Date of Award

2015

Degree Type

Thesis

Degree Name

Master of Science (MS)

First Advisor

Gavino Puggioni

Abstract

Using longitudinal data to model change patterns of behaviors is a major interest in the field of developmental psychology and behavioral science. As het- erogeneity often exists in the population, researchers are more and more interested in a topological representation of the growth trajectories. That is, to identify distinct trajectories depending on their individual characteristics. Latent class models(LCM) are flexible methods of modeling unobserved heterogeneity in a population and it has been recently extended to analyzing longitudinal data. Latent class growth models(LCGM) assume individuals come from a finite number of latent classes and individuals share the same growth trajectory within each class. However, there is little literature on applying latent class models on zero-in outcomes. When the interest is to model rare events or behaviors that are less commonly endorsed, such as health risk behaviors (e.g., smoking, heroin use, suicide attempts, etc.), we often encounter a lot of zero responses causing the distribution of the outcome variable to exhibit a large spike at zero. This work focuses on developing latent class growth models for zero-inflated count response variables. Bayesian analysis, well known for its ability to incorporate prior information and greater flexibility to solve complex problems, was used in this paper. Specifically, appropriate prior distributions were specified for the model parameters, likelihood of the data was derived based on the zero-inflated latent class model, and joint posterior distribution was obtained by combining information from the prior and likelihood. Due to the fact that conditional posterior distributions of the model parameters are numerically intractable, simulation based approach Markov Chain Monte Carlo methods were used to approximate and summarize posterior quantities. A simulation study was first conducted to test the performance of the proposed model. As an illustration, data collected from the National Longitudinal Study of Adolescent Health was then analyzed. This paper modeled the change of cigarettes smoking from early adolescence to adulthood and identified subgroups of trajectory patterns and risk factors contributing to the classification.

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