Robust Two-Parameter Poisson Regression Model Estimator

Abstract

Multicollinearity and outliers are some of the problems of parameter estimation in the Poisson regression analysis. The existing researches used the maximum likelihood estimator, Poisson Ridge estimator, transformed-M Ridge estimator, and the two-parameter estimator of Poisson regression models have taken the issue of multicollinearity and outliers with interest in the explanatory but not with the response variables. This paper suggested use of transform M-estimator assisting in transformation of the response variable, making it less sensitive to extreme and irregular observations and stabilizing variance. This is useful in instances where the response has skewness, or non-constant variance or other non-standard distributional properties. The transform M-estimator is also effective in enhancing efficiency in the Poisson regression as the relationship between means and variances is skewed. A two-parameter estimator is a biased regression estimator, which adds two additional tuning (biasing) parameters to the regression to enhance better estimation, particularly when there is multicollinearity among the predictor variables. The estimator is an extension of single-parameter estimators such as ridge or Liu estimators, is more flexible, and in many cases the estimator is more effective but has the drawback of the response variable being counted. Building on these strengths, the present study integrates the transform M-estimator with the two-parameter estimator to produce a more stable and reliable method suited for complex count-data as the response variable. The proposed estimator is able to reduce the effect of multicollinearity and outliers while dealing with response variables that the data are counted in nature exhibiting outliers. Simulation study and real-life data was used to validate the efficacy of the new estimator.   The result of the finding shows that the introduced estimator (MT-TPE) performed better than existing estimators in the presence of outliers in the response variable and multicollinearity in the explanatory variables using the MSE. The ability of an estimator to maintain efficiency makes it a valuable tool in modeling, particularly in datasets commonly encountered in real-world scenarios. Thus, the estimator (MT-TPE) provided a robust method for mitigating the effects of multicollinearity and outliers in count data.