| Missing problem is very common in today's public health studies because of responses measured longitudinally. In this dissertation we proposed two latent variable models for longitudinal data with informative missingness. In the first approach, a latent variable model is developed for the categorical data, dividing the observed data into two latent classes: a 'regular' class and a 'special' class. Outcomes belonging to the regular class can be modeled using logistic regression and the outcomes in the special class have pre-deterministic values. Under the important assumption of conditional independence in the latent variable models, the longitudinal responses and the missingness process are independent given the latent classes. Parameters that we are interested in are estimated by the method of maximum likelihood based on the above assumption and correlation between responses. In the second approach, the latent variable in the proposed model is continuous and assumed to be normally distributed with unity variance. In the latent variable model, the values of the latent variable are affected by the missing patterns and the latent variable is also a covariate in modeling the longitudinal responses. We use the EM algorithm to obtain the estimates of the parameters and Gauss-Hermite quadrature is used to approximate the integral of the latent variable. The covariance matrix of the estimates can be calculated by using the bootstrap method or obtained from the inverse of the Fisher information matrix of the final marginal likelihood. |
