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 beta-binomial 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.

Key Words
Binomial data; EM algorithm; Extra-binomial variation; Mixture models; Residual analysis.

Peiming Wang is Lecturer, Division of Actuarial Science and Insurance, Nanyang Business School, Singapore 2263 (E-mail: apmwang@delta.ntu.ac.sg). Martin L. Puterman is Professor, Faculty of Commerce and Business Administration, University of British Columbia, 2053 Main Mall, Vancouver, B.C. V6T 1Z2, Canada (E-mail: marty@markov.commerce.ubc.ca).