Analysis Of Multivariate Longitudinal Outcomes With Nonignorable Dropouts

Multivariate statistical analysis is often used to properly characterize the dependence between the random variables and the statistical regularity within them. And the longitudinal study is that measurements of the same individuals are taken repeatedly through time. In this paper, a random sample of 172 methadone treatment units in America took place in 1988, 1990 and 1995. Such as this dataset, the outcome of main interest consists of several indexes, and they are observed repeatedly through time, then this dataset is called multiple longitudinal outcomes. Hence, we try to model the observed outcomes using linear mixed models to the latent variable, which means the treatment practice effectiveness. To account for the improvement of the latent variable though time, we apply the Markov Chain with first oder to express the relationship. Specially, in view of the data with nonignorable dropouts, logistic regression is used to model this missing mechanism. Finally, we develop the EM algorithm to estimate the model parameters, and supply the results of the simulation study.