Mixture Link Models for Binomial Data with Overdispersion

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Andrew M. Raim* and Nagaraj K. Neerchal and Jorge G. Morel
• Companies: U.S. Census Bureau and University of Maryland, Baltimore County and University of Maryland, Baltimore County
• Keywords: Finite Mixture ; GLM ; Random Effects ; Prediction Interval

Abstract

Overdispersion is commonly encountered in the analysis of categorical and count data. When it occurs, standard regression models may not adequately explain variability observed in the data. Finite mixture distributions arise in sampling a heterogeneous population, and data drawn from such a population will exhibit extra variability relative to any single subpopulation. The Mixture Link binomial distribution was recently developed to account for such heterogeneity in a generalized linear model setting. This model is completely likelihood-based, and maintains a link between the regression function and the overall mixture mean by assuming a certain random effects structure on the set representing enforcement of the link. This paper first presents an illustrative example in a heterogeneous population, comparing binomial regression with a binomial finite mixture of regressions and Mixture Link regression. We then compare the three models in a Bayesian setting using a classical dataset studying chromosome aberrations in atomic bomb survivors. The benefits of acknowledging the extra variation are seen through improved residual plots and widened prediction intervals. When regression on the overall mean is of interest and the heterogeneity is considered a nuisance, Mixture Link may be preferred over a finite mixture of regressions because only one regression function must be specified.