An Extension of the Propensity Score Adjustment Method for the Analysis of Group Differences in MIMIC Models

Abstract

This article proposes an extension of the propensity score adjustment method to latent variable models. The propensity score was proposed by Rosenbaum and Rubin (1983) as a means of balancing treatment and control groups with respect to observed covariates in non-randomized studies. The propensity score is defined as the conditional probability of assignment to a treatment group given a set of observed covariates. In a typical application of this approach, each observation is associated with a propensity to be assigned to the treatment group. The distribution of propensity scores is then divided into strata and analyses of treatment group differences are conducted within strata. Comparisons of treatment group differences within and across strata provide evidence for whether or not the bias due to non-random selection into treatment groups has been accounted for by the propensity score adjustment. This article extends the application of the propensity score approach to the analysis of group differences on latent variables. In particular, multi-sample MIMIC modeling is utilized to test hypotheses about treatment group differences on latent variables across strata. The role of factorial invariance as it relates to the approach advocated in this article is also discussed. An application to the problem of academic tracking differences in self-concept and locus-of-control, using data from the National Educational Longitudinal Study of 1988 (National Center for Education Statistics, 1988), illustrates the procedure.