Tests for Equality of Parameter Matrices in Two Multivariate Linear Models

An approximate degrees of freedom test is suggested for hypotheses of the kindH0:C′Φ1M=C′Φ2Min two independent multivariate linear models:Yi=Xi iΦi+εi,i=1, 2, under the assumption of error matrix variate normality and heteroscedasticity. It is shown for specific vector choices of the matricesCandMthat the test reduces to approximate degrees of freedom solutions obtained by Nel (1989), Nel and van der Merwe (1986) and Welch (1947) for simpler models.