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

本研究计画将发展离散变数之纵向资料回归分析之统计方法与模式。 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变量（例如，是或否）的数据。 然而，将离散数据的重复测量之间的相关性的方法更具挑战性，仍然较少探索。 本计画将开发更有效且方便的方法，以整合纵向研究中重复测量间相关性的资料资讯。 该项目将推进当前关于纵向数据建模统计方法及其在多个社会和经济科学领域的应用的知识。 该项目将开发一个统计框架，有效地纳入重复测量之间的相关性，以分析一大类离散纵向数据。 该项目的第一个主要重点将是一个新的无约束参数化的相关矩阵的一般相关和/或集群数据。 这种无约束的回归分析参数化方法具有简洁、灵活、科学和实用的特点。 该项目的第二个重点将针对离散纵向变量的联合分布。 一个回归分析框架将使用一个创新的copula模型，其相关参数表示的无约束参数化。 这种新的框架分析离散分类纵向数据一般将适用于广泛的离散变量。 本研究将从理论和实证两个方面对新框架的有效性和优点进行论证。

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.