A New Ridge Estimator for the Negative Binomial Regression Model

Abstract

The ridge estimator has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The negative binomial regression model is a well-known model in application when the response variable is count data. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the negative binomial regression coefficients. To address this problem, a negative binomial ridge estimator has been proposed by numerous researchers. In this paper, a new negative binomial ridge estimator (NNBRE) is proposed and derived. The idea behind the NNBRE is to get diagonal matrix with small values of diagonal elements that leading to decrease the shrinkage parameter and, therefore, the resultant estimator can be better with small amount of bias. Our Monte Carlo simulation results suggest that the NNBRE estimator can bring significant improvement relative to other existing estimators. In addition, the real application results demonstrate that the NNBRE estimator outperforms both negative binomial ridge regression and maximum likelihood estimators in terms of predictive performance.