Exact Tests for the Comparison of Correlated Response Models With an Unknown Dispersion Matrix

Abstract

In this article exact tests for the equality of parameters from several correlated linear response models with an unknown variance–covariance matrix Σ are presented. The models are assumed to be of the same form and to contain the same set of input variables. The development of the proposed tests is based on a multivariate representation of the system of response models as a single linear multiresponse model. Comparisons among the models' parameter vectors can then be formulated as a general linear hypothesis under the multiresponse model. Any of the commonly used multivariate test statistics—Roy's largest root, Wilks's likelihood ratio, Hotelling–Lawley's trace, or Pillai's trace—can be used subsequently to test this hypothesis. An investigation is made with regard to the effects of design multicollinearity and structure of the variance–covariance matrix Σ on the power of the multivariate tests. A numerical example involving three response models and two input variables is used to illustrate the application of the multivariate tests.

KEY WORDS:

• Multiresponse model
• Roy's largest root
• Wilks's likelihood ratio
• Hotelling-Lawley's trace
• Pillai's trace
• Power of the multivariate tests