Using Bayesian Statistics to Model Uncertainty in Mixture Models: A Sensitivity Analysis of Priors

Abstract

The Bayesian estimation framework has specific benefits that can aid in the estimation of mixture models. Previous research has shown that the use of priors to capture (un)certainty in latent class sizes has the potential to greatly improve estimation accuracy of a mixture model. These priors can be beneficial in mixture modeling, but proper specification is key. A sensitivity analysis of priors is essential to understand the impact of the prior on the latent classes, whether diffuse or informed priors are implemented. We illustrate a full sensitivity analysis on Dirichlet priors for the class proportions of a latent growth mixture model. We show that substantive results can (drastically) shift as the prior setting is modified, even if only slightly. Math assessment data were used from the Early Childhood Longitudinal Study–Kindergarten class. We conclude with a discussion about final model interpretations when estimates are highly influenced by prior settings.