A modified sweep algorithm for interchanging between overparameterized and cell means linear models

Abstract

The overparameterized and cell means models are alternative formulations of the conventional linear model that underlies designed experiments with fixed effects. Each has its relative advantages and adherents. Statistical software packages generally adopt just one of these formulations, and transition between the two is not routinely undertaken. In this paper we present a modified sweep algorithm for undertaking translation in either direction. The algorithm is illustrated with a published data set from Milliken and Johnson (1984). We demonstrate how to generate the cell means model hypothesis corresponding to any testable hypothesis in the overparameterized model, and indicate that the interpretability of the corresponding sums of squares depends heavily on the selected model.

Keywords:

• Cell means model
• Estimable parametric function
• Hermite canonical form
• SAS^R GLM
• Sweep operator

^∗Francis Hsuan is Associate Professor and Burt Holland is Professor and Chair.

^∗Francis Hsuan is Associate Professor and Burt Holland is Professor and Chair.

Notes

^∗Francis Hsuan is Associate Professor and Burt Holland is Professor and Chair.