Hypothesis testing procedures for non-nested regression models

Abstract

Theory often indicates that a given response variable should be a function of certain explanatory variables yet fails to provide meaningful information as to the specific form of this function. To test the validity of a given functional form with sensitivity toward the feasible alternatives, a procedure is needed for comparing non-nested families of hypotheses. Two hypothesized models are said to be non-nested when one model is neither a restricted case nor a limiting approximation of the other. These non-nested hypotheses cannot be tested using conventional likelihood ratio procedures. In recent years, however, several new approaches have been developed for testing non-nested regression models.

A comprehensive review of the procedures for the case of two linear regression models was presented. Comparisons between these procedures were made on the basis of asymptotic distributional properties, simulated finite sample performance and computational ease. A modification to the Fisher and McAleer JA-test was proposed and its properties investigated. As a compromise between the JA-test and the Orthodox F-test, it was shown to have an exact non-null distribution. Its properties, both analytically and empirically derived, exhibited the practical worth of such an adjustment.

A Monte Carlo study of the testing procedures involving non-nested linear regression models in small sample situations (n ≤ 40) provided information necessary for the formulation of practical guidelines. It was evident that the modified Cox procedure, N̄ , was most powerful for providing correct inferences. In addition, there was strong evidence to support the use of the adjusted J-test (AJ) (Davidson and MacKinnon's test with small-sample modifications due to Godfrey and Pesaran), the modified JA-test (NJ) and the Orthodox F-test for supplemental information. Under non normal disturbances, similar results were yielded.

An empirical study of spending patterns for household food consumption provided a practical application of the non-nested procedures in a large sample setting. The study provided not only an example of non-nested testing situations but also the opportunity to draw sound inferences from the test results.