New Developments in Longitudinal and Heterogeneous Data Analysis with Applications to the Social and Behavioral Sciences

这项研究将开发新的统计方法和模型，用于分析社会和行为科学中经常出现的分类反应数据。 主要目标是解决一些统计问题，涉及到复杂的纵向和异质性数据的分析时，标准模型，如广义线性模型是不够的。 该研究将探讨几个不同的建模问题，其中包括自变量（协变量）的参数转换，大规模纵向社会研究数据的增长曲线模型的发展，以及在非参数化缩放链接函数的广义线性模型中适应异方差。 本文将研究估计和推断中的新方法和新算法，包括：1）建立协变量转换模型中转换和回归参数估计的通用计算方法; 2）为一般混合效应模型提供基于随机近似的计算算法; 3）为具有非参数标度连接函数的模型建立有效的估计方程。 研究还将为所提出的方法开发基于大样本的支持理论。 研究主题最初源于社会和行为科学中的一些特定咨询项目，但要开发的方法非常通用，可能应用于许多复杂的数据分析问题。

This research will develop new statistical methodologies and models for the analysis of categorical response data that occur frequently in the social and behavioral sciences. The main objective is to address some statistical issues that are related to the analysis of complex longitudinal and heterogeneous data when standard models such as the generalized linear models are inadequate. The research will explore several distinct modeling issues including, among others, parametric transformations of independent variables (covariates), the development of growth curve models for large-scale longitudinal social study data, and adapting heteroscedasticity in generalized linear models with non-parametrically scaled link functions. New methods and algorithms in estimations and inferences will be developed, including: 1) developing a general computing method for estimating transformation and regression parameters in covariate transformation models; 2) providing a stochastic-approximation-based computing algorithm for general mixed-effects models; and 3) developing efficient estimating equations for models with non-parametrically scaled link functions. The research also will develop large-sample-based supporting theories for the proposed methodologies. The research topics originally stemmed from some specific consulting projects in the social and behavioral sciences, but the methodologies to be developed are very general, with potential applications to many complex data analysis problems.