Symmetric stochastic matrices and structured families of models

The models in structured families correspond to the treatments of a fixed-effects base model. One then studies the action of the factors of the base design on the fixed effects parameters of the models. The analysis of these families allows the study of the action of cross-factors on cross-factor effects and interactions. When the base model has an orthogonal structure, the model family is said to be orthogonal. A general treatment of the case where the base model has an orthogonal structure is presented and special emphasis is given to structured families of factor models.