Examining Longitudinal Patterns of Recovery: A Growth Mixture Modeling Approach using Posterior Mode Estimation

In most approaches to analysis of change, population homogeneity is assumed. However, in settings such as disaster recovery, there are inherent differences among individuals that make the population more heterogeneous. For example, there are individuals that are more resistant to disasters, and there are individuals that are more vulnerable. Using this framework, subpopulations that describe an individual's pattern of recovery can be classified into several latent groups (e.g., resistant, resilient, chronically dysfunctional). Examining recovery as a change over time is meaningful, because they reveal subgroup differences in developmental processes, which may be sensitive to external social factors and various interventions.

This study examines the use of a growth mixture model (GMM; Muthén & Muthén, 2004) that empirically classifies individuals into latent subgroups of recovery based on their recovery growth trajectories; this method estimates separate parameters of the intercept and the slope for each latent subpopulation. However, it has been noted in the literature that there are often boundary problems in numerical computation and estimation when applying maximum likelihood estimation (MLE) for latent class models (Galindo-Garre & Vermunt, 2006) such as the GMM. This problem can be prevented when a Bayesian posterior mode (PME) estimation is used (McLachlan & Krishnan, 2008). This study focuses on comparing the PME approach to the traditional MLE in GMM. Simulations will examine the recovery of parameters and classification; an empirical analysis using a longitudinal cohort of displaced households from Hurricane Katrina will also be used to demonstrate the advantages of this method.