On ridge estimators for the negative binomial regression model
Abstract
The negative binomial (NB) regression model is very popular in applied research when analyzing count data. The commonly used maximum likelihood (ML) estimator is very sensitive to highly intercorrelated explanatory variables. Therefore, a NB ridge regression estimator (NBRR) is proposed as a robust option of estimating the parameters of the NB model in the presence of multicollinearity. To investigate the performance of the NBRR and the traditional ML approach the mean squared error (MSE) is calculated using Monte Carlo simulations. The simulated result indicated that some of the proposed NBRR methods should always be preferred to the ML method.
►Multicollinearity leads to high variance of estimated parameters of regression models. ►Using Monte Carlo simulations this is shown to hold for the negative binomial model. ►A ridge regression estimator is proposed to reduce the variance. ►Some methods of estimating the ridge parameter are suggested. ►The simulated results show that the ridge regression estimator reduces the variance.