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，用于分析在社会科学和行为科学中经常出现的分类回答数据。其主要目标是解决一些统计问题，这些问题与分析复杂的纵向和不同种类的数据有关，当标准模型，如广义线性模型不够充分时。这项研究将探索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，以及在具有非参数尺度连接函数的广义线性模型中适应异方差。在估计和推断方面将发展新的方法和算法，包括：1)发展协变量变换模型中估计变换和回归参数的通用计算方法；2)提供基于随机近似的一般混合效应模型的计算算法；3)建立非参数尺度连接函数模型的有效估计方程。这项研究还将为所提出的方法开发基于大样本的支持理论。这些研究课题最初源于社会科学和行为科学中的一些特定咨询项目，但所开发的方法非常通用，可能会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.