Heteroscedastic Logistic Regression Model

Abstract

Correlated binomial data can be modeled using a mean model if the interest is only on the mean, and the dispersion is considered a nuisance parameter. However, if the intraclass correlation is of interest, then one should consider to apply a joint modeling of the mean and the dispersion. Efron (Journal of the American Statistical Association 81(395):709–721, 1986) was one of the first to model both the mean and the variance. The dispersion sub-model allows extra parameters to model the variance independent of the mean, thus allowing covariates to be included in both the mean and variance sub-models. In this chapter, we present a sub-model that analyzes the mean and a sub-model that analyzes the variance. This model allows both the dispersion and the mean to be modeled. We use the MODEL statement in the SAS/ETS procedure QLIM to specify the model for the mean, and use the HETERO statement to specify the dispersion model. We fit this model in SAS. Our results and presentation are based on work done in some recent graduate research projects at Arizona State University.