In many studies the outcome of main interest cannot be measured by a single response. There is a great deal of literature dealing with such data for cross-sectional studies. However, this problem has not been well studied for longitudinal data. In this dissertation we propose latent variable models to handle this type of multivariate longitudinal data. At the first stage of the model we assume the observed outcomes measure the latent variable with error. The latent variable is then assumed associated with covariates through a linear mixed model. We extend this model to the situation where the probability of dropout is latent variable dependent, and hence non-ignorable. We first show how one can find maximum likelihood estimates when the covariates are completely observed. We then relax this assumption by allowing covariates to be missing due to unit dropout, which is often the case when there are time-varying covariates. Finally, we look at the missing covariate issue in more detail for the single outcome case. We carry out a bias analysis, comparing our proposed method with naive methods for handling the missing covariates. The Gibbs sampler for this model is developed to obtain Bayesian inference. Data from a national panel study on changes in methadone treatment practices are used throughout to illustrate the methodology.
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