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Evaluating differential effects using regression interactions and regression mixture models

Research output: Contribution to journalJournal article

Published
  • M. Lee Van Horn
  • Thomas Jaki
  • Katherine Maysn
  • George Howe
  • Daniel Feaster
  • Andrea E. Lamont
  • Melissa George
  • Minjung Kim
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<mark>Journal publication date</mark>08/2015
<mark>Journal</mark>Educational and Psychological Measurement
Issue number4
Volume75
Number of pages38
Pages (from-to)677-714
Publication statusPublished
Early online date28/10/14
Original languageEnglish

Abstract

Research increasingly emphasizes understanding differential effects. This article focuses on understanding regression mixture models, which are relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their formulation, and their assumptions are compared using Monte Carlo simulations and real data analysis. The capabilities of regression mixture models are described and specific issues to be addressed when conducting regression mixtures are proposed. The article aims to clarify the role that regression mixtures can take in the estimation of differential effects and increase awareness of the benefits and potential pitfalls of this approach. Regression mixture models are shown to be a potentially effective exploratory method for finding differential effects when these effects can be defined by a small number of classes of respondents who share a typical relationship between a predictor and an outcome. It is also shown that the comparison between regression mixture models and interactions becomes substantially more complex as the number of classes increases. It is argued that regression interactions are well suited for direct tests of specific hypotheses about differential effects and regression mixtures provide a useful approach for exploring effect heterogeneity given adequate samples and study design.