Modeling Overdispersion in Binomial Data with Regression Linked to a Finite Mixture Probability of Success

• Activity Number: 376
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Andrew Raim*+ and Nagaraj Neerchal
• Companies: University of Maryland, Baltimore County and University of Maryland, Baltimore County
• Keywords: Overdispersion ; GLM ; Logistic Regression ; Random Effects ; Goodness-of-Fit

Abstract

Logistic regression often cannot account for large variability seen in binomial data due to departures from standard assumptions. Many techniques have been considered to address this issue, commonly known as overdispersion. Finite mixture distributions may be used when the extra variation is explained by the presence of several latent subpopulations. For example, a finite mixture of regressions links the probability for each latent group to a seperate regression. Analogously to the usual logistic regression, we consider linking a regression to the mixture probability of success in a finite mixture of binomials. This can be seen as ``marginal modeling' with respect to the latent groups, as opposed to the mixture of regressions which is seen as ``conditional modeling' on the groups, and would allow more parsimonious models when only a single overall regression is desired. Our approach is likelihood-based, which may be considered an advantage over quasi-likelihood techniques often used to address overdispersion. This work presents the new model and an illustrative example.