On the Liu estimation of Bell regression model in the presence of multicollinearity

Abstract

Recently, the Bell regression model (BRM) is proposed to model a count variable. The BRM is generally preferred over the Poisson regression model to overcome the restriction that the mean is equal to the variance. The BRM is usually estimated using the maximum likelihood estimator (MLE). It is a well-known phenomenon that the MLE is very sensitive to multicollinearity. We propose a Bell Liu regression (BLR) estimator to circumvent the problem of multicollinearity associated with the BRM. Moreover, some new Liu parameters are proposed for the BLR estimator. To evaluate the performance of the proposed estimators, we conduct a Monte Carlo simulation study where the mean squared error is considered as an evaluation criterion. In addition, a real application is also included to show the superiority of the proposed method.

KEYWORDS:

• Bell distribution
• Bell regression model
• maximum likelihood estimator
• multicollinearity
• Liu estimator
• mean squared error

AMS Subject Classifications:

• 62J07
• 62J12

Disclosure statement

No potential conflict of interest was reported by the author(s).