Latent Class Detection and Class Assignment: A Comparison of the MAXEIG Taxometric Procedure and Factor Mixture Modeling Approaches

Abstract

Taxometric procedures such as MAXEIG and factor mixture modeling (FMM) are used in latent class clustering, but they have very different sets of strengths and weaknesses. Taxometric procedures, popular in psychiatric and psychopathology applications, do not rely on distributional assumptions. Their sole purpose is to detect the presence of latent classes. The procedures capitalize on the assumption that, due to mean differences between two classes, item covariances within class are smaller than item covariances between the classes. FMM goes beyond class detection and permits the specification of hypothesis-based within-class covariance structures ranging from local independence to multidimensional within-class factor models. In principle, FMM permits the comparison of alternative models using likelihood-based indexes. These advantages come at the price of distributional assumptions. In addition, models are often highly parameterized and susceptible to misspecifications of the within-class covariance structure. Following an illustration with an empirical data set of binary depression items, the MAXEIG procedure and FMM are compared in a simulation study focusing on class detection and the assignment of subjects to the latent classes. FMM generally outperformed MAXEIG in terms of class detection and class assignment. Substantially different class sizes negatively impacted the performance of both approaches, whereas low class separation was much more problematic for MAXEIG than for the FMM.