Bootstrap Liu-type estimator for Conway-Maxwell-Poisson regression model
Noora Suhail Hawa, Marwah Yahya Mustafa, B. M. Golam Kibria, Zakariya Yahya Algamal
Abstract
Established as a variation of the Poisson regression, the Conway-Maxwell-Poisson regression (CMPR) considers overdispersion, a serious disadvantage existent in count data analysis, where the variance of the data is higher than the mean. These make the response variable to be a function of the one or more of the explanatory variables. In CMPR model and related series, this is very well known that multicollinearity plays an unfavorable role in the properties of the maximum likelihood estimator. This research proposes another bootstrapped Liu-type shrinkage estimator to deal with the multicollinearity problem in the CMPR model. This was done by bootstraps, the methods used to select them; š and š, parameters in the biasing process. The applicability of the above proposed bootstrapping method was checked when there is multicollinearity with other influencing factors. From observational conclusions of the Monte Carlo simulation study, it can be deduced that for all the combination factors all the proposed methods are superior to the standard methods in terms of MSE. The real application provides the required results which in turn corroborates with these simulated results that is to say these proposed methods are better than the other ones.