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

本研究计划将发展统计方法及模型，用于离散变量纵向资料的回归分析。纵向研究越来越多地在社会和经济科学中进行，这些研究通常包括离散（例如，是或否）变量的数据。然而，将离散数据的重复测量之间的相关性结合起来的方法更具挑战性，并且仍然很少被探索。本项目将开发更有效和方便的方法来整合纵向研究中重复测量之间相关性的数据信息。该项目将促进纵向数据建模的统计方法及其在多个社会和经济科学领域的应用方面的知识现状。将开发软件并向公众开放。该项目将开发一个统计框架，有效地结合重复测量之间的相关性，以分析一类广泛的离散纵向数据。该项目的第一个主要重点将是一般相关和/或聚集数据的相关矩阵的一种新的无约束参数化。这种无约束的参数化回归分析将是简洁的，灵活的，科学和实际可解释的。该项目的第二个重点将针对离散纵向变量的联合分布。采用创新的copula模型构建回归分析框架，该模型的相关参数由无约束参数化表示。这种分析离散分类纵向数据的新框架一般将适用于一类广泛的离散变量。将进行理论和实证研究，以证明新框架的有效性和优点。

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.