A new estimator for discrete Weibull regression model with correlated variables: an illustrative example

In real life, count variables may exhibit dispersion. In data analysis, the discrete Weibull regression model (DWRM) is flexible enough to address the under, over, and mixed dispersion. In DWRM, when explanatory variables are highly correlated with each other (presence of multicollinearity), then the method of maximum likelihood estimation (MLE) becomes ineffective. In this study, problems of dispersion and multicollinearity are simultaneously handled using the ridge regression estimator (RRE) and different dispersion parameters in the DWRM. The iterative reweighted least squares method (IRLS) estimates the ridge regression coefficients in DWRM. A theoretical comparison of the proposed ridge estimators with the traditional estimator is also presented. The efficiency of the proposed ridge estimator is evaluated through Monte Carlo simulation and a real application, as it results in a smaller mean square error (MSE). The proposed Discrete Weibull Ridge Estimator (DWRE) is considered an efficient estimator when comparing the results with MLE.