AI Article Synopsis
- The text describes a method for comparing two non-nested regression models, inspired by Davidson and MacKinnon (1981), using an artificial "supermodel."
- It explains how the mixing parameter gamma is employed to connect the two models and introduces an approximate supermodel for estimating and testing gamma.
- The method aligns with traditional F tests for nested models and includes solutions for addressing potential bias in gamma's maximum likelihood estimate, demonstrated through real dataset examples.
Article 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.
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