An Empirical Evaluation of the Disaggregated Effects of Educational Diversity in a National Sample of Law Schools

The use of race-conscious admissions practices to achieve student diversity in academic institutions has recently been challenged. An understanding of how racial diversity in law school affects students is useful to develop administrative policies that support social and intellectual growth of students after they are admitted. A nationally-representative sample of 2,180 students from 64 accredited U.S. law schools was used to model the mechanism through which institutional diversity may influence student outcomes in a multigroup, multilevel SEM framework. Results suggest that racial heterogeneity directly and indirectly increases exchange of ideas and decreases racist/classist attitudes. The effects of racial diversity were mediated by increased contact with racially diverse peers. Results were similar for White and non-White students. This study confirms the usefulness of admissions policies that permit racial diversity in academic institutions, and imply that educators should focus on increasing intergroup contact between students

Evaluating shared parameter mixture models for analyzing change in the presence of non-randomly missing data

Longitudinal researchers have been slow to adopt models for assessing the sensitivity of their results to potentially non-randomly missing data, opting instead to rely exclusively on more traditional approaches to modeling growth like latent curve modeling (LCM). Implicit in this choice is the strict assumption that missing data are missing at random (MAR). Failure to meet this assumption leads to inaccurate inferences regarding growth. A number of models for assessing the impact of non-randomly missing data on growth trajectory estimates have been presented over the past quarter century. These models are briefly discussed, and a new variation on some recently developed models is introduced. The shared parameter mixture model (SPMM) described here is preferable to some other models for a few reasons. Most notably, it approximates the dependence between the missing data process and the repeated measures without requiring an explicit specification of the missingness mechanism while simultaneously allowing conditional independence between the growth model and the missing data. Performance of the SPMM is evaluated using simulation methodology across a range of plausible missingness mechanisms and across a range of longitudinal data conditions. SPMM performs well when the missing data mechanism is either latent class- or growth coefficient- dependent. Fixed effect recovery is more robust than variance component recovery. The SPMM performs best with longer observation lengths and with erratically spaced missing data than with dropout. Finally, this manuscript illustrates how the SPMM might be used in practiceby analyzing change over time in psychological symptoms of patients enrolled in psychotherapy. Results are generally encouraging for SPMM performance under a range of simulated data conditions, and for feasibility with real data. Researchers who suspect the presence of random coefficient-dependent missing data are urged to consider using the SPMM to assess sensitivity of their model results to the MAR assumption

Explicating the Conditions Under Which Multilevel Multiple Imputation Mitigates Bias Resulting from Random Coefficient-Dependent Missing Longitudinal Data

Random coefficient dependent (RCD) missingness is a non-ignorable mechanism through which missing data can arise in longitudinal designs. RCD, for which we cannot test, is a problematic form of missingness that occurs if subject-specific random effects correlate with propensity for missingness or dropout. Particularly when covariate missingness is a problem, investigators typically handle missing longitudinal data by using single-level multiple imputation procedures implemented with long-format data, which ignores within-person dependency entirely, or implemented with wide-format (i.e., multivariate) data, which ignores some aspects of within-person dependency. When either of these standard approaches to handling missing longitudinal data is used, RCD missingness leads to parameter bias and incorrect inference. We explain why multilevel multiple imputation (MMI) should alleviate bias induced by a RCD missing data mechanism under conditions that contribute to stronger determinacy of random coefficients. We evaluate our hypothesis with a simulation study. Three design factors are considered: intraclass correlation (ICC; ranging from .25 to .75), number of waves (ranging from 4 to 8), and percent of missing data (ranging from 20% to 50%). We find that MMI greatly outperforms the single-level wide-format (multivariate) method for imputation under a RCD mechanism. For the MMI analyses, bias was most alleviated when the ICC is high, there were more waves of data, and when there was less missing data. Practical recommendations for handling longitudinal missing data are suggested

Parental involvement protects against self-medication behaviors during the high school transition

We examined how drinking patterns change as adolescents transition to high school, particularly as a function of parental involvement. Stress associated with the transition to high school may deplete psychological resources for coping with negative daily emotions in an environment when opportunities to drink are more common. A cohort of elevated-risk middle school students completed daily negative affect (sadness, worry, anger, and stress) and alcohol use assessments before and after the transition to high school, resulting in a measurement burst design. Adolescents who reported less parental involvement were at higher risk for drinking on any given day. After (but not before) the transition to high school, daily within-person fluctuations of sadness predicted an increased probability of same-day alcohol use for adolescents who reported that their parents were minimally involved in their lives. The other negative affect indicators were not predictive of use. Our results suggest that the transition to high school may represent an important intervention leverage point, particularly for adolescents who lack adequate parental support to help them cope with day-to-day changes in sadness

Sample Size Considerations in Prevention Research Applications of Multilevel Modeling and Structural Equation Modeling

When the goal of prevention research is to capture in statistical models some measure of the dynamic complexity in structures and processes implicated in problem behavior and its prevention, approaches such as multilevel modeling (MLM) and structural equation modeling (SEM) are indicated. Yet the assumptions that must be satisfied if these approaches are to be used responsibly raise concerns regarding their use in prevention research involving smaller samples. In this manuscript we discuss in nontechnical terms the role of sample size in MLM and SEM and present findings from the latest simulation work on the performance of each approach at sample sizes typical of prevention research. For each statistical approach, we draw from extant simulation studies to establish lower bounds for sample size (e.g., MLM can be applied with as few as 10 groups comprising 10 members with normally distributed data, restricted maximum likelihood estimation, and a focus on fixed effects; sample sizes as small as N = 50 can produce reliable SEM results with normally distributed data and at least three reliable indicators per factor) and suggest strategies for making the best use of the modeling approach when N is near the lower bound

Drinking to Dampen Affect Variability: Findings From a College Student Sample

We hypothesized that individuals who are unable to effectively regulate emotional reactivity, which we operationalized as variability in self-reported affect throughout the day, would use alcohol more frequently and would report higher levels of drinking to cope. Further, we hypothesized that affect variation would be a stronger predictor of alcohol use or drinking to cope than level of negative affect

Modeling Change in the Presence of Nonrandomly Missing Data: Evaluating a Shared Parameter Mixture Model

In longitudinal research, interest often centers on individual trajectories of change over time. When there is missing data, a concern is whether data are systematically missing as a function of the individual trajectories. Such a missing data process, termed random coefficient-dependent missingness, is statistically non-ignorable and can bias parameter estimates obtained from conventional growth models that assume missing data are missing at random. This paper describes a shared-parameter mixture model (SPMM) for testing the sensitivity of growth model parameter estimates to a random coefficient-dependent missingness mechanism. Simulations show that the SPMM recovers trajectory estimates as well as or better than a standard growth model across a range of missing data conditions. The paper concludes with practical advice for longitudinal data analysts

The epidemiology of observed temperament: Factor structure and demographic group differences

This study investigated the factor structure of observational indicators of children’s temperament that were collected across the first three years of life in the Family Life Project (N = 1205) sample. A four-factor model (activity level, fear, anger, regulation), which corresponded broadly to Rothbart’s distinction between reactivity and regulation, provided an acceptable fit the observed data. Tests of measurement invariance demonstrated that a majority of the observational indicators exhibited comparable measurement properties for male vs. female, black vs. white, and poor vs. not-poor children, which improved the generalizability of these results. Unadjusted demographic group comparisons revealed small to moderate sized differences (Cohen ds = |.23 – .42|) in temperamental reactivity and moderate to large sized differences (Cohen ds = −.64 – −.97) in regulation. Collectively, demographic variables explained more of the variation in regulation (R2 = .25) than in reactivity (R2 = .02 – .06). Follow-up analyses demonstrated that race differences were substantially diminished in magnitude and better accounted for by poverty. These results help to validate the distinction between temperamental reactivity and regulation using observational indicators

Maximizing the Yield of Small Samples in Prevention Research: A Review of General Strategies and Best Practices

The goal of this manuscript is describe strategies for maximizing the yield of data from small samples in prevention research. We begin by discussing what “small” means as a description of sample size in prevention research. We then present a series of practical strategies for getting the most out of data when sample size is small and constrained. Our focus is the prototypic between-group test for intervention effects; however, we touch on the circumstance in which intervention effects are qualified by one or more moderators. We conclude by highlighting the potential usefulness of graphical methods when sample size is too small for inferential statistical methods

Analyzing repeated measures data on individuals nested within groups: Accounting for dynamic group effects.

Researchers commonly collect repeated measures on individuals nested within groups such as students within schools, patients within treatment groups, or siblings within families. Often, it is most appropriate to conceptualize such groups as dynamic entities, potentially undergoing stochastic structural and/or functional changes over time. For instance, as a student progresses through school more senior students matriculate and more junior students enroll, administrators and teachers may turn over, and curricular changes may be introduced. What it means to be a student within that school may thus differ from one year to the next. This paper demonstrates how to use multilevel linear models to recover time-varying group effects when analyzing repeated measures data on individuals nested within groups that evolve over time. Two examples are provided. The first example examines school effects on the science achievement trajectories of students, allowing for changes in school effects over time. The second example concerns dynamic family effects on individual trajectories of externalizing behavior and depression