Stephen W. Raudenbush

Application of hierarchical linear models to assessing change.

Recent advances in the statistical theory of hierarchical linear models should enable important breakthroughs in the measurement of psychological change and the study of correlates of change. A two-stage model of change is proposed here. At the first, or within-subject stage, an individuals status on some trait is modeled as a function of an individual growth trajectory plus random error. At the second, or between-subjects stage, the parameters of the individual growth trajectories vary as a function of differences between subjects in background characteristics, instructional experiences, and possibly experimental treatments. This two-stage conceptualization, illustrated with data on Head Start children, allows investigators to model individual change, predict future development, assess the quality of measurement instruments for distinguishing among growth trajectories, and to study systematic variation in growth trajectories as a function of background characteristics and experimental treatments.

Relationship Between Urban Sprawl and Physical Activity, Obesity, and Morbidity

Purpose. To determine the relationship between urban sprawl, health, and health-related behaviors. Design. Cross-sectional analysis using hierarchical modeling to relate characteristics of individuals and places to levels of physical activity, obesity, body mass index (BMI), hypertension, diabetes, and coronary heart disease. Setting. U.S. counties (448) and metropolitan areas (83). Subjects. Adults (n = 206,992) from pooled 1998, 1999, and 2000 Behavioral Risk Factor Surveillance System (BRFSS). Measures. Sprawl indices, derived with principal components analysis from census and other data, served as independent variables. Self-reported behavior and health status from BRFSS served as dependent variables. Results. After controlling for demographic and behavioral covariates, the county sprawl index had small but significant associations with minutes walked (p = .004), obesity (p < .001), BMI (p = .005), and hypertension (p = .018). Residents of sprawling counties were likely to walk less during leisure time, weigh more, and have greater prevalence of hypertension than residents of compact counties. At the metropolitan level, sprawl was similarly associated with minutes walked (p = .04) but not with the other variables. Conclusion. This ecologic study reveals that urban form could be significantly associated with some forms of physical activity and some health outcomes. More research is needed to refine measures of urban form, improve measures of physical activity, and control for other individual and environmental influences on physical activity, obesity, and related health outcomes.

Seeing Disorder: Neighborhood Stigma and the Social Construction of "Broken Windows".

This article reveals the grounds on which individuals form perceptions of disorder. Integrating ideas about implicit bias and statistical discrimination with a theoretical framework on neighborhood racial stigma, our empirical test brings together personal interviews, census data, police records, and systematic social observations situated within some 500 block groups in Chicago. Observed disorder predicts perceived disorder, but racial and economic context matter more. As the concentration of minority groups and poverty increases, residents of all races perceive heightened disorder even after we account for an extensive array of personal characteristics and independently observed neighborhood conditions. Seeing disorder appears to be imbued with social meanings that go well beyond what essentialist theories imply, generating self-reinforcing processes that may help account for the perpetuation of urban racial inequality.

Ecometrics: Toward a Science of Assessing Ecological Settings, With Application to the Systematic Social Observation of Neighborhoods

This paper considers the quantitative assessment of ecological settings such as neighborhoods and schools. Available administrative data typically provide useful but limited information on such settings. We demonstrate how more complete information can be reliably obtained from surveys and observational studies. Survey-based assessments are constructed by aggregating over multiple item responses of multiple informants within each setting. Item and rater inconsistency produce uncertainty about the setting being assessed, with definite implications for research design. Observation-based assessments also have a multilevel error structure. The paper describes measures constructed from interviews, direct observations, and videotapes of Chicago neighborhoods and illustrates an “ecometric” analysis—a study of bias and random error in neighborhood assessments. Using the observation data as an illustrative example, we present a three-level hierarchical statistical model that identifies sources of error in aggregating across items within face-blocks and in aggregating across face-blocks to larger geographic units such as census tracts. Convergent and divergent validity are evaluated by studying associations between the observational measures and theoretically related measures obtained from the U.S. Census, and a citywide survey of neighborhood residents

A Hierarchical Model for Studying School Effects.

When researchers investigate how school policies, practices, or climates affect student outcomes, they use multilevel, hierarchical data. Though methodologists have consistently warned of the formidable inferential problems such data pose for traditional statistical methods, no comprehensive alternative analytic strategy has been available. This paper presents a general statistical methodology for such hierarchically structured data and illustrates its use by reexamining the High School and Beyond data and the controversy over the effectiveness of public and Catholic schools. The model enables the researcher to utilize mean achievement and certain structural parameters that characterize the equity in the social distribution of achievement as multivariate outcomes for each school. Variation in these school-level outcomes is then explained as a function of school characteristics.

Social Anatomy of Racial and Ethnic Disparities in Violence

We analyzed key individual, family, and neighborhood factors to assess competing hypotheses regarding racial/ethnic gaps in perpetrating violence. From 1995 to 2002, we collected 3 waves of data on 2974 participants aged 8 [corrected] to 25 years living in 180 Chicago neighborhoods, augmented by a separate community survey of 8782 Chicago residents. The odds of perpetrating violence were 85% higher for Blacks compared with Whites, whereas Latino-perpetrated violence was 10% lower. Yet the majority of the Black-White gap (over 60%) and the entire Latino-White gap were explained primarily by the marital status of parents, immigrant generation, and dimensions of neighborhood social context. The results imply that generic interventions to improve neighborhood conditions and support families may reduce racial gaps in violence.

Resources, Instruction, and Research

Many researchers who study the relations between school resources and student achievement have worked from a causal model, which typically is implicit. In this model, some resource or set of resources is the causal variable and student achievement is the outcome. In a few recent, more nuanced versions, resource effects depend on intervening influences on their use. We argue for a model in which the key causal agents are situated in instruction; achievement is their outcome. Conventional resources can enable or constrain the causal agents in instruction, thus moderating their impact on student achievement. Because these causal agents interact in ways that are unlikely to be sorted out by multivariate analysis of naturalistic data, experimental trials of distinctive instructional systems are more likely to offer solid evidence on instructional effects.

Statistical analysis and optimal design for cluster randomized trials.

In many intervention studies, therapy outcome evaluations, and educational field trials, random treatment assignment of clusters rather than persons is desirable for political feasibility, logistics, or ecological validity. However, cluster randomized designs are widely regarded as lacking statistical precision. This article considers when and to what extent using a pretreatment covariate can increase experimental precision. To answer this question, the author first optimizes allocation of resources within and between clusters for the no-covariate case. Optimal sample sizes at each level depend on variation within and between clusters and on the cost of sampling at each level. Next, the author considers optimal allocation when a covariate is added. In this case, the explanatory power of the covariate at each level becomes highly relevant for choosing optimal sample sizes. A key conclusion is that statistical analysis that fully uses information about the covariate-outcome relationship can substantially increase the efficiency of the cluster randomized trial, especially when the cost of sampling clusters is high and the covariate accounts for substantial variation between clusters. Recent multilevel studies indicate that these conditions are common.

The Estimation of School Effects

The increasing public demand to hold schools accountable for their effects on student outcomes lends urgency to the task of clarifying statistical issues pertaining to studies of school effects. This article considers the specification and estimation of school effects, the variability of effects across schools, and the proportion of variation in student outcomes attributable to differences in school context and practice. We present a statistical model that defines two different types of school effect: one appropriate for parents choosing schools for their children, the second for agencies evaluating school practice. Studies of both types of effect are viewed as quasi-experiments posing formidable obstacles to valid causal inference. A multilevel decomposition of variance within and between schools has important and perhaps counterintuitive implications for school evaluation. The potential for unbiased estimation depends on the type of effect under consideration because the two types of school effect have markedly different data requirements. Commonly used estimators of each effect are shown to be biased and, in some cases, inconsistent. Analyses of survey data from Scotland illustrate the recommended techniques. We conclude with a brief discussion of the role of school evaluation in a broader agenda of research in support of school improvement.

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.