Quantile Regression for Count Data as a Robust Alternative to Negative Binomial Regression

Abstract:

The study investigated the robustness of Quantile regression of count data over negative binomial regression, when there is overdispersion and presence of outlier. The study made use of a complete data and the data with 30% missing data which was imputed using Multiple Imputation by Chain Equation (MICE) in R and also an outlier was injected into the data during imputation of missing values. The Quantile Regression and Negative Binomial Regression estimates were compared and their model fits were also compared. Results showed that the quantile regression for count data provided a better model estimate with both complete data and data with multiple imputed value with comparison to the negative binomial regression in terms of AIC, BIC RMSE and MSE. Hence, Quantile Regression is better than the negative binomial regression when the researcher is interested in the effect of the independent variable on different points of the distribution of the response variable and when there is overdispersion and presence of an outlier.