Multilevel data are very common in sociological, behavioral and biomedical researches. The data could come from longitudinal community surveys, genetic family studies or spatial-temporal studies to investigate some health outcomes. Typically, the interest focuses on the impact of some treatment intervention. Such data could be very complex when there are multiple levels of data structures. The data might have factors such as community, family, patient and repeated measures over time nested or crossed in each other. For continuous response, hierarchical models such as linear mixed-effects models or latent variable models have been studied and applied. In the analysis, the major interest is to study the impact of specific cause pathway on health outcome. Since the records in each cluster are often correlated, investigator has to adjust the heterogeneity within a cluster of observations or between clusters. Overdispersion is also very common in such data. The major interest of this project is to investigate the analytic methods for continuous and discrete outcomes of the above nature. In this area, typically, people apply generalized linear mixed-effects models GLMM, marginal models or transition models to non-continuous data. The difficulties for such models such as GLMM is that estimation methods often have troubles to achieve unbiasness, consistency and efficiency. We are interested in the development of more robust methods to achieve these goals for continuous and discrete multilevel data with arbitrary dimension. The final result is a software library with flexible multilevel modeling approaches for the analysis of complex multilevel data. The software will be useful to biomedical researchers working on sociological, behavioral and biomedical studies with complex data structures. Manuscripts and course packs will be developed to assist practitioners in applying appropriate methods and the software tool to their studies. ? ? ? ?
