.400 -3000 Oct87 -57.127 31.263 -15.588 -37 -0.300 1000 Nov87 -39.019 -23.302 -49.292 -8 -0.100 -10000 Dec87 -62.892 15.663 20.938 -144 -0.300 18000 144 PLOT OF AUTOCORRELATIONS OF TOTAL ABUSE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 11.801 STANDARD DEVIATION OF SERIES = 5.435 LAG CORE .291 .387 .320 .374 .217 .281 .184 .218 .283 .231 .221 .256 .161 .178 .207 .155 .067 .021 .168 .056 .086 .028 .059 .129 -.058 .006 -.121 -.009 -.151 0 .001 1 -.038 -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 v—f—f—f—f—f—f—f—f—.f—f ( X XXX XXI XIXDIX mi) mi mm II XXXII)xxi m n ) nun) mx m u xmm m n xxxxi m m m i mi m n m i xm i XI i m APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF TOTAL ABUSE SERIES NUMBER OF CASES = 8 4 MEAN OF SERIES = 11.801 STANDARD DEVIATION OF SERIES - 5.435 COBB SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 „ t — f — f — t — * — * — t . .291 .109 ( |XIXX)XX .308 .109 ( IIIXIIII .189 .109 ( IXIIX) .217 .109 ( inn) -.013 .109 ( 1 ) .066 .109 ( IX ) -.030 .109 ( I ) .024 .109 ( I ) .167 .109 ( IXXXX) .054 .109 ( IX ) .045 .109 ( IX ) .063 .109 ( IX ) -.085 .109 ( XXI ) -.015 .109 ( 1 ) .045 .109 ( II ) -.001 .109 ( 1 ) -.088 .109 ( XXI ) -.172 .109 (inn ) .113 .109 ( i n ) -.018 .109 ( 1 ) .005 .109 ( I ) -.023 .109 ( I ) -.053 .109 ( XI ) .121 .109 ( i m ) -.210 .109 (XXIII ) -.011 .109 ( 1 ) -.155 .109 ( XIX t ) -.001 .109 ( 1 ) -.049 .109 ( XI ) .070 .109 ( IX ) .116 .109 ( IXI ) .152 .109 ( IXXI ) -.128 .109 ( xixi ) -.017 .109 ( 1 ) .116 .109 ( III ) -.037 .109 ( 1 ) 146 APPENDIX C SUMMARY OF PARAMETER CALCULATIONS OF  MODELLED ABUSE TOTALS SERIES' ITERATION SUM OF SQUARES PARAMETER VALUES 0 .1417847D+05 .100 .100 1 .7800583D+04 .271 -.071 2 .7146844D+04 .355 -.010 3 .4380606D+04 .682 .226 4 •4106994D+04 .715 .250 5 .2600680D+04 .997 .495 6 .2591730D+04 .980 .482 7 .2557987D+04 .992 .526 8 .2508786D+04 1.000 .606 9 .2478935D+04 .991 .689 10 •2477519D+04 .991 .666 11 •2477389D+04 .991 .670 12 .2477389D+04 .991 .671 13 .2477389D+04 .991 .671 14 .2477389D+04 .991 .671 15 •2477389D+04 .991 .671 16 .2477389D+04 .991 .671 17 .2477389D+04 .991 .671 18 •2477389D+04 .991 .671 FINAL VALUE OF MSE IS 30.21 2 INDEX TYPE ESTIMATE A . S . E . LOWER <95%> UPPER 1 AR 0.991 0.017 0.957 1.025 2 MA 0.671 0.084 0.504 0.837 ASYMPTOTIC CORRELATION MATRIX OF PARAMETERS 1 2 1 1.000 2 0.314 1.000 147 APPENDIX PLOT OF AUTOCORRELATIONS OF RESIDUALS OF  MODELLED ABUSE TOTALS SERIES NUMBER OF CASES = 8 4 MEAN OF SERIES = 0.544 STANDARD DEVIATION OF SERIES = 5.403 LAG COBS SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 «•—-f—-t— -f—-t—• -.043 .109 ( XI .013 .109 ( 1 .016 .109 ( 1 .112 .109 ( I I I -.073 .111 ni n in ( XI 1 1 . UJU .111 -.054 .111 I 1 ( XI -.094 .112 ( x i i .047 .113 ( IX -.013 .113 ( 1 -.049 .113 ( II .048 .113 ( IX -.029 .113 ( 1 .023 .113 ( 1 .106 .114 ( i n .071 .115 ( 11 -.036 .115 ( 1 -.120 .115 ( x i i .116 .117 ( 1X1 -.033 .118 ( 1 .030 .118 ( 1 -.029 .118 ( 1 .001 .118 ( 1 .144 .118 ( m i -.099 .121 ( II I .023 .122 ( 1 -.126 .122 ( m i .066 .123 ( I i -.149 .124 ( m i .056 .126 ( l i .003 .126 ( I .090 .126 ( H i -.137 .127 ( m i -.013 .128 ( 1 .140 .128 ( i m .057 .130 ( IX APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF RESIDUALS OF  ARIMA MODELLED ABUSE TOTALS SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 0.544 STANDARD DEVIATION OF SERIES = 5.403 LAG COBB SB -1.0 -.8 - . ( -.4 -.2 .0 .2 .4 .6 .8 1.0 • - — » — - t — - f -1 -.043 .109 ( II ) 2 .011 .109 ( 1 ) 3 .017 .109 ( 1 ) 4 .113 .109 ( H I ) 5 -.065 .109 ( II ) i .022 .109 ( 1 ) 7 -.056 .109 ( II ) 8 -.111 .109 ( H I ) 9 .057 .109 ( II ) 10 -.016 .109 ( 1 ) 11 -.032 .109 ( 1 ) 12 .061 .109 ( II ) 13 -.049 .109 ( II ) 14 .036 .109 ( 1 ) 15 .107 .109 ( H I ) 16 .057 .109 ( II ) 17 -.007 .109 ( 1 ) 18 -.160 .109 ( H i l l ) 19 .089 .109 ( III ) 20 -.014 .109 ( 1 ) 21 .031 .109 ( 1 ) 22 .022 .109 ( 1 ) 23 -.021 .109 ( 1 ) 24 .182 .109 ( u m ) 25 -.140 .109 ( n i l ) 26 .020 .109 ( 1 ) 27 -.115 .109 ( II I ) 28 .005 .109 ( 1 ) 29 -.099 .109 ( II I ) 30 .019 .109 ( 1 ) 31 .041 .109 ( II ) 32 .128 .109 ( I I I ! ) 33 -.135 .109 ( m l ) 34 -.034 .109 ( 1 ) 35 .134 .109 ( I I I I ) 36 .007 .109 ( 1 ) 149 APPENDIX C PLOT OF AUTOCORRELATIONS OF REGION 19 ABUSE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 4.133 STANDARD DEVIATION OF SERIES = 2.648 LAG COBS SB -1.0 f --.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1. — • — • — * — * — • — * — f — f — f 1 .130 .109 ( U H ) 2 .230 .111 ( i m i ) 3 .190 .116 ( i m x ) 1 .198 .120 ( i n n ) 5 .200 .124 ( i n i n ) 6 .163 .128 ( i x x n ) 7 .157 .130 ( IXXI ) 8 .065 .132 ( I i ) 9 .133 .133 ( U H ) 10 .124 .134 ( i x n ) 11 .052 .136 ( IX ) 12 .149 .136 ( U H ) 13 .012 .138 ( I ) 14 .180 .136 ( u m ) 15 .099 .141 < i n ) 16 .165 .141 ( m n ) 17 .081 .144 ( i n ) 18 .079 .144 ( I I ) 19 .131 .145 ( i m ) 20 -.004 .146 ( i ) 21 .147 .146 ( i x n ) 22 -.093 .148 ( xu ) 23 .025 .149 ( 1 ) 24 .126 .149 < m i ) 25 -.038 .150 ( I ) 26 -.059 .150 ( I I ) 27 -.026 .150 ( 1 ) 28 .042 .150 ( I I ) 29 -.073 .151 ( XI ) 30 .057 .151 ( II ) 31 .010 .151 ( 1 ) 32 .051 .151 ( II ) 33 -.089 .151 ( III ) 34 .021 .152 ( 1 ) 35 .049 .152 ( II ) 36 -.086 .152 ( III ) 150 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF REGION 19 ABUSE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 4.133 STANDARD DEVIATION OF SERIES = 2.648 L i G COBS SB -1.0 -.8 -.6 -.4 -.2 .0 „ i — t — f — f — f — 1 .130 .109 ( I H I 2 .217 .109 ( u m 3 .148 .109 ( m i 4 .130 .109 ( m i 5 .120 .109 ( m i 6 .065 .109 ( II 7 .049 .109 ( II 8 -.053 .109 ( II 9 .030 .109 ( i 10 .045 .109 ( II 11 -.040 .109 ( i 12 .079 .109 ( II 13 -.058 .109 ( II 14 .120 .109 ( i m 15 .048 .109 ( II 16 .090 .109 ( i n 17 -.003 .109 ( i 18 -.018 .109 ( i 19 .033 .109 ( i 20 -.102 .109 ( H I 21 .056 .109 ( II 22 -.178 .109 ( m i l 23 -.029 .109 ( 1 24 .126 .109 ( i m 25 -.057 .109 ( i l 26 -.121 .109 ( I H I 27 .004 .109 ( 1 28 .044 .109 ( II 29 -.064 .109 ( II 30 .048 .109 ( II 31 .014 .109 ( 1 32 .114 .109 ( H I 33 -.188 .109 ( i n n 34 .047 .109 ( II 35 .047 .109 ( II 36 -.099 .109 ( III .2 .4 .6 .8 1.0 151 APPENDIX C PLOT OF AUTOCORRELATIONS OF REGION 13 ABUSE SERIES NUMBER OF CASES = 8 4 MEAN OF SERIES = 4.476 STANDARD DEVIATION OF SERIES = 2.483 ,AG CORE SB -1.0 f - -.8 -.6 -.4 -.2 .0 .2 — t — — f — f — f - -1 .086 .109 ( i n ) 2 .241 .110 ( 11111)1 3 .001 .116 ( 1 ) 4 .239 .116 ( i n " ) 5 -.004 .122 ( I ) 6 .133 .122 ( IHX ) 7 -.019 .123 ( 1 ) 8 .100 .124 ( IXX ) 9 .086 .124 ( IXX ) 10 .059 .125 ( IX ) 11 .043 .126 ( II ) 12 .131 .126 ( U H ) 13 .042 .127 ( II ) 14 -.007 .127 ( 1 ) 15 -.061 .127 ( I I ) 16 -.082 .128 ( III ) 17 -.048 .128 ( II ) 18 -.092 .129 ( III ) 19 -.006 .129 ( 1 ) 20 -.061 .129 ( II ) 21 -.012 .130 ( 1 ) 22 .067 .130 ( II ) 23 .071 .130 ( II ) 24 .092 .131 ( II I ) 25 .071 .131 ( II ) 26 -.030 .132 ( 1 ) 27 -.083 .132 ( II I ) 28 -.040 .133 { 1 ) 29 -.053 .133 ( I I ) 30 -.036 .133 ( 1 ) 31 .072 .133 ( II ) 32 .088 .134 ( II I ) 33 -.011 .134 ( 1 ) 34 .055 .134 ( II ) 35 .097 .135 ( III ) 36 .034 .135 ( 1 ) 152 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF REGION 13 ABUSE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 4.476 STANDARD DEVIATION OF SERIES = 2.483 LAG CORE SE -1.0 -.8 -.6 -.4 -.2 .0 T" 1 .086 .109 ( I H 2 .236 .109 ( u m 3 -.837 .109 ( 1 4 .197 .109 ( u m 5 -.032 .109 ( l 6 .047 .109 ( n 7 -.017 .109 ( 1 8 .02$ .109 ( l 9 .108 .109 ( i n 10 -.020 .109 ( 1 11 .024 .109 ( l 12 .104 .109 ( i n 13 -.021 .109 ( l 14 -.066 .109 ( i i IS -.087 .109 ( m 16 -.110 .109 ( u i 17 -.024 .109 ( 1 18 -.077 .109 ( i i 19 .049 .109 ( II 20 -.012 .109 ( l 21 -.026 .109 ( 1 22 .146 .109 ( U H 23 .062 .109 ( II 24 .101 .109 ( III 25 .073 .109 ( II 26 -.086 .109 ( XII 27 -.089 .109 ( i n 26 -.050 .109 ( II 29 -.043 .109 ( II 30 -.010 .109 ( I 31 .086 .109 ( u i 32 .106 .109 ( i n 33 -.070 .109 ( i i 34 -.007 .109 ( 1 35 .087 .109 ( u i 36 -.059 .109 ( n 153 APPENDIX C PLOT OF AUTOCORRELATIONS OF REGION 12 ABUSE SERIES NUMBER OF CASES = 8 4 MEAN OF SERIES = 3.192 STANDARD DEVIATION OF SERIES = 1.883 CORR SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1 • — f — t - - „ t— f—*—*— f.T„ f— f— .408 .10) ( i n n m u x .340 .126 ( m i n m .450 .136 ( m i i i i m i i .373 .153 ( m i n i m .262 .164 ( m i n i i .281 .168 ( m i n i i ) .288 .174 ( m i n m .232 .180 ( m m ) .232 .183 ( m m ) .280 .187 ( m i n i ) .184 .192 ( u m ) .148 .194 ( I H I ) .168 .195 < u m ) .074 .197 ( II ) .126 .197 ( m i ) .228 .198 < m m ) .115 .201 ( m ) .004 .202 ( i ) .147 .202 < m i ) .175 .203 ( u m i .000 .205 ( i ) .018 .205 ( i ) .061 .205 ( II ) .111 .205 ( m ) .008 .206 ( i ) .021 .206 ( i ) -.036 .206 ( i ) -.083 .206 ( H I ) -.124 .206 ( H U ) -.031 .207 ( 1 ) -.127 .207 ( H U ) -.061 .208 ( II ) -.086 .208 ( H I ) -.071 .209 ( II ) -.011 .209 ( 1 ) -.060 .209 ( II ) 154 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF REGION 12 ABUSE SERIES NUMBER OF CASES = 8 4 MEAN OF SERIES = 3.192 STANDARD DEVIATION OF SERIES = 1.883 L1G CORB SB -1.0 -.8 -.8 -.4 -.2 .0 .2 .4 .6 .8 1.0 f — f -.408 .109 ( m i u i x n x .20) .109 ( m i l ) .320 .109 ( m x i m i .128 .109 ( m i ) -.014 .109 ( 1 ) .028 .109 ( I ) .051 .109 ( IX ) .01) .109 ( l ) .043 .109 ( IX ) .0)4 .109 ( m ) -.048 .109 ( i i ) -.04) .109 ( i i ) -.024 .109 ( I I -.107 .109 ( xn ) .06) .109 ( l i ) .17) .109 < m n ) -.014 .109 < i ) -.165 .109 d i m ) .036 .109 ( i ) .0)2 .109 ( m ) -.067 .109 ( i t ) -.056 .109 ( II ) -.041 .109 ( II ) .154 .109 < m i ) -.051 .109 ( II ) -.086 .109 ( i n ) -.151 .109 < H U ) -.068 .109 ( II ) -.0)7 .109 ( IXI ) .123 .109 ( m i i -.059 .109 ( i i ) .052 .109 ( ix i -.020 .109 i i ) .066 .109 < II ) .046 .109 < II ) -.073 .109 ( II ) 155 APPENDIX C PLOT OF AUTOCORRELATIONS OF RESIDUALS OF  MODELLED REGION 12 ABUSE SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 3.277 STANDARD DEVIATION OF SERIES = 41.442 M COBB SB -1.0 -.8 -.6 -.4 -.2 .0 f — t — f — f — 1 -.123 .no ( m i 2 .059 .111 ( II 3 .064 .112 ( II 4 -.060 .112 ( II 5 .149 .113 ( III I ( .066 .115 ( II 7 .040 .115 ( II $ -.039 .116 ( I 9 .069 .116 ( |I 10 -.103 .116 ( III 11 .088 .117 ( III 12 .032 •118 ( 1 13 .080 .118 ( III 14 .094 .119 ( III 15 -.100 .120 ( III 16 -.020 .121 ( | 17 .089 .121 ( I H 18 .018 .122 ( 1 19 -.064 .122 ( II 20 .045 .122 ( II 21 -.091 .122 ( III 22 .085 .123 ( I I I 23 .003 •124 ( 1 24 -.013 .124 ( 1 25 .077 .124 ( II 26 .113 .124 ( I II 27 -.062 .126 ( II 28 -.066 .126 ( II 29 .118 .126 ( I II 30 -.016 .128 ( | 31 .042 .128 ( II 32 -.035 .128 ( 1 33 -.146 .128 ( II I I 34 -.010 .130 ( 1 35 .039 .130 ( 1 36 -.054 .130 ( II .2 .4 .6 .8 1.0 156 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF RESIDUALS OF  ARIMA MODELLED REGION 12 ABUSE SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 3.277 STANDARD DEVIATION OF SERIES = 41.442 COBB 8B -1.0 -.8 -.6 —~.4 -.2 .0 — f — f — ^ — t — t — -.123 .110 ( m i .044 .110 ( IX .077 .110 ( IX -.047 .110 ( i l .132 .110 ( i m .103 .110 ( i n .054 .110 ( IX -.060 .110 ( II .059 .110 ( ix -.107 .110 ( xn .045 .110 ( IX .027 .110 ( l .115 .110 ( i n .090 .110 ( i n -.065 .110 ( i l -.076 .110 ( it .084 .110 ( i n .009 .110 ( l -.189 .110 ( m -.001 .110 ( 1 -.032 .110 ( 1 .077 .110 ( i i -.002 .110 ( l .015 .118 ( I .052 .110 ( i i .154 .110 ( U H -.069 .110 ( II -.111 .110 ( H I .096 .110 ( III .038 .110 ( 1 -.071 .110 ( XI -.027 .110 ( 1 -.105 .110 ( III -.060 .110 ( II .026 .110 ( 1 -.048 .110 ( II .2 .4 .6 .8 1.0 157 APPENDIX C PLOT OF AUTOCORRELATIONS OF INCOME ASSISTANCE TOTALS SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 5477.548 STANDARD DEVIATION OF SERIES = 993.067 LAG CORK 1 .980 2 .958 SB -1.0 -.8 -.6 -.4 f—-f—-I—--.2 .0 .2 .4 .6 .8 1.0 12 13 18 19 20 .931 .900 .867 .829 .791 .752 .713 10 .669 11 .624 .577 .528 14 .479 15 .430 16 .379 17 .330 .283 .238 .195 21 .156 22 .118 23 .083 24 .052 25 .021 26 -.008 27 -.036 28 -.065 29 -.093 30 -.120 31 -.146 32 -.171 33 -.194 34 -.215 35 -.235 36 -.250 .109 .187 .238 .278 .311 .338 .362 .382 .399 .414 .427 .437 .446 .454 .460 .464 .468 .471 .473 .474 .475 .476 .476 .476 .476 .476 .476 .476 .477 .477 .477 .478 .478 .479 .481 .482 —I.—|.— f—|.— t—t ( i i i i n i i i i i i n m i i i i i i i i ( IIIXXIXXX'IXIXXIIIXXXXXI IIXXIIXXXIXIXIXXXXXIXIIX IXXXIXIXIIXXDXXIIXXXXX IIXXXXXXXXXXXXDXXXXIX |IXXXXIXXXXIIXXX)IXXX IXXXIIXIIIIIIIXIXDX immmmxxmx) l i imxxmmmi) IXXXXXXXIXXXXXXXI ) I m i n i m u m ) IXXIIXXXXIXXXIX ) I m u m I I m ) IXXXIXXXIXXX ) lixxxxxxxxx i m m m l i i i i m i ixxxxxxx IXXXXX IXXXX I I I I III III IX XI XXI XII XXXI m i l xxxil m i n nun m i n i ) 158 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF INCOME ASSISTANCE TOTAL SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 5477.548 STANDARD DEVIATION OF SERIES = 993.067 COBS SB -1.0 -.8 -.6 -.4 -.2 .0 - - t — t — f — f — f - -.980 .109 ( H I -.071 .109 ( II -.139 .109 ( nil -.111 .109 ( in -.052 .109 ( il -.096 .109 ( in -.009 .109 ( 1 -.030 .109 ( 1 -.005 .109 ( 1 -.118 .109 ( ui -.073 .109 ( il -.029 .109 ( 1 -.085 .109 ( ui -.022 .109 ( 1 .004 .109 ( 1 -.052 .109 ( il .005 .109 ( 1 .012 .109 ( 1 .007 .109 ( 1 .014 .109 ( 1 .067 .109 ( Ii -.013 .109 ( 1 -.002 .109 ( 1 .026 .109 ( 1 -.026 .109 ( 1 -.025 .109 ( 1 -.028 .109 ( 1 -.078 .109 ( il -.047 .109 ( il -.041 .109 ( il -.019 .109 ( 1 -.027 .109 ( 1 -.019 .109 ( 1 .010 .109 ( 1 -.016 .109 ( 1 .051 .109 ( Ii 2 .4 .6 .8 1.0 —-f—-f—-»— - i I I I I I I I I I I I I I I I I I H 159 APPENDIX C SUMMARY OF PARAMETER CALCULATIONS FOR MODELLED  INCOME ASSISTANCE TOTALS SERIES ITERATION SUM OF SQUARES PARAMETER VALUES 0 .6320089D+06 .100 1 .5942913D+06 .222 2 .5748852D+06 .393 3 .5748852D+06 .393 4 .5748852D+06 .393 FINAL VALUE OF MSE IS 7010.795 INDEX TYPE ESTIMATE A . S . E . LOWER <95%> UPPER 1 SAR 0.393 0.102 0.189 0.596 160 APPENDIX C PLOT OF AUTOCORRELATIONS PLOT OF RESIDUALS OF  MODELLED INCOME ASSISTANCE TOTALS SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 14.314 STANDARD DEVIATION OF SERIES = 81.984 LAG CORE SE -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1 1 .055 .110 ( U ) 2 -.021 .110 ( 1 1 3 .134 .110 ( IIIX ) 1 -.173 .112 (XXXII ) 5 .231 .115 ( um) 6 .218 .121 ( mm) 7 -.005 .125 ( i j 8 -.066 .125 ( n ) 9 -.004 .126 ( i ) 10 -.121 .126 ( IIII ) 11 .070 .127 ( II ) 12 .362 .128 ( miiimi 13 -.011 .140 ( i ) H -.023 .140 ( i ) IS -.049 .140 ( XI ) 16 -.197 .140 (mn ) 17 .223 .143 ( mm) 18 .053 .147 ( II ) 19 -.065 .147 ( II ) 20 -.022 .148 ( i ) 21 -.277 .148 (mini ) 22 -.056 .154 ( II ) 23 .152 .154 ( mi ) 24 .053 .156 ( II ) 25 .047 .156 ( II ) 26 .015 .156 ( i ) 27 -.095 .156 ( in ) 28 -.066 .157 ( n ) 29 .158 .157 ( mi ) 38 .010 .159 ( I ) 31 .048 .159 ( II ) 32 -.074 .160 ( XI ) 33 -.312 .160 ( m i n i ) 34 -.054 .167 ( il ) 35 .049 .167 ( ii ) 36 .053 .167 ( li ) 161 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS PLOT OF RESIDUALS  OF ARIMA MODELLED INCOME ASSISTANCE TOTALS SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 14.314 STANDARD DEVIATION OF SERIES = 81.984 LAG CORE SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 f. f ^ f 1. .055 .110 ( II ) -.025 .110 ( 1 ) .137 .110 ( i m ) -.194 .110 ( i n n ) .282 .110 ( u m ) i i .150 .110 ( i m ) .039 .110 ( I ) -.186 .110 ( m i l ) .076 .110 ( l i ) -.159 .110 ( m i ) .067 .110 ( l i ) .300 .110 ( I I I I D U .045 .110 ( II ) -.072 .110 ( II ) -.088 .110 ( III ) -.095 .110 ( III ) .109 .110 ( III ) -.120 .110 ( m i ) .010 .110 ( I ) -.041 .110 ( i l ) -.173 .110 ( i n n ) .003 .110 ( 1 ) .151 .110 ( i m ) -.028 .110 ( I ) .028 .110 ( I ) .082 .110 ( i n ) .087 .110 ( i n ) -.114 .110 ( HI ) .008 .110 ( 1 I -.004 .110 ( 1 ) .061 .110 ( II ) -.198 .110 (XXXI| ) -.042 .110 ( II ) -.103 .110 ( III ) .002 .110 i 1 ) .023 .110 ( 1 ) 162 APPENDIX C PLOT OF AUTOCORRELATIONS OF REGION 19 INCOME ASSISTANCE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 2132.440 STANDARD DEVIATION OF SERIES = 401.842 LAG COBB SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 .975 .1 09 ( IX i i n m i i i i i m i m m i .952 .1 86 ( 11 mmmmmmxm .925 .2 37 ( IX IIII I I I I D I I I I I I I I I I I I .894 .2 77 { IX mmmiDximim .8(0 09 ( IX m m i m i i D i i i m .821 .: 36 ( 11 m i m i m m i m i .783 59 [ 11 m i n i m u m )ii .744 .] 79 ( IX mmmiumi) .703 .'. 96 ( IX m m i i i i m m i .659 A U ( 11 m m i m i m i ) .814 A 23 ( 11 m i m u i m i ) .570 A 34 ( 11 m n i u i m i ) .522 .' 42 ( IX m u i i i i m ) .473 50 ( II u m i i i i i ) .426 A 56 ( 11 i i m u i i ) .378 (0 ( 11 i i i i m i ) .330 .< 64 ( 11 m i n i ) .285 A 67 ( 11 m m ) .242 A 69 ( |1 u m ) .282 A 70 ( 11 m i ) .166 A 71 ( 11 m ) .129 72 ( |1 II ) .095 A .067 A !33 ! ii 1 j .036 A .007 A 73 1 ! j -.018 A 73 ( 1 ) -.045 A 73 ( XI I -.072 A 73 ( 11 1 -.098 A 73 ( XXI ) -.122 A 73 ( XXXI j -.144 74 ( XXII ) -.165 174 ( m i l j -.186 A 75 ( mil ) -.205 .4 76 ( IIIIII ) -.219 A 77 ( IIIIII l 163 APPENDIX PLOT OF PARTIAL AUTOCORRELATIONS OF REGION 19  INCOME ASSISTANCE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 2132.440 STANDARD DEVIATION OF SERIES = 401.842 COBS SB -1.0 -.8 -.6 -.4 -.2 .0 „ t — t — * — t — .975 .109 ( III .004 .109 ( 1 -.069 .109 ( II -.112 .109 ( -III -.085 .109 ( H I -.099 .109 ( H I -.014 -.006 .109 .109 ( 1 ( 1 -.033 .109 ( 1 -.107 .109 ( H I -.033 .109 ( 1 -.008 .109 ( 1 -.108 .109 ( III -.036 .109 ( 1 .043 .109 ( II -.059 .109 ( II -.036 .109 ( 1 .026 .109 ( 1 .041 .109 ( II .008 .109 ( 1 .051 .109 ( II -.067 .028 .109 .109 ( II ( 1 .053 .109 ( II -.088 .109 ( H I .005 .109 ( 1 .009 • .109 ( 1 -.075 .109 ( II -.064 .109 ( II -.033 .109 ( 1 .008 -.009 .109 .109 ( 1 ( 1 -.038 .109 ( 1 -.012 .109 ( 1 -.004 .109 ( 1 .039 .109 ( 1 .2 .4 .6 .8 1.0 I I I I I I I I I I I I I I I I I I I I APPENDIX C SUMMARY OF PARAMETER CALCULATIONS FOR MODELLED  REGION 19 INCOME ASSISTANCE SERIES ITERATION SUM OF SQUARES PARAMETER VALUES 0 .1289736D+06 .100 1 .1285781D+06 -.863 2 .1009155D+06 -.645 3 .9296118D+05 -.447 4 .9278346D+05 -.415 5 .9278052D+05 -.410 6 .9278052D+05 -.410 7 .9278052D+05 -.410 8 .9278052D+05 -.410 FINAL VALUE OF MSE IS 1325.436 INDEX TYPE ESTIMATE A . S . E . LOWER <95%> UPPER 1 SMA -0.410 0.099 -0.607 -0.213 165 APPENDIX C PLOT OF AUTOCORRELATIONS OF RESIDUALS OF  MODELLED REGION 19 INCOME ASSISTANCE SERIES NUMBER OF CASES = 71 MEAN«OF SERIES = 0.676 STANDARD DEVIATION OF SERIES = 36.143 LAG CORK SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 f f — f — * — f — i — f . „ . I I m m n I I I I I I I I I I I I I I I I I I I I I I ) m i n I I ) i n ) m n ) m n ) n i n n n 166 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF RESIDUALS OF ARIMA MODELLED REGION 19 INCOME ASSISTANCE SERIES NUMBER OF CASES = 71 MEAN OF SERIES = 0.676 STANDARD DEVIATION OF SERIES = 36.143 LAG COBB -.009 .256 .107 .100 .178 .236 -.167 -.120 -.109 -.097 -.051 -.293 .108 .064 .064 -.098 .022 .056 -.113 -.007 .050 -.080 .097 -.138 .104 .013 .135 .013 .008 -.161 -.099 -.053 -.094 -.047 .111 -.123 -1.0 -.8 -.6 -.4 -f . — I — . —i-... 2 .0 .2 .4 .6 .8 1.1 XX I IXXXI) III I I I I I I I I ) IXXXI) XIII | III I I I I III II I I I I I III II II III II I I I II III III I I I I III I I I I I I I m i l n i il n i il Hi m i APPENDIX C PLOT OF AUTOCORRELATIONS OP REGION 13 INCOME ASSISTANCE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 2217.881 STANDARD DEVIATION OF SERIES = 394.731 LAG COBB SB -l.( -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 f-1 .983 .109 ( iiiiDimmmmimxi 2 .964 .187 ( imnm) m i n i m u m 3 .940 .239 ( l i m m m i m m m m 4 .911 .279 ( i m m m m i m m m 5 .880 .313 ( l i x i i i i i i i i i x x u i x x i i x 6 .847 .341 ( IIXXXIXIXIXXIXXIDIIIX 7 .812 .365 ( IIIIXXIXIIIIXXIXIXIXI 8 .776 .386 ( IXXIXXXXXXXIXXXXXIX) 9 .739 .404 ( IXXXIXXXXXXXXXXXXIX ) 10 .698 .420 ( l i m m i m m m ) 11 .654 .434 ( IXXXXXXXXXIXXIIXI ) 12 .608 .445 ( i m m m m m ) 13 .560 .455 ( i m n m m m ) 14 .511 .463 ( IIXXIXXXIIXXX ) 15 .462 .470 ( l i m m i m ) 16 .412 .475 ( IIXXIIXXIIX ) 17 .363 .479 ( IXXIXXIXXX ) 18 .315 .483 IXXXXIXI ) 19 .268 .485 IXXXXXX ) 20 .223 .487 IXXXXI ) 21 .181 .488 IXIXX ) 22 .140 .489 IXIX ) 23 .101 .489 IXX ) 24 .064 .498 II ) 25 .030 .490 1 ) 26 -.002 .490 1 ) 27 -.033 .490 1 ) 28 -.064 .490 XI ) 29 -.093 .490 xxi ) 30 -.122 .490 XXXI ) 31 -.149 .490 IXXI ) 32 -.176 .491 mil ) 33 -.200 .492 XXXIX| ) 34 -.223 .493 mm ) 35 -.244 .494 IXXXXI1 ) 36 -.260 .495 XXIXXXI ) 168 APPENDIX PLOT OF PARTIAL AUTOCORRELATIONS OF REGION 13  INCOME ASSISTANCE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 2217.881 STANDARD DEVIATION OF SERIES = 394.731 LAG CORE SB -1.0 -.8 -.6 -.4 -.2 .0 1 .983 .109 ( III 2 -.070 .109 ( XI 3 -.171 .109 (IXXXI 4 -.140 .109 ( XXXI 5 -.042 .109 ( II 6 -.031 .109 ( 1 7 -.049 .109 ( II 8 -.035 .109 ( 1 5 -.014 .109 < 1 10 -.120 .109 ( H U 11 -.135 .109 ( I I I I 12 -.043 .109 ( II 13 -.051 .109 ( II 14 -.028 .109 ( 1 15 .004 .109 ( 1 18 -.032 .109 ( 1 17 -.005 .109 ( 1 18 -.031 .109 ( 1 19 -.002 .109 ( 1 20 .061 .109 ( II 21 .053 .109 ( II 22 -.018 .109 ( 1 23 -.024 .109 ( 1 24 .023 .109 -•• ( 1 25 .044 .109 ( IX 26 -.040 .109 ( 1 27 -.028 .109 ( 1 28 -.039 .109 ( 1 29 -.036 .109 { 1 30 -.065 ,.109 ( XI 31 -.027 .109 ( 1 32 -.069 .109 ( II 33 .047 .109 ( II 34 -.021 .109 ( 1 35 -.026 .109 ( 1 36 .075 .109 ( II •f i—-f * 1 X I I I I I I I I I I I X X I I I I I APPENDIX C SUMMARY OF PARAMETER CALCULATIONS FOR MODELLED  REGION 13 INCOME ASSISTANCE SERIES ITERATION SUM OF SQUARES PARAMETER VALUES 0 .1081542D+06 .100 1 .1041121D+06 .392 2 .1033027D+06 .308 3 .1033027D+06 .308 4 .1033027D+06 .308 FINAL VALUE OF MSE IS 1259.789 INDEX TYPE ESTIMATE A . S . E . LOWER <95%> UPPER 1 SAR 0.308 0.106 0.097 0.518 170 APPENDIX C PLOT OF AUTOCORRELATIONS OF RESIDUALS OF  MODELLED REGION 13 INCOME ASSISTANCE SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 6.275 STANDARD DEVIATION OF SERIES = 34.717 LAG CORE SE -1.0 -.8 -.6 -.4 -.2 .0 .2 A .8 .8 1.0 f — t — f — » - - - f — • — 1 -1 .079 .110 ( II ) 2 .235 .110 ( m n ) 3 -.127 .116 ( IIII ) 4 -.040 .118 ( i ) 5 .075 .118 ( II ) 6 .220 .119 ( m n ) 7 .103 .124 ( m ) 8 .041 .125 < II ) 9 -.073 .125 ( II ) 10 -.036 .125 ( i ) 11 .036 .125 ( i ) 12 .246 .125 ( m m ) 13 .076 .131 ( II ) 14 -.112 .132 ( i n ) 15 -.045 .133 ( II ) 16 -.143 .133 ( m i ) 17 .126 .135 ( m i ) 18 .064 .136 ( i i ) 19 .022 .137 ( 1 ) 20 -.072 .137 ( i l ) 21 -.190 .137 ( m n ) 22 -.122 23 -.018 :!!! 1 n n ( I 24 .004 25 .077 1 I ( l i 26 -.141 .142 ( m i 27 .003 .144 ( I 28 -.074 .144 ( i l 29 .166 .144 ( u m 30 -.047 .146 ( i l 31 .003 .147 ( I 32 -.132 .147 ( m i 33 -.175 .148 ( m n 34 -.099 .151 ( H I 35 -.003 .151 ( 1 36 .021 .151 ( 1 171 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF RESIDUALS OF ARIMA MODELLED REGION 13 INCOME ASSISTANCE SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 6.275 STANDARD DEVIATION OF SERIES = 34.717 •AG CORE SE -1.0 -.8 -.6 -.4 -.2 .0 —^—fr—|.—^— 1 .079 .110 ( II 2 .230 .110 ( u m 3 -.170 .110 ( m u 1 -.077 .110 ( n 5 .171 .110 ( u m ( .233 .110 ( u m 7 -.015 .110 ( l 1 -.075 .110 ( i l 9 -.021 .110 ( 1 10 .031 .110 ( 1 11 .036 .110 ( l 12 .200 .110 ( u m 13 -.014 .110 ( 1 14 -.288 .110 I K I I I I I 15 .064 .110 ( U 16 .066 .110 ( l i 17 .060 .110 ( l i 18 -.079 .110 ( i l 19 -.104 .110 ( i n 20 -.002 .110 ( I 21 -.099 .110 ( in 22 -.038 .110 ( 1 23 .018 .110 ( I 24 -.122 .110 ( m i 25 .040 .110 ( l i 28 .004 .110 ( l 27 .100 .110 ( i n 28 .020 .110 ( 1 29 .119 .110 ( i n 30 -.148 .110 ( m i 31 -.067 .110 ( i l 32 .025 .110 ( I 33 -.085 .110 ( n i 34 -.101 .110 ( i n 35 -.040 .110 ( i l 36 .061 .110 ( I i .2 .4 .6 .8 1.0 fr—f—|.—f.—j 172 PLOT OF AUTOCORRELATIONS OF REGION 12 INCOME ASSISTANCE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 1127.226 STANDARD DEVIATION OF SERIES = 205.975 L1G COBB SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1 1 .981 .109 ( U I I D I I I I U I I I I I X I I I I U I 2 .931 .184 ( IX ummmumxiuu 3 .897 .234 ( IX minm) m i n i m i 4 .860 .271 ( IX m u m i m m u m 5 .824 .302 ( |X i m i m i m i umi 6 .781 .328 ( IX u m u u m m m 7 .736 .349 ( IX uuummuDx 8 .687 .367 1 IX mumumui) 9 .644 .382 ( IX m i n i m u m ) 10 .595 .395 ( IX l U I U I I I I I I I ) 11 .549 .406 ( IX U X X I I I I I I I I ) 12 .500 .414 I IX m i n i m i ) 13 .448 .421 ( IX m i i m i i ) H .394 .427 { IX i l i u m ) 15 .338 .431 ( |X m i n i ) 16 .284 .434 ( |X u m i ) 17 .235 .437 ( IX m i ) 18 .188 .438 ( |X m ) 19 .141 .439 ( |X I I ) 20 .099 .440 ( IX i ) 21 .063 .440 ( IX l 22 .034 .440 ( 1 ) 23 .004 .440 ( 1 1 24 -.020 .440 ( 1 j 25 -.041 .440 ( II j 28 -.062 .440 ( XI j 27 -.087 .440 ( III 1 28 -.112 .440 ( XXI I 29 -.137 .441 ( XIII ) 30 -.162 .441 ( mil 1 31 -.188 .442 ( mil j 32 -.213 .443 ( mm ) 33 -.237 .444 ( mm ) 34 -.252 .446 ( mini ) 35 -.267 .447 ( m i n i ) 36 -.284 .449 ( mum 1 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF REGION 12  INCOME ASSISTANCE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 1127.226 STANDARD DEVIATION OF SERIES = 205.975 LAG COBB SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 f—-f—-t—-f— 4-—». f — * — — 1 .961 .109 ( iiiinxxixxmixxiiixxiii 2 .090 .109 ( in ) 3 -.060 .109 ( H ) 4 -.054 .109 ( XI ) 5 -.023 .109 ( I 1 8 -.112 .109 ( xii ) 7 -.069 .109 ( il ) 8 -.071 .109 ( H ) 9 .039 .109 ( I ) 10 -.076 .109 ( il ) 11 -.006 .109 ( 1 ) 12 -.060 .109 ( il ) 13 -.070 .109 ( il ) 14 -.076 .109 ( il ) 15 -.069 .109 ( il ) 16 -.016 .109 ( I ) 17 .031 .109 ( I ) 18 .020 .109 ( 1 ) 19 -.021 .109 ( 1 ) 20 .026 .109 ( I ) 21 .057 .109 ( li ) 22 .066 .109 ( li ) 23 -.050 .109 ( il ) 24 .050 .109 ( li ) 25 .020 .109 ( 1 ) 26 -.037 .109 ( I ) 27 -.116 .109 ( in ) 28 -.064 .109 ( il ) 29 -.047 .109 ( il ) 30 -.065 .109 ( il ) 31 -.079 .109 ( il ) 32 -.015 .109 ( 1 ) 33 -.035 .109 ( I ) 34 .078 .109 ( li ) 35 -.016 .109 ( I ) 36 -.060 .109 ( il ) 174 APPENDIX PLOT OF AUTOCORRELATIONS OF RESIDUALS OF  MODELLED REGION 12 INCOME ASSISTANCE SERIES NUMBER OF CASES = 8 3 MEAN OF SERIES = 3.277 STANDARD DEVIATION OF SERIES = 41.442 CORP. SE -1.0 -.8 -.6 -.4 -.2 .0 -.123 .110 ( HXI .059 .111 ( II .064 .112 ( II -.060 .112 ( II .149 .113 I i m .066 .115 ( 11 .040 .115 ( II -.039 .116 ( | .069 .116 ( II -.103 .116 ( III .088 .117 ( H I .032 .118 ( | .080 .118 ( H I .094 .119 ( H I -.100 .120 ( H I -.020 .121 ( | .089 .121 ( H I .018 .122 ( | -.064 .122 ( II .045 .122 ( II -.091 .122 ( H I .085 not .123 ( III .UUJ -.013 !l24 ! ! .077 .124 < II .113 .124 t in -.062 .126 t i i -.066 .126 < II .118 .126 t u i -.016 .128 t i .042 .128 ( II -.035 .128 i i -.146 .128 ( HU -.010 .130 ( | .039 .130 ( | -.054 .130 ( II .2 .4 .6 .8 1.0 4 — f — f — f — f APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF RESIDUALS OF ARIMA MODELLED REGION 12 INCOME ASSISTANCE SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 3.277 STANDARD DEVIATION OF SERIES = 41.442 .16 CORK SB -1.0 f--.8 -.6 -.4 -.2 .0 1 -.123 .110 ( mi 2 .044 .110 ( IX 3 .077 .110 ( IX 4 -.047 .110 ( il 5 .132 .110 ( im 6 .103 .110 ( in 7 .054 .110 ( li 1 -.060 .110 ( II 9 .059 .110 ( li 10 -.107 .110 ( xxi 11 .045 .110 ( IX 12 .027 .110 ( 1 13 .115 .110 ( III 14 .090 .110 ( III 15 -.065 .110 ( II 16 -.076 .110 ( II 17 .084 .110 ( III 18 .009 .110 - ( 1 19 -.109 .110 ( III 20 -.001 .110 ( 1 21 -.032 .110 ( 1 22 .077 .110 ( II 23 -.002 .110 ( 1 24 .015 .110 ( 1 25 .052 .110 ( IX 26 .154 .110 ( IIII 27 -.069 .110 ( II 28 -.111 .110 ( III 29 .096 .110 ( III 30 .038 .110 ( 1 31 -.071 .110 ( II 32 -.027 .110 ( 1 33 -.105 .110 ( III 34 -.060 .110 ( II 35 .026 .110 ( 1 36 -.048 .110 ( II .2 .4 .6 .8 1.0 I.—|.—f—t—t 176 APPENDIX PLOT OF AUTOCORRELATIONS OF LABOUR FORCE SERIES NUMBER OF CASES = MEAN OF SERIES = STANDARD DEVIATION 84 632428.571 SERIES = 31861.040 COBB SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1 .917 . 109 ( H I i D i m m m i m m .836 . 179 I III i m n m m m m .731 . 220 ( III i m i i i D i m m .833 . 248 ( III i m i m n u i .550 . 266 ( III mmmi) .481 . 279 ( III mmmi) .439 . 289 ( III m i m i ) .423 . 297 ( III m u m ) .441 . 304 ( III I I I U U I I ) .460 . 311 I III i u i u i i i ) .478 . 319 ( III m i m i i ) .498 . 328 ( III mmmi ) .466 . 337 ( III I I I I I I U I ) .413 . 344 ( III m u m ) .339 . 350 ( III m m ) .265 . 354 ( III m i ) .179 . 356 ( III II ) .102 . 357 ( H I ) .041 . 358 ( II .001 . 356 ( | l -.020 . 358 ( | ) -.032 . 358 ( | l -.060 . 358 ( II ) -.095 . 358 ( III j -.145 . 358 ( IIII l -.194 . 359 ( mil l -.250 . 360 ( mull ) -.293 . 362 ( mmil )• -.328 . 365 ( I mum ) -.361 . 368 ( n mum ) -.365 . 373 ( I I mmil ) -.376 . 377 ( II muni ) -.366 . 381 ( II mmil ) -.353 . 385 ( I mmil ) -.345 . 389 I I mmil ) -.337 . 393 { I mmil ) APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF LABOUR FORCE SERIES NUMBER OF CASES = 8 4 MEAN OF SERIES = 632428.571 STANDARD DEVIATION OF SERIES = 31861.040 LAG COBB SB -1.0 -.8 -.6 -.4 -.2 .0 1 .917 .109 ( u m 2 -.039 .109 ( 1 3 -.186 .109 u m i 4 -.021 .109 ( l S .051 .109 ( u 6 .037 .109 ( I 7 .099 .109 ( ux 8 .130 .109 ( i m 9 .179 .109 ( u m 10 .001 .109 ( I 11 -.018 .109 ( I 12 .021 .109 ( I 13 -.168 .109 u m i 14 -.165 .109 ( i n n 15 -.076 .109 ( i l 16 .035 .109 ( I 17 -.109 .109 ( i n 18 -.061 19 .007 .109 .109 ( i l ( I 20 .008 .109 ( I 21 -.062 .109 ( i l 22 -.076 .109 ( XI 23 -.184 .109 d i m 24 -.119 .109 ( xn 25 -.146 .109 ( m i 26 .031 .109 ( I 27 -.001 .109 ( I 28 .066 .109 ( l i 29 .057 .109 ( II 30 -.046 .109 ( XI 31 .084 .109 ( ux 32 -.133 .109 ( m i 33 .026 .109 ( 1 34 .034 .109 ( 1 35 .023 .109 ( l 36 .097 .109 ( i n 2 .4 .6 .8 1.0 —t—«.—^—t IIIIIIIIIXIIIIIII APPENDIX C PLOT OF AUTOCORRELATIONS OF RESIDUALS  OF MODELLED LABOUR FORCE SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 638.554 STANDARD DEVIATION OF SERIES = 11077.578 LAG CORE SE -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 f — f — * — f — . f f — f — f . . . . f . — j 1 .091 .110 ( i n ) 2 .144 .111 ( i m ) 3 -.050 .113 ( II ) 4 -.147 .113 ( IIII ) 5 -.145 .115 ( I I I I ) 8 -.265 .118 m i n i ) 7 -.141 .125 ( n i l 8 -.138 .126 ( m i S .063 .128 ( l i 10 .123 .129 I m i 11 .101 .130 ( i n 12 .179 .131 i i n n 13 .182 .134 i m n 14 .023 .137 ( i 15 -.053 .137 i i i 18 -.022 .137 ( i 17 -.059 .137 ( II 18 -.129 .138 ( m i 19 -.065 .139 ( n 28 -.019 .139 ( l 21 -.045 .139 ( XI 22 .162 .140 ( m n 23 .045 .142 ( l i 24 .209 .142 ( m m 25 .081 .146 ( m 26 -.044 .146 ( i l 27 -.129 .146 ( m i 28 -.134 .148 ( m i 29 -.031 .149 ( I 30 -.141 .149 ( m i 31 .024 .151 ( I 32 -.039 .151 ( 1 33 .006 .151 ( I 34 .050 .151 ( l i 35 .060 .151 ( Ii 36 .129 .151 ( m i 179 APPENDIX PLOT OF PARTIAL AUTOCORRELATIONS OF RESIDUALS  OF ARIMA MODELLED LABOUR FORCE SERIES NUMBER OF CASES = 83 MEAN OF SERIES * 638.554 STANDARD DEVIATION OF SERIES = 11077.578 LAG CORB SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .( .8 1.0 f—-f— - f — f — t — f . . . . f . . . . f — 1 .091 .110 ( III ) 2 .137 .110 ( I I H ) 3 -.076 .110 ( XI ) 4 -.161 .110 ( m i l ) 5 -.108 .110 I XXI ) ( -.218 .110 (XXXII ) 7 -.105 .110 ( I I I ) 8 -.110 .110 ( III ) 9 .045 .110 ( II ) 10 .066 .110 ( II ) 11 -.014 .110 ( 1 ) 12 .061 .110 ( II ) 13 .134 .110 ( I I I I ) 14 -.039 .110 ( 1 ) 15 -.056 .110 ( II ) 16 .083 .110 ( III ) 17 .066 .110 ( II ) 18 -.056 .110 ( II ) 19 .008 .110 ( 1 ) 20 .052 .110 ( II ) 21 -.061 .110 ( I I ) 22 .117 .110 ( I I I ) 23 .009 .110 ( 1 ) 24 .169 .110 ( IIIXX) 25 .039 .110 ( 1 ) 26 -.123 .110 ( I I I I ) 27 -.119 .110 ( III ) 28 -.004 .110 ( 1 ) 29 .032 .110 ( 1 ) 30 -.059 .110 ( II ) 31 .074 .110 ( II ) 32 -.065 .110 ( II ) 33 -.134 .110 ( I I I I ) 34 -.079 .110 ( II ) 35 -.008 .110 ( 1 ) 38 .088 .110 ( I I I ) PLOT OF AUTOCORRELATIONS OF UNEMPLOYMENT RATE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 10.868 STANDARD DEVIATION OF SERIES = 3.008 COBB SB -1.0 -.8 -.6 -.4 - .2 .0 .2 .4 .6 .8 .918 .109 ( HI [ D m m m m i i m .848 .179 ( IH (HH)HHimiim .786 .222 ( IH [HIIIIDIIIIIIII .714 .253 ( IH [IIIUHDHHI .636 .276 ( |H [HHIHUIH .562 .293 ( |H minimi) .495 .305 ( |XX m m m i ) .431 .315 ( IH H I I I I I I ) .378 .321 ( IH i i i i m ) .322 .327 ( IH m m ) .267 .330 ( IH i m ) .225 .333 I |H H I ) .180 .335 ( | U H ) .131 AAA .336 ( III i 1 .VOU .052 '.337 ( | .021 .337 ( | -.009 -.007 :!!! ! ! j -.008 -.021 :!!! ! ] ] -.034 .337 ( i ) -.052 .337 ( II j -.072 .337 ( II ) -.081 .337 ( HI l -.106 .338 ( HI j -.115 .338 ( HI j -.150 .338 ( Hit ) -.157 .339 { IIII ) -.171 .346 ( Hill I -.192 .341 ( Hil l I -.210 .342 ( m i n ) -.228 .344 ( m i n ) -.253 .346 ( m m i l -.283 .348 ( m m i l ) -.302 .351 ( I I X I I I n 1 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS OF UNEMPLOYMENT RATE SERIES NUMBER OF CASES = 84 MEAN OF SERIES = 10.868 STANDARD DEVIATION OF SERIES = 3.008 LAG COBS SB -1.0 -.8 -.6 -.4 -.2 .0 .2 .4 .6 .8 1.0 t f 4 1 f f 4. 1. 1._—f f m x i i i i n i x i n i i i .918 .109 ( u m .040 .109 ( 1 .011 .109 ( 1 -.090 .109 ( HI -.084 .109 ( HI -.031 .109 ( 1 -.005 .109 ( 1 -.012 .109 ( 1 .038 .109 ( 1 -.057 .109 ( XI -.040 .109 ( XI .032 .109 ( 1 -.043 .109 ( II -.061 .109 ( II -.065 .109 ( II .088 .109 ( HI -.013 .109 ( 1 -.019 .109 ( 1 .161 .109 ( u m -.004 .109 ( 1 -.098 .109 ( III -.056 .109 ( II -.072 .109 ( II -.026 .109 ( 1 .058 .109 ( II -.107 .109 ( III .115 .109 ( III -.227 .109 ( H i l l .139 .109 ( II I I -.063 .109 ( II -.058 .109 ( II -.042 .109 ( II -.045 .109 ( II -.054 .109 ( II -.041 .109 ( II -.004 .109 ( 1 182 APPENDIX PLOT OF AUTOCORRELATIONS OF RESIDUALS OF  MODELLED UNEMPLOYMENT RATE SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 0.059 STANDARD DEVIATION OF SERIES = 0.975 LAG CORE -.049 .063 .090 -.043 -.066 -.014 -.032 .070 -.002 -.113 .023 .126 -.035 -.120 .057 .091 -.199 .009 .109 .013 .071 .060 .057 .061 -.108 .126 -.219 .053 .047 .014 -.004 .017 .109 -.041 .014 -1.0 -.8 t — -.6 -.4 -.2 .0 f — f — f — III II II III II III I .2 .4 - f — f -II III I I I I I I I I [| II III mil in I Ii Ii li Ii HI i m ( m m li li i n i l .6 .8 1.0 APPENDIX C PLOT OF PARTIAL AUTOCORRELATIONS PLOT OF RESIDUALS OF ARIMA MODELLED UNEMPLOYMENT RATE SERIES NUMBER OF CASES = 83 MEAN OF SERIES = 0.059 STANDARD DEVIATION OF SERIES = 0.975 CORE SE -1.0 -.8 -.6 -.4 -.2 .0 t — — f — f - - "t—f—--.090 .110 ( III -.058 .110 ( II .053 .110 ( II .099 .110 ( III -.020 .110 ( 1 -.089 .110 ( III -.046 .110 ( II -.051 .110 ( II .081 .110 ( III .031 .110 ( 1 -.105 .110 ( III -.013 .110 ( 1 .101 .110 ( III .001 .110 ( 1 -.091 .110 ( III .014 .110 ( 1 .067 .110 ( II -.175 .110 (mil .002 .110 ( 1 .112 .110 ( III .035 .110 ( 1 .089 .110 ( III .079 .110 ( II .071 .110 ( II .057 .110 ( II -.173 .110 (mil .162 .110 ( um -.185 .110 (mn -.015 .110 ( I .072 .110 ( li .108 .110 ( in .030 .110 ( 1 -.051 .110 ( il .111 .110 { in .029 .110 ( l -.094 .110 ( H I 184 

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