Finite Mixture Models with Student t Distributions: an Applied Example

The use of finite mixture modeling (FMM) to identify unobservable or latent groupings of individuals within a population has increased rapidly in applied prevention research. However, many prevention scientists are still unaware of the statistical assumptions underlying FMM. In particular, finite mixture models (FMMs) typically assume that the observed indicator variables are normally distributed within each latent subgroup (i.e., within-class normality). These assumptions are rarely met in applied psychological and prevention research, and violating these assumptions when fitting a FMM can lead to the identification of spurious subgroups and/or biased parameter estimates. Although new methods have been developed that relax the within-class normality assumption when fitting a FMM, prevention scientists continue to rely on FMM methods that assume within-class normality. The purpose of the current article is to introduce prevention researchers to a FMM method for heavy-tailed data: FMM with Student t distributions. We begin by reviewing the distributional assumptions that underlie FMM and the limitations of FMM with normal distributions. Next, we introduce FMM with Student t distributions, and show, step by step, the analytic and substantive results of fitting a FMM with normal and Student t distributions to data from a smoking-cessation trial. Finally, we extend the results of the applied example to draw conclusions about the use of FMM with Student t distributions in applied settings and to provide guidelines for researchers who wish to use these methods in their own research.