THURSDAY, March 3, 2005
Time: 2:00 - 3:00 PM
ECSB 2120

Ph.D. Dissertation Defense
Title: Statistical Analysis of Longitudinal and Multivariate Discrete Data

Deepak Mav
Department of Mathematics & Statistics, Old Dominion University

Correlated Poisson and binary variables occur naturally in medical, biological and epidemiological longitudinal studies. Modeling and simulating such variables is difficult because the correlations are restricted by the marginal means via Frechet bounds, in a complicated way. In this talk we will first discuss partially specified models and methods for estimating the regression and correlation parameters. Using simulations based on extensions of the algorithm due to Sim (1993, J. Stat. Comp. and Simulation, 47, pp.1-10), we will study performance of these procedures via asymptotic relative efficiencies and coverage probabilities for Poisson and binary outcomes.

In the second part of the talk, we will discuss fully specified models constructed using copulas. In particular we will discuss models based on normal copulas, probit models, mixture models, Poisson log-normal models, and discrete choice models including multinomial logit and probit models. Computation of maximum likelihood estimates and the Fisher information matrix for these models requires computation of multivariate normal probabilities. We will also discuss several efficient algorithms for calculating multivariate normal integrals. For the multivariate probit and multivariate Poisson log-normal models, we will implement maximum likelihood estimation, deriving the necessary equations, and illustrate it on two real life data sets. In partially specified models the marginal dispersion parameter is treated as nuisance. In applications where the populations are subject to post-sampling- effects, the dispersion parameter cannot be treated as redundant. We introduce the quasi-multinomial and Lagrange families of distributions, which provide meaningful inference on direction and strength of population dynamics. We then illustrate quasi-multinomial distribution using the optical scanner panel data (Paap and Franses 2000, Journal of Applied Econometrics, 15, pp. 717-744) on the multiple purchase decisions and marketing predictors by Rome (Georgia) households.