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Biometrika 2009 96(3):677-690; doi:10.1093/biomet/asp034
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© 2009 Biometrika Trust

Article

Optimal repeated measurement designs for a model with partial interactions

P. Druilhet

Laboratoire de Mathématiques, UMR CNRS 6620, Université Blaise Pascal, 63 177 Aubière CEDEX, France pierre.druilhet{at}math.univ-bpclermont.fr

W. Tinsson

Laboratoire de Mathématiques Appliquées, UMR CNRS 5142, Université de Pau, BP 1155, 64013 PAU CEDEX, France walter.tinsson{at}univ-pau.fr

Received for publication 1 January 2007. Revision received 1 December 2008.
  Abstract

We consider crossover designs for a model with partial interactions. In this model, the carryover effect depends on whether the treatment is preceded by itself or not. When the aim of the experiment is to study the total effects corresponding to a single treatment, we obtain approximate optimal symmetric designs, within the competing class of circular designs, by generalizing the method introduced by Kushner (1997) and Kunert & Martin (2000). This generalization places the method proposed by Bailey & Druilhet (2004) into Kushner's context. The optimal designs obtained are not binary, as in Kunert & Martin (2000). We also propose efficient designs generated by only one sequence.

Key Words: Approximate design • Crossover design • Optimal design • Total effect • Universal optimality


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