On invariance and randomization in factorial designs with applications to D-optimal main effect designs of the symmetrical factorial |
| |
| Institution: | 1. Department of Recreation and Leisure Studies, University of Waterloo, Waterloo, ON N2L 3G1, Canada;2. University of Ottawa, Ontario, Canada;1. Department of Civil Engineering, University College of Engineering, Ramanathapuram, TN, India;2. Department of Chemistry, University College of Engineering, Ramanathapuram, TN, India;3. Department of Civil Engineering, Paavai Engineering College, Namakkal, TN, India;4. Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai, India;1. Animal Environment Division, Department of Animal Biotechnology and Environment, National Institute of Animal Science, RDA, Jeonju, South Korea;2. Sino-Forest Applied Research Centre for Pearl River Delta Environment, and Department of Biology, Hong Kong Baptist University, Hong Kong Special Administrative Region;3. Department of Biomedical Engineering, Sathyabama University, Chennai, India;4. Environmental Technology Division, Central Leather Research Institute, Chennai, India;1. Department of Forest Resources Conservation and Ecotourism, Faculty of Forestry, IPB University (Bogor Agricultural University), Kampus IPB Darmaga Bogor 16680, Indonesia;2. Tropical Biodiversity Conservation Program, Department of Forest Resources Conservation and Ecotourism, Faculty of Forestry, IPB University (Bogor Agricultural University), Kampus IPBDarmaga Bogor 16680, Indonesia;3. Department of Biology, Faculty of Mathematics and Natural Sciences, IPB University (Bogor Agricultural University), Kampus IPB Darmaga Bogor 16680 Indonesia;4. Comportement Et Ecologie De La Faune Sauvage, I.N.R.A.E, Université De Toulouse, CS 52627, 31326 Castanet-Tolosan Cedex, France;5. Research Centre for Biology, Zoology Division, The Indonesian Institute of Sciences, Cibinong 16911 Indonesia;1. Department of Medicine and Therapeutics, Faculty of Medicine, The Chinese University of Hong Kong, Hong Kong, SAR, People''s Republic of China;2. Li Ka Shing Institute of Health Sciences, Faculty of Medicine, The Chinese University of Hong Kong, Hong Kong, SAR, People''s Republic of China;3. School of Health Sciences, University of Manchester, Manchester, United Kingdom;4. Tianjin Key Laboratory of Ionic-Molecular Function of Cardiovascular Disease, Department of Cardiology, Tianjin Institute of Cardiology, Second Hospital of Tianjin Medical University, Tianjin, People''s Republic of China;6. School of Life Sciences, The Chinese University of Hong Kong, Hong Kong, SAR, People''s Republic of China;5. Second Department of Cardiology, Laboratory of Cardiac Electrophysiology, “Evangelismos” General Hospital of Athens, Athens, Greece;7. Royal Brompton Hospital and Imperial College London, London, United Kingdom;11. Department of Anaesthesia and Intensive Care, State Key Laboratory of Digestive Disease, LKS Institute of Health Sciences, The Chinese University of Hong Kong, Hong Kong, SAR, People''s Republic of China;12. Department of Cardiology, Theodor Burghele Clinical Hospital, Carol Davila University of Medicine and Pharmacy, Bucharest, Romania;8. Electrophysiology Unit, Sri Jayadeva Institute of Cardiovascular Sciences and Research, Bangalore, India;10. Department of Cardiology, University Heart Center, Zurich, Switzerland;9. Cardiovascular Research Center, Shahid Sadoughi University of Medical Sciences, Yazd, Iran;71. Department of Cardiovascular Medicine, First Affiliated Hospital of Dalian Medical University, Dalian, People''s Republic of China;112. Lankenau Institute for Medical Research and Lankenau Medical Center, Wynnewood, Pennsylvania;123. Beijing Anzhen Hospital, Capital Medical University, Beijing, People''s Republic of China;1. Department of Rehabilitation Science and Technology, School of Health and Rehabilitation Sciences, University of Pittsburgh, Pittsburgh, PA 15260, USA;2. Department of Occupational Therapy, School of Health and Rehabilitation Sciences, University of Pittsburgh, Pittsburgh, PA 15260, USA;3. Department of Emergency Medicine, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15260, USA |
| |
| Abstract: | Under the setting of the columnwise orthogonal polynomial model in the context of the general factorial it is shown that (i) the determinant of the information matrix of a design relative to an admissible vector of effects is invariant under a permutation of levels; (ii) the unbiased estimation of a linear function of an admissible vector of effects can be obtained under equal probability randomization. These results extend the work on invariance and randomization carried out under the more restrictive assumption of the orthonormal polynomial model by Srivastava, Raktoe and Pesotan (1976) and Pesotan and Raktoe (1981). Moreover, the problem of the construction of D-optimal main effect designs in the symmetrical factorial is reduced to a study of a special class of (0,1)-matrices using the Helmat matrix model. Using this class of (0,1)-matrices and the determinant invariance result, some classes of D-optimal main effect designs of the s2 and s3 factorial respectively are presented. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
