Statisticians often encounter data in the form of a combination of discrete and continuous outcomes. A special case is zero-inflated longitudinal data where the response variable has a large portion of zeros. These data exhibit correlation because observations are obtained on the same subjects over time. In this dissertation, we propose a two-part mixed distribution model to model zero-inflated longitudinal data. The first part of the model is a logistic regression model that models the probability of nonzero response; the other part is a linear model that models the mean response given that the outcomes are not zeros. Random effects with AR(1) covariance structure are introduced into both parts of the model to allow serial correlation and subject specific effect.

Estimating the two-part model is challenging because of high dimensional integration necessary to obtain the maximum likelihood estimates. We propose a Monte Carlo EM algorithm for estimating the maximum likelihood estimates of parameters. Through simulation study, we demonstrate the good performance of the MCEM method in parameter and standard error estimation.

To illustrate, we apply the two-part model with correlated random effects and the model with autoregressive random effects to executive compensation data to investigate potential determinants of CEO stock option grants.