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.
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Acknowledgments
We thank the editors and two reviewers for their helpful comments and suggestions on an earlier version of this paper. We also thank Miguel Fonseca for his constructive comments from which our paper has benefited greatly. This work was partially supported by CMA/FCT/UNL, under the project PEst-OE/MAT/UI0297/2011.
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P. C. Rodrigues and E. E. Moreira contributed equally to this work.
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Rodrigues, P.C., Moreira, E.E., Jesus, V.M. et al. Structured orthogonal families of one and two strata prime basis factorial models. Stat Papers 55, 603–614 (2014). https://doi.org/10.1007/s00362-013-0507-0
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DOI: https://doi.org/10.1007/s00362-013-0507-0