This paper defines the contraction of a resolvable row-column design for more than two replicates. It shows that the (M,S)-optimality criterion for the row-column designs can be expressed simply in terms of the elemen...
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This paper defines the contraction of a resolvable row-column design for more than two replicates. It shows that the (M,S)-optimality criterion for the row-column designs can be expressed simply in terms of the elements of the row and column incidence matrices of the contraction. This allows the development of a very fast algorithm to construct optimal or near-optimal resolvable row-column designs. The performance of such an algorithm is compared with an existing algorithm.
A cross-over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may de...
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A cross-over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the carry-over effects of the treatments applied in one or more previous periods. Various models have been proposed to explain the nature of the carry-over effects. An experimental design that is optimal under one model may not be optimal if a different model is the appropriate one. In this paper an algorithm is described to construct efficient cross-over designs for a range of models that involve the direct effects of the treatments and various functions of their carry-over effects. The effectiveness and flexibility of the algorithm are demonstrated by assessing its performance against numerous designs and models given in the literature. Copyright (C) 2004 John Wiley Sons, Ltd.
In a changeover design, each subject receives a sequence of treatments over consecutive time periods. We provide simple recursive formulae for updating the average efficiency factors of both direct and residual treatm...
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In a changeover design, each subject receives a sequence of treatments over consecutive time periods. We provide simple recursive formulae for updating the average efficiency factors of both direct and residual treatment effects, after two treatments are interchanged. We have incorporated these formulae into two interchange algorithms. From a comparison with designs generated from other algorithms using surrogate objective functions, we show that these recursive methods generally produce more efficient designs more quickly. (C) 2002 Elsevier Science B.V. All rights reserved.
interchange algorithms are widely used to construct efficient block and row-column designs. We provide simple recursive formulae for updating this average efficiency factor, so that it is no longer computationally exp...
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interchange algorithms are widely used to construct efficient block and row-column designs. We provide simple recursive formulae for updating this average efficiency factor, so that it is no longer computationally expensive to calculate it after each possible interchange.
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