Developing a two-parameter Liu estimator for the COM–Poisson regression model: Application and simulation

Abstract

The Conway–Maxwell–Poisson (COMP) model is defined as a flexible count regression model used for over- and under-dispersion cases. In regression analysis, when the explanatory variables are highly correlated, this means that there is a multicollinearity problem in the model. This problem increases the standard error of maximum likelihood estimates. To manage the multicollinearity effects in the COMP model, we proposed a new modified Liu estimator based on two shrinkage parameters (k, d). To assess the performance of the proposed estimator, the mean squared error (MSE) criterion is used. The theoretical comparison of the proposed estimator with the ridge, Liu, and modified one-parameter Liu estimators is made. The Monte Carlo simulation and real data application are employed to examine the efficiency of the proposed estimator and to compare it with the ridge, Liu, and modified one-parameter Liu estimators. The results showed the superiority of the proposed estimator as it has the smallest MSE value.

Modified Two-Parameter Liu Estimator for Addressing Multicollinearity in the Poisson Regression Model

“…According to the research conducted by Akay and Ertan [27], Qasim et al [29], Amin et al [12], Abonazel et al [16], and Lukman et al [23], the optimal value of d can be determined as follows:…”

“…Lukman et al [13], Amin et al [12], and Abonazel et al [16] determined the most suitable value of d 0 as follows:…”

“…Based on the research conducted by Abonazel et al [16] and Abonazel [21], we suggest using the estimator d * 0 for the d * 0 parameter in the PMTPLE. This can be achieved by incorporating the value of d * 0 within Equation ( 29), as outlined below:…”

“…An additional practical application is presented to demonstrate the enhanced performance of the proposed estimator. This application's dataset pertained to entertainment demand, a field that has previously been explored by Abonazel et al [16]. These data, originally introduced by Cameron and Trivedi [35], were employed to estimate a function representing recreation demand.…”

“…These articles have demonstrated that estimators relying on two parameters outperform those relying on only one parameter. Notable studies include those of Algamal and Abonazel [14]; Yang and Chang [15]; Abonazel et al [16]; Omara [17]; and Abonazel et al [18]. The objective of this article was to introduce a new modified two-parameter Liu estimator for the Poisson model, and to propose methods for selecting its parameters.…”