Structured orthogonal families of one and two strata prime basis factorial models

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• 作者：Paulo C. Rodrigues (1) (2)
  Elsa E. Moreira (1)
  Vera M. Jesus (1)
  Jo?o T. Mexia (3)
  
• 关键词：Orthogonal models ; Families of models ; Nested models ; Two strata models ; Factorial designs ; 62J99 ; 62K15
• 刊名：Statistical Papers
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：55
• 期：3
• 页码：603-614
• 全文大小：163 KB
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• 作者单位：Paulo C. Rodrigues (1) (2)
  Elsa E. Moreira (1)
  Vera M. Jesus (1)
  Jo?o T. Mexia (3)
  
  1. CMA–Research Center for Mathematics and Applications, Faculty of Sciences and Technology, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal
  2. ISLA Campus Lisbon, Laureate International Universities, Lisbon, Portugal
  3. CMA–Research Center for Mathematics and Applications, and Department of Mathematics, Faculty of Sciences and Technology, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal
  
• ISSN：1613-9798

文摘

The models in structured families correspond to the treatments of a fixed effects base design \(\pi \) . Then the action of factors in \(\pi \) , on the fixed effects parameters of the models, is studied. Analyzing such a families enables the study of the action of nesting factors on the effects and interactions of nested factors. When \(\pi \) has an orthogonal structure, the family of models is said to be orthogonal. The models in the family can have one, two or more strata. Models with more than one stratum are obtained through nesting of one stratum models. A general treatment of the case in which the base design has orthogonal structure is presented and a special emphasis is given to the families of prime basis factorials models. These last models are, as it is well known, widely used in fertilization trials.