Mixture modeling methods for the assessment of normal and abnormal personality, part I: cross-sectional models

Abstract

Over the past 75 years, the study of personality and personality disorders has been informed considerably by an impressive array of psychometric instruments. Many of these tests draw on the perspective that personality features can be conceptualized in terms of latent traits that vary dimensionally across the population. A purely trait-oriented approach to personality, however, might overlook heterogeneity that is related to similarities among subgroups of people. This article describes how factor mixture modeling (FMM), which incorporates both categories and dimensions, can be used to represent person-oriented and trait-oriented variability in the latent structure of personality. We provide an overview of different forms of FMM that vary in the degree to which they emphasize trait- versus person-oriented variability. We also provide practical guidelines for applying FMM to personality data, and we illustrate model fitting and interpretation using an empirical analysis of general personality dysfunction.

Figure 1

A graphical depiction of the common factor model. Note. This figure largely follows the reticular action model notation (McArdle & McDonald, 1984), whereby latent variables are denoted by circles and observed variables are denoted by rectangles. Triangles containing the number one denote the inclusion of mean/intercept structure in the model for the variables pointed to by the path arrows.

Figure 2

A graphical depiction of the general factor mixture model.

Figure 3

Latent trait distributions for continuous normal, semi-parametric, and non-parametric factor models. Note. Data were simulated from unidimensional factor mixture models with 1) a single normal trait distribution representing the population (left panel); 2) three normal subpopulations representing latent subgroups with unique factor means and variances; and 3) three discrete subpopulations representing latent subgroups differing only in latent means. All data were then analyzed using a unidimensional confirmatory factor analysis model, and the resulting factor scores were plotted to illustrate relevant variations in latent structure.

Figure 4

Four-class LCA solution for the GPD criteria. Note. The stacked bars denote the observed proportions of individuals in each class with absent, present, or strongly present levels of each GPD criterion.