A COMPARISON OF NONNESTED TESTS FOR MISSPECIFIED MODELS USING THE METHOD OF APPROXIMATE SLOPES

Comparisons of the Cox, Wald, and J tests are conducted under a standa rd framework and in a misspecified setting - the data generation proce ss includes a regressor that is not in either model. Most power compar isons have been carried out for 'local alternatives' but comparisons u nder a 'nonlocal alternatives' framework using the method of approxima te slopes developed by Bahadur (1960, 1967) are made in this paper. Mo nte Carlo experiments are conducted and the Cox test is shown to have the highest small sample power and approximate slope for most of the c ases considered. The results from response surface regressions provide strong evidence that the approximate slope is a good predictor of the small power of nonnested tests. It is also useful for directly compar ing the small sample power of one degree of freedom tests of nonnested hypotheses.