Some almost unbiased ridge regression estimators for the zero-inflated negative binomial regression model

Abstract

Zero-inflated negative binomial regression (ZINB) models are commonly used for count data that show overdispersion and extra zeros. The correlation among variables of the count data leads to the presence of a multicollinearity problem. In this case, the maximum likelihood estimator (MLE) will not be an efficient estimator as the value of the mean squared error (MSE) will be large. Several alternative estimators, such as ridge estimators, have been proposed to solve the multicollinearity problem. In this paper, we propose an estimator called an almost unbiased ridge estimator for the ZINB model (AUZINBRE) to solve the multicollinearity problem in the correlated count data. The performance of the AUZINBRE is investigated using a Monte Carlo simulation study. The MSE is used as a measure to compare the results of the proposed estimators with those of the ridge estimators and the MLE. In addition, the AUZINBRE is applied to a real dataset.