Interaction in balanced cross nested designs

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Commutative Jordan Algebras, CJA, are used in the study of mixed models obtained, through crossing and nesting, from simpler ones. In the study of cross nested models the interaction between nested factors have been systematically discarded. However this can constitutes an artificial simplification of the models. We point out that, when two crossed factors interact, such interaction is symmetric, both factors playing in it equivalent roles, while when two nested factors interact, the interaction is determined by the nesting factor. These interactions will be called interactions with nesting. In this work we present a coherent formulation of the algebraic structure of models enabling the choice of families of interactions between cross and nested factors using binary operations on CJA.

Original languageEnglish
Title of host publicationNumerical Analysis and Applied Mathematics, ICNAAM 2011
Subtitle of host publicationInternational Conference on Numerical Analysis and Applied Mathematics
EditorsTheodōros Simos, George Psihoyios
Place of PublicationMelville
PublisherAmerican Institute of Physics (AIP)
Number of pages4
ISBN (Print)9780735409569
Publication statusPublished - 2011
EventICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics - Halkidiki, Greece
Duration: 19 Sept 201125 Sept 2011

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


ConferenceICNAAM 2011
Abbreviated titleICNAAM 2011


  • Balanced cross nested designs
  • commutative Jordan algebras
  • interaction


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