Quantile Regression with Count Data: Example of Overdispersion Data

Abstract

Classical regression assumptions are not valid in count models. Therefore, Poisson and negative binom distribution are the most common methods for count data. The Poisson model can be used in case of equal spread, while negative binom distributions in case of overdispersion. In practice, data is often over dispersed. If there are too many zero values in the count data, zero-inflated Poisson models in case of equal spread, zero-inflated negative binom models, Poisson Hurdle and negative binom Hurdle models or their generalized models can be preferred in case of overdispersion. These models generally focus on modeling the conditional average of the dependent variable. However, conditional average regression models may be sensitive to outliers of the dependent variable or provide no information about other conditional distribution properties. In this case, quantile regression, which is one of the robust methods for count data, can be used. The quantile regression has the advantages of robust prediction in the presence of outliers. In this study, count data was taken to show the dependent variable number of articles. Independent variables include of gender, marital status, number of children under the age of 5, prestige of the doctorate, and the number of articles by the consultant in the last 3 years. After applying Poisson and negative binom distribution in the study, 25%, 50%, 75% and 90% quantile regression estimates were obtained.