Modified Jackknife Ridge Estimator for Beta Regression Model With Application to Chemical Data

Abstract

The linear regression model is not applicable when the response variable's value comes in percentages, proportions, and rates, which are restricted to the interval (0, 1). In this situation, we applied the beta regression model (BRM) popularly used to model chemical, environmental and biological data.  The parameters in the model are often estimated using the conventional method of maximum likelihood. However, this estimator is unreliable and inefficient when the explanatory variables are linearly correlated- a condition known as multicollinearity. Thus, we developed the Jackknife Beta ridge and the modified Jackknife Beta ridge estimator to estimate the regression coefficient when multicollinearity exists efficiently. The properties of the new estimators were derived. We compared the estimator's performance with the existing estimators theoretically using the mean squared error criterion. Furthermore, we conducted a simulation study and chemical data to evaluate the new estimators’ performance. The theoretical comparison, simulation, and real-life application results established the dominance of the proposed methods.