An Approximate Test for Comparing Heteroscedastic Regression Models

Abstract

Abstract This article addresses the problem of testing whether the vectors of regression coefficients are equal for two independent regression models when the error variances are unequal. The usual Chow statistic, appropriate when equality of variances can be assumed, is modified by replacing the pooled residual variance in the denominator with a weighted average of the residual variances from each data set. The weights are functions of the mean of the eigenvalues of W = X′ 1 X 1(X′ 1 X 1 + X′ 2 X 2)-1. Both numerator and denominator are then approximated by scalar multiples of chi-squared distributions. The parameters of these approximated distributions are chosen to equate their first two moments to those of the exact distribution. The resulting approximation for the modified Chow statistic, C*, is an F distribution with degrees of freedom that depend on the two sample sizes, the number of regressor variables, the average eigenvalue of W, and the true ratio of error variances. Since the latter is unknow...