Understanding the impact of partial factorial invariance on selection accuracy: An R script


Much of the previous literature on partial measurement invariance has focused on (a) statistically detecting noninvariance, and (b) modeling partial invariance to obtain correct inferences for latent mean comparisons across groups in a single research study. However, very little guidance is provided on the practical implications of partial invariance on the instrument itself in the context of selection. In a frequently cited paper, Millsap and Kwok (2004) provided a framework for evaluating the impact of partial invariance by quantifying the magnitude of noninvariance on the efficacy of the test for selection purposes, yet our literature review found that only a few of the citations have fully captured the essence of Millsap and Kwok’s method. In this article, we briefly review the selection accuracy analysis for partial invariance and provide a user-friendly R script (also available as a Web application) that takes parameter estimates as input, automatically produces summary statistics for evaluating selection accuracy, and generates a graph for visualizing the results. Hypothetical and real data examples are provided to illustrate the use of the R script. The goal of this article is to help readers understand Millsap and Kwok’s framework of evaluating the impact of partial invariance through an accessible computer program and step-by-step demonstrations of the selection accuracy analysis.

Structural Equation Modeling: A Multidisciplinary Journal, 24, 5. 783–799
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