Analyzing multivariate bounded discrete data poses significant challenges across various disciplines. In the context of dementia-related studies, such data often arises when individuals take neuropsychological tests. In this talk, we are motivated by our study of Alzheimer's disease data, and we focus on the complexities encountered in modeling such data. Building on prior work on the mixtures of experts and latent class models, we introduce a comprehensive modeling and inference procedure to capture the joint distribution of multivariate bounded discrete data, conditional on baseline covariates. We also present relevant identification and estimation theories. Furthermore, we illustrate how the work can be extended when the outcome data is missing at random using a nested Expectation-Maximization (EM) procedure.

Key functionalities of the proposed model include the incorporation of covariate information, the ability to perform imputation and clustering in the presence of missing data, and the inference of latent trajectories over time. We present results from its application to a real-world Alzheimer's disease data set. We conclude with a discussion on further extensions of this methodology to a rich class of missing not at random assumptions and modeling strategies.