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- Algebraic structure for interaction on mixed modelsPublication . Ramos, Paulo; Fernandes, Célia; Mexia, João TiagoBinary operations on commutative Jordan algebras, CJA, can be used to study interactions between sets of factors belonging to a pair of models in which one nests the other. It should be noted that from two CJA we can, through these binary operations, build CJA. So when we nest the treatments from one model in each treatment of another model, we can study the interactions between sets of factors of the first and the second models.
- Study of the interactions in a three-way crossed classification modelPublication . Ramos, Paulo; Fernandes, CéliaCrossed classification models are applied in many investigations taking in consideration the existence of interaction between all factors or, in alternative, excluding all interactions, and in this case only the effects and the error term are considered. In this work we use commutative Jordan algebras in the study of the algebraic structure of these designs and we use them to obtain similar designs where only some of the interactions are considered. We finish presenting the expressions of the variance componentes estimators.