On the ridge estimation of the Conway‐Maxwell Poisson regression model with multicollinearity: Methods and applications

Abstract

AbstractIn data analysis, count data modeling contributing a significant role. The Conway‐Maxwell Poisson (COMP) is one of the flexible count data models to deal over and under dispersion. In the COMP regression model, when the explanatory variables are correlated, then the maximum likelihood estimator does not give efficient results due to the large standard error (SE) of the estimates. To overcome the effect of multicollinearity, we have proposed some ridge regression estimators in the COMP regression model by introducing dispersion parameter in the context of overdispersion, equidispersion, and underdispersion. The Iterative reweighted least method is used for the estimation of ridge regression coefficients in the COMP regression model. To evaluate the performance of the proposed estimators, we use mean squared error (MSE) as the performance evaluation criteria. Theoretical comparison of the proposed estimators with the competitor estimators is made and conditions of efficiency have been derived. The proposed estimator is evaluated with the help of a simulation study and two real applications. The results of the simulation study and real applications show the superiority of the proposed estimator because the proposed estimator produces smaller MSE and SEs of the COMP regression estimates with multicollinearity.