Chapter 9: Mean and Covariance Structure Mixture Models

Mixture modeling is becoming an increasingly useful tool in applied research settings. At the most basic level, such methods might be used to determine whether a single univariate data set arose from a homogeneous population or from a heterogeneous population consisting of unknown or latent groups (often called classes) that differ in their distributional parameters (e.g., means and/or variances). More advanced applications of mixture modeling are used to assess whether a population consists of a mixture of groups that have different multivariate distributions (e.g., mean vectors and/ or covariance matrices). Mixture modeling can also be used in conjunction with a variety of different latent variable models, such as factor models and latent growth curve models. For instance, factor mixture models can be used to assess whether the population consists of groups that differ in their factor model parameters (e.g., factor variances, loadings) and growth mixture modeling can be used to investigate whether unknown groups exist in the population that differ in how their members’ change over time.