On the Choice of Appropriate Error Terms in Profile Analysis

Abstract

Univariate mixed models constitute an appealing statistical tool for profile analysis. Besides the well-known computational advantages, an important reason for this is that, for a variety of hypotheses, exact F-tests derived under such models remain valid even when the underlying covariance structure satisfies less stringent conditions (sphericity) than those imposed by the assumed models (uniformity). Furthermore, simple adjustments are available to produce approximate F-tests in cases where even the sphericity condition is not tenable. In either case, the choice of convenient error terms may constitute a source of potential difficulty. On the basis of the specification of the relevant hypotheses in terms of a cell means parameterization we present some guidelines that may be helpful towards the construction of the appropriate tests.