Regression models for count and proportion data

Overview

Abstract

In this talk we will present two classes of regression models. The first class is focused on overdispersed count models and is given by assuming that the response variable is obtained by mixing the Poisson distribution with an absolutely continuous distribution in the exponential family. The second class is focused on proportion data and assumes that the response variable follows a distribution given by the fraction $X/(X+Y)$, where $X$ and $Y$ are independent absolutely continuous random variables from the exponential family. Usually, the marginal likelihood of the response variables of these models depends on complicated special functions and their direct maximization suffers from numerical instability. We propose an alternative estimation procedure based on EM-algorithm approach. We verify that they have good numerical stability, typically outperforming the direct maximization of the marginal likelihood. Finally, for some of these models we obtained local influence diagnostics, and for the proportion data we obtained a discrimination criterion for choosing between some of the models. We will also present application to real data. This talk will not be very technical and should be accessible for students with a more applied background.

Brief Biography

Alexandre Simas is a research scientist at the Stochastic Processes and Applied Statistics group led by Professor David Bolin at KAUST university.  He received his Ph.D. in mathematics at Instituto de Matematica Pura e Aplicada (IMPA)-Brazil, where he was also a visiting Ph.D. student at the Courant Institute of Mathematical Sciences (CIMS-NYU)-USA. Prior to joining KAUST, he has worked as an associate professor at Federal University of Paraiba-Brazil. His research interest lies on stochastic partial differential equations, partial differential equations and their applications in statistics.