Models and Strategies for Factor Mixture Analysis: An Example Concerning the Structure Underlying Psychological Disorders

Abstract

The factor mixture model (FMM) uses a hybrid of both categorical and continuous latent variables. The FMM is a good model for the underlying structure of psychopathology because the use of both categorical and continuous latent variables allows the structure to be simultaneously categorical and dimensional. This is useful because both diagnostic class membership and the range of severity within and across diagnostic classes can be modeled concurrently. Although the conceptualization of the FMM has been explained in the literature, the use of the FMM is still not prevalent. One reason is that there is little research about how such models should be applied in practice and, once a well-fitting model is obtained, how it should be interpreted. In this article, the FMM is explored by studying a real data example on conduct disorder. By exploring this example, this article aims to explain the different formulations of the FMM, the various steps in building a FMM, and how to decide between an FMM and alternative models.

Keywords:

• factor mixture model
• finite mixture model
• latent class analysis

Notes

^a Input numbers are in reference to the example Mplus syntax in the Appendix. In the class varying parameters column α = factor mean; Ψ = factor covariance matrix; τ = item threshold; λ = factor loading.

^a Log-likelihood not replicated.

^a Fixed parameter.

*p < .05.