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

Author

Listed:
  • Paulo Rodrigues
  • Elsa Moreira
  • Vera Jesus
  • João Mexia

Abstract

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. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Paulo Rodrigues & Elsa Moreira & Vera Jesus & João Mexia, 2014. "Structured orthogonal families of one and two strata prime basis factorial models," Statistical Papers, Springer, vol. 55(3), pages 603-614, August.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:603-614
    DOI: 10.1007/s00362-013-0507-0
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    References listed on IDEAS

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    1. Wangli Xu & Yanwen Li & Dawo Song, 2013. "Testing normality in mixed models using a transformation method," Statistical Papers, Springer, vol. 54(1), pages 71-84, February.
    2. Elsa Moreira & João Mexia & Miguel Fonseca & Roman Zmyślony, 2009. "L models and multiple regressions designs," Statistical Papers, Springer, vol. 50(4), pages 869-885, August.
    3. Mexia, Joao Tiago, 1990. "Best linear unbiased estimates, duality of F tests and the Scheffe multiple comparison method in the presence of controlled heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 271-281, December.
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