Mutual Information Reliability for Latent Class Analysis

Abstract

Latent class models are powerful tools in psychological and educational measurement. These models classify individuals into subgroups based on a set of manifest variables, assisting decision making in a diagnostic system. In this article, based on information theory, the authors propose a mutual information reliability (MIR) coefficient that summaries the measurement quality of latent class models, where the latent variables being measured are categorical. The proposed coefficient is analogous to a version of reliability coefficient for item response theory models and meets the general concept of measurement reliability in the Standards for Educational and Psychological Testing. The proposed coefficient can also be viewed as an extension of the McFadden’s pseudo R-square coefficient, which evaluates the goodness-of-fit of logistic regression model, to latent class models. Thanks to several information-theoretic inequalities, the MIR coefficient is unitless, lies between 0 and 1, and receives good interpretation from a measurement point of view. The coefficient can be applied to both fixed and computerized adaptive testing designs. The performance of the MIR coefficient is demonstrated by simulated examples.