On the Restricted Poisson Ridge Regression Estimator

Abstract

For modeling count data, the Poisson regression model is widely used in which the response variable takes non-negative integer values. However, the presence of strong correlation between the explanatory variables causes the problem of multicollinearity. Due to multicollinearity, the variance of the maximum likelihood estimator (MLE) will be inflated causing the parameters estimation to become unstable. Multicollinearity can be tackled by using biased estimators such as the ridge estimator in order to minimize the estimated variance of the regression coefficients. An alternative approach is to specify exact linear restrictions on the parameters in addition to regression model. In this paper, the restricted Poisson ridge regression estimator (RPRRE) is suggested to handle multicollinearity in Poisson regression model with exact linear restrictions on the parameters. In addition, the conditions of superiority of the suggested estimator in comparison to some existing estimators are discussed based on the mean squared error (MSE) matrix criterion. Moreover, a simulation study and a real data application are provided to illustrate the theoretical results. The results indicate that the suggested estimator, RPRRE, outperforms the other existing estimators in terms of scalar mean squared error (SMSE). Therefore, it is recommended to use the RPRRE for the Poisson regression model when the problem of multicollinearity is present.