Covariance analyses with heterogeneity of slopes in fixed models

Techniques that describe the use of covariance when heterogeneity of slopes exists are severely limited. Although a few procedures for model selection have been recommended, none, except the hierarchical approach, is straightforward and usable with present computer programs. The hierarchical subset selection procedure presented in this paper is based on the proposition that heterogeneity may be present only for certain terms in the model. After hierarchical selection, those terms which do not involve heterogeneity are interpreted as in the usual analysis for covariance. The interpretations of those terms which do involve heterogeneity are modified with respect to significance tests performed at various values of the covariate. The hierarchical subset selection method allows one to investigate heterogeneity of slopes in covariance models as functions of the classification variables present in the design.