title: Examining heterogeneity in residual variance to detect differential response to treatments.
abstract: Individual differences in response to treatments have been a long-standing interest in education, psychology, and related fields. This article presents a conceptual framework and hierarchical modeling strategies that may help identify the subgroups for whom, or the conditions under which, a particular treatment is associated with better outcomes. The framework discussed in this article shows how differences in residual dispersion between treatment and control group members can signal omitted individual characteristics that may interact with treatments (Bryk & Raudenbush, 1988) and sensitizes us to individual- and cluster-level confounders of inferences concerning dispersion in quasi-experimental studies in multilevel settings. Based on the framework, hierarchical modeling strategies are developed to uncover interactions between treatments and individual characteristics, which are readily applicable to various settings in multisite evaluation studies. These strategies entail jointly modeling the mean and dispersion structures in hierarchical models. We illustrate the implementation of this framework through fully Bayesian analyses of the data from a study of the effectiveness of a reform-minded mathematics curriculum.
authors.affiliation: National Center for Research on Evaluation, Standards, and Student Testing, University of California, Los Angeles, 300 Charles E. Young Drive North, GSE & IS Building, 3rd Floor, Mailbox 951522, Los Angeles, CA 90095-1522, USA. jinok@ucla.edu
authors.forename: Jinok
authors.initials: J
authors.lastname: Kim
authors.forename: Michael
authors.initials: M
authors.lastname: Seltzer
mesh_terms: D000124:Achievement; D000704:Analysis of Variance; D001499:Bayes Theorem; D002648:Child; D016000:Cluster Analysis; D003479:Curriculum; D006801:Humans; D007206:Individuality; D008433:Mathematics / Q000193:education*; D017145:Models, Educational; D015233:Models, Statistical; D011340:Problem Solving; D011588:Psychology, Educational / Q000706:statistics & numerical data*; D011594:Psychometrics / Q000706:statistics & numerical data*; D012107:Research Design / Q000706:statistics & numerical data*