Testing The Equality Of Regression Coefficients And A Pooling Methodology From Multiple Samples When The Data Is Multicollinear

Abstract

Testing the equality of regression coefficients between two regression equations is a common practice in statistics today. The theory and methods are sufficiently developed under ordinary least squares (OLS) estimation. However, there is no method for conducting such tests when OLS estimation is not an appropriate method. For example, when multicollinearity exists in the data.Therefore, there is a need for a method to test the equality of regression coefficients when the data is multicollinear. In this research, we will present methods for conducting such a test using ridge regression coefficient estimators and principal component estimators. We will also present a method for testing the equivalence of the OLS regression coefficients between two or more samples even in the presence of multicollinearity. Lastly, we will present a method for determining a ridge preliminary test estimator (PTE) and a PTE that incorporates the ridge and a stacked estimator.