Exploring Joint Modeling Approaches for Longitudinal Data: Parsimonious Correlation Modeling and Discrete Observations

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This research project will develop statistical methods and models for regression analysis for longitudinal data with discrete variables. Longitudinal studies increasingly are conducted in the social and economic sciences, and these studies often include data with discrete (for example, yes or no) variables. However, methods for incorporating the correlations between repeated measurements for discrete data are more challenging and remain less explored. This project will develop more effective and convenient ways for incorporating data information about correlations between the repeated measurements in longitudinal studies. The project will advance the current state of knowledge regarding statistical methods for longitudinal data modeling and their applications in multiple social and economic sciences areas. Software will be developed and made publicly available.This project will develop a statistical framework that effectively incorporates correlations between repeated measurements for analyzing a broad class of discrete longitudinal data. The first major focus of the project will be on a new unconstrained parametrization for the correlation matrices of general correlated and/or clustered data. This unconstrained parametrization for regression analysis will be parsimonious, flexible, and scientifically and practically interpretable. The second focus of the project will target the joint distributions of the discrete longitudinal variable. A regression analysis framework will be constructed by using an innovative copula model whose correlation parameters are represented by the unconstrained parametrization. This new framework for analyzing discrete categorical longitudinal data generally will be applicable for a broad class of discrete variables. Theoretical and empirical studies will be carried out for justifying the validity and merits of the new framework.