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

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.