Performance analysis of shrinkage estimators in Conway-Maxwell-Poisson regression model

In the literature of generalized linear models (GLMs), there have been many shrinkage estimation methods in the presence of multicollinearity. Applications of these estimators are often done on logistic, Poisson, gamma, and negative binomial regression models. While Poisson and negative binomial regression models are frequently used for count data with equi-dispersion and over-dispersion, respectively, Conway-Maxwell Poisson (COM-Poisson) is a distribution that is frequently used for modelling count data with either over-dispersion or under-dispersion. Since the COM-Poisson distribution includes Bernoulli, Poisson, geometric, and negative binomial distributions as special cases, it is inevitable to see the characterization of shrinkage estimation methods in the COM-Poisson distribution. The aim of this study is to propose the OK estimator in COM-Poisson regression and practically to compare the performance of maximum likelihood, ridge, Liu, and OK estimators in the context of COM-Poisson regression in terms of root mean square and mean absolute error. While making these comparisons, the tuning parameters that the OK estimator depends on were selected by genetic algorithm, Akaike information criterion, and Bayesian information criterion and the effects of different tuning parameter selection methods on the estimators as well as on the deviance residuals of the estimators were examined via a numerical example.