Mixed logistic regression models

This article studies binomial mixture models that include covariates in binomial parameters and mixing probabilities. This model contains logistic regression, nonparametric mixed logistic regression (Follmann and Lambert 1989) and independent binomial mixture models as special cases, and provides an alternative to quasi-likelihood and betabinomial regression for modeling extra-binomial variation. Estimation methods based on the EM and quasi-Newton algorithms, properties of these estimates, a model selection procedure, residual analysis, and goodness of fit are discussed. This methodology is motivated and illustrated with an example. A Monte Carlo study investigates behavior of the estimates and model selection criteria.

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