Some determinant optimality aspects of main effect fold-over designs |
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Authors: | H Pesotan BL Raktoe |
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Institution: | Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada NIG 2W1;Department of Economics and Statistics, National University of Singapore, Kent Ridge, Singapore 0511 |
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Abstract: | Saha and Mohanty (1970) presented a main effect fold-over design consisting of 14 treatment combinations of the 24×33 factorial, which had the nice property of being even balanced. Calling this design DSM, this paper establishes the following specific results: (i) DSM is not d-optimal in the subclass Δe of all 14 point even balanced main effect fold-over designs of the 24×33 factorial; (ii) DSM is not d-optimal in the subclass of all 14 point even and odd balanced main effect fold-over designs of the 24×33 factorial; (iii) DSM is even optimal in and Δe. In addition to these results two 14 point designs in are presented which are d-optimal and via a counter example it is shown that these designs are not odd optimal. Finally, several general matrix algebra results are given which should be useful in resolving d-optimality problems of fold-over designs of the kn11×kn22 factorial. |
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Keywords: | Primary 62K15 Secondary 05B20 Factorial Information matrix Main effects Fold-over design Determinant optimal Odd optimal design Even optimal design |
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