A Huang-Yang-type Estimator to Reduce Multicollinearity in a Negative Binomial Regression Model

Abstract

Researchers often choose the Poisson distribution when analyzing count data. However, the Poisson distribution requires the constraint that the expected value and variance are equal, known as the "equidispersion" condition. Because this condition is rarely encountered in real life, the Negative Binomial distribution is used as an alternative to the Poisson distribution. In this study, a new biased estimator combiningthe properties of the Kibria-Lukman and Huang-Yang estimators is proposed as an alternative to existing estimators when the response variable follows a negative binomial distribution to reduce the effect of multicollinearity in regression models. Several estimators based on the mean square error have been proposed to estimate the optimal value of the biasing parameter(s). Furthermore, a simulation study is conducted to investigate the performance of the proposed biased estimators. Finally, the superiority of the proposed estimators is examined using real and experimental data.