| The goal of this dissertation is to propose and investigate random effects models for repeated measures situations when there are two or more response variables. The emphasis is on maximum likelihood estimation and on applications with outcomes of different types. We propose a multivariate generalized linear mixed model that can accommodate any combination of outcome variables in the exponential family. This model assumes conditional independence between the response variables given the random effects. We also consider a correlated probit model that is suitable for mixtures of binary, continuous, censored continuous, and ordinal outcomes. Although more limited in area of applicability, the correlated probit model allows for more general correlation structure between the response variables than the corresponding multivariate generalized linear mixed model.; We extend three estimation procedures from the univariate generalized linear mixed model to the multivariate generalization proposed herein. The methods are Gauss-Hermite quadrature, Monte Carlo EM algorithm, and pseudo-likelihood. Standard error approximations are considered along with parameter estimation. A simulated data example and two 'real-life' examples are used for illustration. We also consider hypothesis testing based on quadrature and Monte Carlo approximations to the Wald, score, and likelihood ratio tests. The performance of the approximations to the test statistics is studied via a small simulation study for checking the conditional independence assumption.; We propose a Monte Carlo EM algorithm for maximum likelihood estimation in the correlated probit model. Because of the computational inefficiency of the algorithm we consider a modification based on stochastic approximations which leads to a significant decrease in the time for model fitting. To address the issue of advantages of joint over separate analyses of the response variables we design a simulation study to investigate possible efficiency gains in a multivariate analysis. Noticeable increase in the estimated standard errors is observed only in the binary response case for small number of subjects and observations per subject and for high correlation between the outcomes. We also briefly consider an identifiability issue for one of the variance components. |
