Comparing personal trajectories and drawing causal inferences from longitudinal data.

This review considers statistical analysis of data from studies that obtain repeated measures on each of many participants. Such studies aim to describe the average change in populations and to illuminate individual differences in trajectories of change. A person-specific model for the trajectory of each participant is viewed as the foundation of any analysis having these aims. A second, between-person model describes how persons very in their trajectories. This two-stage modeling framework is common to a variety of popular analytic approaches variously labeled hierarchical models, multilevel models, latent growth models, and random coefficient models. Selected published examples reveal how the approach can be flexibly adapted to represent development in domains as diverse as vocabulary growth in early childhood, academic learning, and antisocial propensity during adolescence. The review then considers the problem of drawing causal inferences from repeated measures data.

Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change.

Consider a study in which 2 groups are followed over time to assess group differences in the average rate of change, rate of acceleration, or higher degree polynomial effect. In designing such a study, one must decide on the duration of the study, frequency of observation, and number of participants. The authors consider how these choices affect statistical power and show that power depends on a standardized effect size, the sample size, and a person-specific reliability coefficient. This reliability, in turn, depends on study duration and frequency. These relations enable researchers to weigh alternative designs with respect to feasibility and power. The authors illustrate the approach using data from published studies of antisocial thinking during adolescence and vocabulary growth during infancy.

Tests for linkage of multiple cohorts in an accelerated longitudinal design.

In accelerated longitudinal design, one samples multiple age cohorts and then collects longitudinal data on members of each cohort. The aim is to study age-outcome trajectories over a broad age span during a study of short duration. A threat to valid inference is the Age x Cohort interaction effect. S. W. Raudenbush and W. S. Chan (1993) developed a test for such interactions in the context of 2 cohorts by using a hierarchical model. The current article extends this approach to include any number of cohorts. Using the National Youth Survey, the authors combine data collected on 7 cohorts over 5 years to approximate change in antisocial attitudes between 11 and 21 years of age. They show how to test for cohort differences in trajectories, how to calculate the power of the test, and how to use graphical procedures to aid understanding. The approach allows unbalanced designs and the clustering of participants within families, neighborhoods, or other social units.

Statistical power and optimal design for multisite randomized trials.

The multisite trial, widely used in mental health research and education, enables experimenters to assess the average impact of a treatment across sites, the variance of treatment impact across sites, and the moderating effect of site characteristics on treatment efficacy. Key design decisions include the sample size per site and the number of sites. To consider power implications, this article proposes a standardized hierarchical linear model and uses rules of thumb similar to those proposed by J. Cohen (1988) for small, medium, and large effect sizes and for small, medium, and large treatment-by-site variance. Optimal allocation of resources within and between sites as a function of variance components and costs at each level are also considered. The approach generalizes to quasiexperiments with a similar structure. These ideas are illustrated with newly developed software.

Measurement and structural models for children's problem behaviors.

This article considers an analytic strategy for measuring and modeling child and adolescent problem behaviors. The strategy embeds an item response model within a hierarchical model to define an interval scale for the outcomes, to assess dimensionality, and to study how individual and contextual factors relate to multiple dimensions of problem behaviors. To illustrate, the authors analyze data from the primary caregiver ratings of 2,177 children aged 9-15 in 79 urban neighborhoods on externalizing behavior problems using the Child Behavior Checklist 4-18 (T. M. Achenbach, 1991a). Two subscales, Aggression and Delinquency, are highly correlated, and yet unidimensionality must be rejected because these subscales have different associations with key theoretically related covariates.

Assessing exposure to violence in urban youth.

This study reports on the development of a structured interview, My Exposure to Violence (My ETV), that was designed to assess child and youth exposure to violence. Eighty participants between the ages of 9 and 24 were assessed. Data from My ETV were fit to a Rasch model for rating scales, a technique that generates interval level measures and allows the characterization of both chronic and acute exposure. Results indicated that the fit statistics for six scales, covering both lifetime and past year victimization, witnessing of violence, and total exposure, were all good. These scales were found to have high internal consistency (r = .68 to .93) and test-retest reliability (r = .75 to .94). Evidence of construct validity was provided by the item analysis, which revealed a theoretically sensible ordering of item extremity, and also by analysis of bivariate associations. As expected, younger subjects generally reported less exposure to violence than did older subjects, males reported more exposure than did females, African-American subjects reported higher levels of exposure than did White subjects, violent offenders reported more exposure than did non-offenders, and those living in high crime areas reported more exposure than did those residing in low crime areas. Future areas of investigation and the potential contribution to studies of antisocial behavior and post-traumatic stress disorder are discussed.

Neighborhoods and violent crime: a multilevel study of collective efficacy.

It is hypothesized that collective efficacy, defined as social cohesion among neighbors combined with their willingness to intervene on behalf of the common good, is linked to reduced violence. This hypothesis was tested on a 1995 survey of 8782 residents of 343 neighborhoods in Chicago, Illinois. Multilevel analyses showed that a measure of collective efficacy yields a high between-neighborhood reliability and is negatively associated with variations in violence, when individual-level characteristics, measurement error, and prior violence are controlled. Associations of concentrated disadvantage and residential instability with violence are largely mediated by collective efficacy.

Change in job and marital experiences and change in psychological distress: a longitudinal study of dual-earner couples.

Are changes in job quality more closely linked to changes in distress for men than for women? Conversely, are changes in marital quality more closely linked to changes in distress for women than for men? These questions were addressed in a longitudinal analysis of a random sample of 210 full-time employed dual-earner couples. Change over time in job role quality was significantly associated with change over time in distress, and the magnitude of the relationship differed little, if at all, by gender. In contrast, change over time in marital role quality was also associated with change in distress, but the magnitude of the association depended on gender. Among full-time employed married women, change in marital experience was more closely linked to change in distress than among their husbands.

Application of a hierarchical linear model to the study of adolescent deviance in an overlapping cohort design.

Hierarchical linear models provide a conceptual orientation and a flexible set of analytic techniques for studying psychological change in repeated measures studies. The researcher first formulates a model for individual change over time, with each individual's development characterized by a unique set of parameters. These parameters are then viewed as varying randomly over the population of persons. We illustrate this approach with data on attitudes toward deviance during adolescence (Raudenbush & Chan, 1992), indicating how one may assess the psychometric properties of an instrument for studying change, compare the adequacy of linear and curvilinear growth models, control for time invariant and time-varying covariates, and link overlapping cohorts of data. The results suggest that prodeviant attitudes characteristically increase during early adolescence, achieving a peak between 17 and 18 years of age. The typical trajectories for male and female adolescents have the same shape, although female adolescents tend to be less deviant than male adolescents at each age. We briefly consider the statistical power of tests of cohort differences at the points where they overlap.

Gender and the relationship between job experiences and psychological distress: a study of dual-earner couples.

This article examines the association between job role quality and psychological distress in a sample of 300 full-time employed dual-earner couples, controlling for such individual level variables as age, education, occupational prestige, and marital quality and for such couple level variables as length of marriage, parental status, and household income. The magnitude of this effect is compared for men and for women. Results indicate that job role quality is significantly negatively associated with psychological distress for women as well as for men and that the magnitude of the effect depends little, if at all, on gender, casting doubt on the widely held view that job experiences more significantly influence men's mental health states than women's. The results are discussed in the context of differentiating between sex differences and gender differences.

Neurobehavioral outcomes in diseases of childhood. Individual change models for pediatric human immunodeficiency viruses.

The growing incidence of human immunodeficiency virus-1 (HIV-1) and acquired immunodeficiency syndrome (AIDS) in children is a major public health problem. Current research emphasizes treatments for ameliorating deleterious effects on the child's neurological and behavioral development. This article outlines approaches to the assessment of individual change that may provide alternatives to more traditional approaches to the assessment of neurobehavioral outcomes in children with chronic diseases. These approaches provide more precise conceptualizations of changes that lead directly to statistical designs and measurement strategies for assessing effects of HIV-1 and AIDS on development. Such assessments can be superimposed on current clinical trial methodologies to evaluate the efficacy of pharmacological and behavioral interventions designed to improve quality of life in HIV-1 infected children.