Abstract: A Comparison of the Factor Mixture Model and Taxometric Procedures

Abstract

Taxometric procedures and the Factor Mixture Model (FMM) have a complimentary set of strengths and weaknesses. Both approaches purport to detect evidence of a latent class structure. Taxometric procedures, popular in psychiatric and psychopathology literature, make no assumptions beyond those needed to compute means and covariances. However, Taxometric procedures assume that observed items are uncorrelated within a class or taxon. This assumption is violated when there are individual differences in the trait underlying the items (i.e., severity differences within class). FMMs can model within-class covariance structures ranging from local independence to multidimensional within-class factor models and permits the specification of more than two classes. FMMs typically rely on normality assumptions for within-class factors and error terms. FMMs are highly parameterized and susceptible to misspecifications of the within-class covariance structure.

The current study compared the Taxometric procedures MAXEIG and the Base-Rate Classification Technique to the FMM in their respective abilities to (1) correctly detect the two-class structure in simulated data, and to (2) correctly assign subjects to classes. Two class data were simulated under conditions of balanced and imbalanced relative class size, high and low class separation, and 1-factor and 2-factor within-class covariance structures. For the 2-factor data, simple and cross-loaded factor loading structures, and positive and negative factor correlations were considered. For the FMM, both correct and incorrect within-class factor structures were fit to the data.

FMMs generally outperformed Taxometric procedures in terms of both class detection and in assigning subjects to classes. Imbalanced relative class size (e.g., a small minority class and a large majority class) negatively impacted both FMM and Taxometric performance while low class separation was much more problematic for Taxometric procedures than the FMM. Comparisons of alterative FMMs based on information criteria generally resulted in correct model choice but deteriorated when small class separation was combined with imbalanced relative class size.