Finite mixtures of count data regression models have been successfully used for modeling discrete responses arising from heterogeneous populations. But the maximum likelihood (ML) estimator for such models are sensitive to data contamination and extreme values. This dissertation develops two robust estimators for finite mixtures of count data regression models. One is the minimum Hellinger distance (MHD) estimator and the other is the minimum L₂ error (L₂E) estimator, a special case of the minimum density power divergence estimator. Two Monte Carlo simulation studies show that the MHD and L ₂E estimators are more robust than the ML one but come at the cost of efficiency. However, the robustness property of the MHD and L₂E estimators is deteriorated as the mixing probability approaches one.

For empirical application, this dissertation uses the data from Dionne et al. (1996), the extent of non-payments of personal loans in Spain, and from Deb and Trivedi (2002), counts of utilization from the RAND Health Insurance Experiment, respectively. The estimated results show that the two-component Poisson mixture regression model is the best fit model for the first data set and the two-component negative binomial one mixture regression model for the second data set. But both of the model specifications are preferred to be estimated by the ML estimation that could be attributed to the flexibility of the finite mixture model and data processing procedures.