# Statistics Colloquium : Dr. Colin Wu

## National Heart, Lung and Blood Institute, NIH

11:00 AM - 12:00 PM

Title: Multivariate Longitudinal Analysis with Dynamic Conditional Distribution Models

Abstract: A major objective of longitudinal studies is to evaluate dynamic patterns of the conditional distribution functions for multivariate outcomes over time. Existing longitudinal methods rely on separate regression models for conditional moments and distributions. These approaches lack cohesiveness when the scientific objectives require a unified modelling scheme that simultaneously describes the conditional moments and distributions. We develop a class of nonparametric time-varying copula models that incorporate the time-varying moments and distributions into a unified regression structure. Our models assume that the conditional distributions of the outcomes belong to some copula families with dynamic functional parameters over time. We propose a basis approximation method to estimate the conditional distribution functions, and demonstrate its application through an epidemiological study of childhood cardiovascular risks and a simulation study. Theoretical justification for the estimation method is shown through its consistency. This method gives a comprehensive approach to analyze dynamic patterns and dependence structures of multivariate longitudinal data.

This is joint work with Wei Zhang, Xin Tian and Qizhai Li