Performance of robust count regression estimators in the case of overdispersion, zero inflated, and outliers: simulation study and application to German health data

Abstract

This paper considers the count regression models in case of the dataset contains overdispersion and outliers. Seven robust and non-robust estimators are provided for four count regression (Poisson, negative binomial (NB), zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB)) models. The non-robust estimators were obtained by applying the maximum likelihood estimation on the four count models. While two robust estimators were obtained by applying the M-estimation on the Poisson and NB models (MP and MNB estimators), and the third robust estimator is the quantile regression of the count model (QRC estimator). Simulation study and empirical application were conducted to evaluate the performance and the efficiency for the robust and non-robust estimators of the four count regression models. The results showed that, in general, all robust estimators gave better performance than all non-robust estimators if the model contains outliers. And the QRC estimator reforms well even if the percent of the outlier values up to 25% when the sample size is large, dispersion value is small (less than or equal one). While when the dispersion value more than one, the MNB estimator is the efficient. The results of our application, which based on German health survey data in 1998, indicate that the significant variable that effect on the number of visits to doctor is the patient's condition (bad health or not in bad health), and the QRC estimator is the best for this data.