A Test for the Equality of Parameters for Separate Regression Models in the Presence of Heteroskedasticity

Abstract

Testing for the equality of regression coefficients across two regressions is a problem considered by analysts in a variety of fields. If the variances of the errors of the two regressions are not equal, then it is known that the standard large sample F -test used to test the equality of the coefficients is compromised by the fact that its actual size can differ substantially from the stated level of significance in small samples. This article addresses this problem and borrows from the literature on the Behrens-Fisher problem to provide some simple modifications of the large sample test which allows one to better control the probability of committing a Type I error. Empirical evidence is presented which indicates that the suggested modifications provide tests which are superior to well-known alternative tests over a wide range of the parameter space.

A computational approach test for comparing two linear regression models with unequal variances

“…Moreno et al [23] proposed a Bayesian solution to the problem of testing the equality of two linear regression models when the error variances were unknown and arbitrary. Oberhelman and Kadiyala [24] made some modifications of the standard F-test for large samples commonly used to test the equality of two linear regression models when the variances of the regression errors are not equal. Recently, there are many studies for testing the equality of regression models in several heteroscedasticity normal regression models [28,32,35].…”