Comparing Non-Nested Regression Models

Abstract

A method for comparing the fits of two non-nested models, based on a suggestion of Davidson and MacKinnon (1981), is developed in the context of linear and nonlinear regression with normal errors. Each model is regarded as a special case of an artificial "supermodel" and is obtained by restricting the value of a mixing parameter gamma to 0 or 1. To enable estimation and hypothesis testing for gamma, an approximate supermodel is used in which the fitted values from the individual models appear in place of the original parametrization. In the case of nested linear models, the proposed test essentially reproduces the standard F test. The calculations required are for the most part straight-forward (basically, linear regression through the origin). The test is extended to cover situations in which serious bias in the maximum likelihood estimate of gamma occurs, simple approximate bounds for the bias being given. Two real datasets are used illustratively throughout.