Comparing Several Regression Models with Unequal Variances

We consider the problem of comparing k regression models, when the variances are not assumed to be equal. For this problem, the classical F test can lead to misleading results, and there is no simple test which adequately controls the size when the sample sizes are small. For k = 2, the most widely used test is the “weighted F test,” also known as the “asymptotic Chow test.” But this test does not work well for small samples, and various modifications have been proposed in the literature. For k > 2, few tests are available and only the parametric-bootstrap (PB) test of Tian et al. (2009) controls the size fairly adequately. In this article, we propose three fairly simple F tests which can easily be applied in the general case, k ⩾ 2, and avoid the complications of the PB test. Our simulations indicate that these tests have satisfactory performance. Also, our simulations confirm that the power properties of our proposed tests are similar to the PB test. Therefore, our proposed tests provide simple alternatives to the PB test, which can easily be used by practitioners who may not be familiar with the PB.