Multi-Level Effects on Behaviour Outcomes in Canadian Children - May 2001

2.2 Method

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To investigate the research questions proposed, these analyses use Cycle One (Release Three) of the National Longitudinal Survey of Children and Youth (NLSCY) gathered in Canada in 1994-95. The research design of this data source is first briefly described, followed by an overview of the analytical techniques and measurement of variables that are used in these analyses.

2.2.1 Research Design

The NLSCY is a nationally representative prospective longitudinal sample of newborns through eleven year old children in Canada. A complex sampling design was developed by Statistics Canada to identify dwellings with eligible children for inclusion in this study (HRDC/STC, 1997, p. 239). Households with children in the appropriate age range were first selected from an area frame. Once eligible households were selected, procedures were followed to randomly select one target child in the 0-11 year old age range who lived a majority of time in the household. Other children in the same economic family as the target child, up to a maximum of four children in the eligible age range per household, were also selected. The final NLSCY sample includes 13,439 household and 22,831 children, with a response rate of 86.3%. The "share file" (HRDC/STC, 1997) used for these analyses includes 21,455 of the 22,831 children (94%) of those included in the "master file". These analyses use information on the child provided by the person most knowledgeable about the child (PMK) and census variables appended to the NLSCY files to measure the children's neighbourhoods.

2.2.2 Analyses

The research objectives of this report are addressed through linking the macro- (e.g., neighbourhood and family) and micro- (e.g., child) levels of analysis. This linkage is accomplished through the use of multi-level regression modelling techniques (DiPrete & Forristal, 1994). Multilevel models also address the statistical complexities that arise when children live in the same family and/or neighbourhood, as in the NLSCY where observations were gathered through a complex sampling design (see also Boyle & Lipman, 1998; Tremblay et al., 1996). The individual observations in these circumstances are generally not completely independent as is assumed in standard statistical tests (Hox, 1995, p. 6; see also HRDC/STC, 1997, p. 167), due to common influences from residing in the same location (Ross, 2000, p. 179). Ordinary least squares regression in such circumstances can produce too liberal estimates of standard errors yielding seemingly statistically significant results that are not significant (Bryk & Raudenbush, 1992, p. 86; Hox, 1995, p. 7; Kreft & De Leeuw, 1998, p. 9-10; Murray, 1998, p. 81).

The hierarchical linear models used child population weights normalized per individuals in the respective analyses. The population weight assigned to a child "reflects the number of children represented by a particular respondent" (HRDC/STC, 1997, p. 163). For analyses where statistical significance tests are required, sample weights are used (HRDC/STC, 1997, p. 163). The effective sample size is retained in these analyses with the use of a normalized weight, while generating unbiased population estimates for generalizing to a national population of children in Canada in this age range (HRDC/STC, 1997, p. 84). Coefficients reported in the results section follow the "normal rounding technique" described in the NLSCY User's documentation (HRDC/STC, 1997, p. 162).

These analyses use the HLM software to assess multilevel models of neighbourhood and family effects on childhood aggression (Bryk, Raudenbush, & Congdon, 1996). In this section, the three level hierarchical linear model is briefly presented. Model assumptions and hypothesis testing procedures are also briefly described.

The first model considered is a one-way ANOVA with random effects (see Bryk & Raudenbush, 1992, p. 17-18). This model is used to assess childhood aggression among siblings nested in families, who are further nested in census tracts. This unconditional three level random intercept model can be represented by three equations (Bryk & Raudenbush, 1992, p. 176-177):

In the first equation, the aggression score of a child _i in family _j and census tract _k is predicted and is represented by Y_ijk The level two model which is presented in equation two, in turn examines the level one intercepts as outcomes . Pi subscripted with (_ojk) indicates the mean level of aggression for family _i in census tract _k. Finally, e_ijk is the random "child effect", or the deviation of the child's score from the family mean level of aggression. The assumptions of the level one model are that the level one errors (e_ijk) are normally distributed with a mean of zero and a constant variance at level one,

The second equation indicates that the family level mean is a randomly varying outcome around a tract mean. is the tract level mean on childhood aggression, and r_ojk is a random "family effect", indicating the deviation of the family (_jk's) mean from the tract level mean. These effects (r_ojk) are assumed normally distributed with a mean of zero and a variance of , which is assumed within census tracts to have a similar variance among the families (see Bryk & Raudenbush, 1992, p. 176-177). The random effect at level two is assumed be normally distributed with a mean of zero and a variance of . The term random effects is used with this model as the group effects are considered random.

Finally, the third equation indicates the variability in childhood aggression between census tracts. The census tract level means randomly vary around a grand mean . The random census tract effect is indicated by u_ook, which is the deviation of the census tract k's mean from the grand mean. These random effects are also assumed normally distributed with a mean of zero and a variance of (see Bryk & Raudenbush, 1992, p. 177).

The variance in the individual level outcome is comprised of three components and with the first tau parameter in this list indicating the between-family variability, the second tau parameter indicating the between-tract level variability, and the sigma squared indicating the within-group or between-individual variances respectively (Bryk & Raudenbush, 1992, p. 17). The intraclass correlation for estimating the proportion of variance in the individual level outcome that is between census tracts is derived by the following formula:

The hierarchical linear model can be expanded to include covariates at the three levels of analysis (Bryk & Raudenbush, 1992, p. 19,23). In the tables that follow, the covariates are listed and indicated at what level they were incorporated into the model. The models assessed are random intercepts models with multiple independent variables (see also Bryk & Raudenbush, 1992, p. 23). These latter coefficients are generally considered fixed.

The research design of the NLSCY is "unbalanced" in the sense that there are differing numbers of children (level 1 units) per level two units (families) and families per three level units (census tracts). Under these circumstances, maximum likelihood procedures may be used to achieve estimation of the variance/covariance components of the model (Bryk & Raudenbush, 1992, p. 44). Model fit is assessed by two procedures: the model deviance statistic and the variance components. The model fitting process uses multiparameter hypothesis tests involving comparative reductions in the deviance (indicating an improvement in fit) between models with the same sample size, testing for a statistically significant reduction compared to the change in the parameters between models using the critical values of the chi-square distribution (Appendix B of Knoke & Bohrnstedt, 1994, p. 509; see also Bryk & Raudenbush, 1992, p. 58-59). The variance explained at each level of analysis is also examined. With centered variables, these levels should decrease or stay the same (Snijders & Bosker, 1999; Thomese & Van Tilburg, 2000; Willms, personal communication). Single parameter T-tests are also used to assess the significance of the fixed effects in the models in the form of p-values indicating whether the effect (gamma) is significantly different from zero.

The proportion of variance explained in hierarchical linear models takes into account how the variance in the individual level outcome is partitioned across levels. Variables entered into the models at level two can only explain variance at that level (Bryk & Raudenbush, 1992, p. 94), or that "only the parameter variance or , is explainable" (p. 94). Therefore, a model may show that very little of the total variance in childhood aggression is explained by neighbourhood features, but may instead show that a sizeable proportion of the available variance has been explained through these characteristics. As Bryk and Raudenbush (1992) indicate, attention to this difference can lead to quite different conclusions regarding the substantive implications of research using higher level variables in hierarchical linear models. Later analyses in this report examine several features of hierarchical linear modelling, including model fit, the change in the random variance components across models, the variance explained, and patterns of fixed effects across models.

2.2.3 Measurement

The items used to measure direct physical aggression for 4-11 year olds were included in the NLSCY from the Montreal Longitudinal Survey and the Ontario Child Health Study (HRDC/STC, 1995, p. 41). The person most knowledgeable about the child was asked how often would you say your child: 1) Gets into many fights?; 2) When another child accidentally hurts her/him (such as bumping into her/him), assumes that the other child meant to do it, and reacts with anger and fighting?; 3) Physically attacks people?; 4) Threatens people?; 5) Is cruel, bullies, or is mean to others?; 6) Kicks, bites, hits other children? (Cronbach's ) (HRDC/STC, 1998, p. 167, 170-204; Tremblay et al., 1996). Three items were also asked of younger children's physical aggression, permitting the inclusion of two through eleven year olds in some analyses. These are items one, six, and two from the above listing; which were summed to create a score of physical aggression for two to eleven year olds. The response scale of 1-3 was recoded to 0-2, with higher scores indicating a higher frequency of the behaviour.

The five items used to measure indirect aggression for 4-11 year olds in the NLSCY were drawn from the work of Lagerspetz et al. (1988). The person most knowledgeable about the child was asked: How often would you say your child: 1) When mad at someone, tries to get others to dislike that person?; 2) When mad at someone, becomes friends with another as revenge?; 3) When mad at someone, says bad things behind the other's back?; 4) When mad at someone, says to others: let's not be with her/him?; 5) When mad at someone, tells the other one's secrets to a third person? (Cronbach's ; HRDC/STC, 1998, p. 170-204; Tremblay et al., 1996).

The person most knowledgeable about the child rated childhood behaviour on up to four children per household. Although high within family correlations may be obtained due to a common reporter, parental reports have been found to be reliable for aggression. Parents may be the best informed about the child's behaviour across a range of contexts (see Tremblay et al., 1996, p. 129). These results also control for a measure of PMK depression that may influence their perceptions of children's behaviours (see McLeod & Shanahan, 1993).

Several approaches to neighbourhood measurement were used in this study. One set of analyses used the results obtained by Law and Willms (1998) from a cluster analysis of six features of enumeration areas from the 1991 Canadian Census: median income, average number of years of education, percentage of youth that were employed, percentage of adults that were employed, percent non-immigrant population, and percent two-parent families. These researchers found eight types of neighbourhoods characterized enumeration areas in Canada. These types reflect a combination of the six characteristics but show ordinality from Type One to Eight in terms of mean socioeconomic status (Law & Willms, 1998). The combinations of salient characteristics that define each type are listed in later tables. The neighbourhood types were operationalized as dummy variables, with Type Six, or Middle Class environments serving as the reference category. These characteristics were entered at the family level of analysis. An average of three families in the national analyses were located per census tract.

The second set of analyses with highly clustered families in this report used characteristics of the ninety six census tract units with more highly clustered families. These tract characteristics include the percentage of low income families and the size of the population in the census tract.

Subjective perceptions of physical and social neighbourhood problems were also used in these analyses. The national results use a scale constructed by Statistics Canada from five items rated by the PMK including: "How much of a problem is the following in the neighbourhood": 1) garbage, litter, or broken glass in the street or road, on the sidewalks, or in yards; 2) selling or using drugs; 3) alcoholics and excessive drinking in public?; 4) groups of young people who cause trouble; 5) burglary of home or apartments? A high score on this scale indicates higher levels of problems with an observed range of 0-10 () (Barnes McGuire, 1997; HRDC/STC, 1998, p. 374-375). A subscale with items two, three, and four measuring social disorder was used to measure the subjective neighbourhood operationalizing perceived social disorder (see Skogan, 1990) in the clustered subsample analyses.

Finally, in addition to children's gender (female=1, and male=0) and age, both family structural and processual features are included in these analyses to measure aspects of the family context (see Rutter et al., 1998; Sampson & Laub, 1995). Measures of the home environment also include parenting practices (see Landy & Tam, 1996). Three parenting measures were used in these analyses as a second order confirmatory factor analyses indicated that hostile and punitive parenting were highly interrelated. A measure of the PMK's rating of the child's exposure to violence in the home was also included. The PMK's symptoms of depression were assessed through a shortened version of the Centre for Epidemiological Studies Scale (CES-D) () (Radloff, 1977). Control variables include family socioeconomic status (see HRDC/ STC, 1997, Appendix 3, p. 114-116; Tremblay et al., 1996), family structure (e.g. single parent, two parents-blended family, and two biological parents) (see Avison, 1999a), the age of the biological mother at her first birth (see Nagin, Pogarsky, & Farrington, 1997), the number of siblings in the household, whether the dwelling was owned by a member of the household, and residential crowding (see Rutter et al., 1998; Sampson & Laub, 1995). These controls facilitate comparisons of children in similar families living in different neighbourhoods (Jencks & Mayer, 1990, p. 119). Descriptive statistics on the childhood aggression measures and risk factors used in these analyses are presented in Appendix Tables A.1 and A.2. The HLM analyses use the zero point of a dummy variable or a standardized variable; otherwise grand mean centering was used.

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