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.
Highlights
In a Poisson regression, the maximum likelihood estimator (MLE) can be affected by multicollinearity problem in which inflates the variance of the estimates, and the estimate of the parameters will be unstable (Kibria et al [14])
The restricted Poisson ridge regression estimator (RPRRE) was suggested for Poisson regression model with exact linear restrictions on the parameters to tackle the problem of multicollinearity
A Monte Carlo simulation study and a real data application were conducted to evaluate the performance of the RPRRE with the MLE, Poisson ridge regression estimator (PRRE), and restricted maximum likelihood estimator (RMLE) according to scalar mean squared error (SMSE) criterion
Summary
In a Poisson regression, the maximum likelihood estimator (MLE) can be affected by multicollinearity problem in which inflates the variance of the estimates, and the estimate of the parameters will be unstable (Kibria et al [14]). For more details on biased estimators, one can refer to Muniz and Kibria [22], Kibria et al [13], Inan and Erdogan [11], Asar [4], Kibria et al [14], Şiray et al [29], Alanaz and Algamal [1], Algamal [2], and Qasim et al [25] Another technique for dealing with multicollinearity is to include exact linear restrictions for the parameters in addition to regression model. Enas Gawdat Yehia: On the Restricted Poisson Ridge Regression Estimator named as, restricted Poisson ridge regression estimator (RPRRE) to handle the problem of multicollinearity in Poisson regression model by combining the RMLE and the PRRE, and compare the estimators considered in this paper with the suggested estimator through a simulation study and a real data application.
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