Specification Issues in Bayesian Growth Mixture Modeling

This dissertation is comprised of three different studies that all surround topics related to growth mixture modeling (GMM) within the Bayesian estimation framework.

GMM provides information about growth over time (e.g., growth in reading achievement throughout elementary school).

This model also allows researchers to account for different latent groups (called mixtures) of individuals by modeling distinctively different growth trajectories for each latent group.

The general design of this dissertation uses a 3-mixture class GMM and assesses various aspects of this model.

In particular, Study 1 examines the ability for a Bayesian estimator to uncover a mixture class that is very small in size but substantively different from the other mixture classes.

The results of a Bayesian framework are compared to the more traditional estimator of maximum likelihood via the EM algorithm.

Study 2 is based solely in the Bayesian context and examines the impact of tight and (in)accurate prior distributions on parameter estimates.

Specifically, the investigation is focused on whether or not very inaccurate subjective opinions about model parameters can have an actual impact on the estimates produced within the Bayesian framework.

Study 3 is also computed solely in the Bayesian context and is a study of model mis-specification.

Specifically, the focus is on a procedure called posterior predictive checking (PPC), which is theoretically built to detect specification error in a Bayesian modeling context.

The aim is to determine under what circumstances PPC correctly identifies model mis-specification and why it fails to identify the error in other cases.