Inferential Techniques in Structured Families of Models: Application to Durum Wheat Breeding Data

ABSTRACT This study introduces an extended inferential framework within the structured families of models (SFM), designed to analyze orthogonal fixed effects models with crossed factors using symmetric stochastic matrices (SSM) and spectral decomposition analysis. The complexity of the model is defined by the dominant eigenvalues in the model matrices, facilitating cross‐sectional and longitudinal analyses. Our innovative approach provides a strong foundation in the mathematical principles behind SFM and enables direct application to stochastic symmetric and cross‐product matrices. That allows us to introduce a more robust inference structure based on F tests. In addition, the assumptions of homoscedasticity between the vectors of homologous components were validated using ANOVA, which increases the use of factor design analyses in families of models. Empirical validation is provided through a case study on durum wheat cultivars ( Triticum turgidum L., Durum Group), revealing significant effects of year and location on cultivar behavior. Our technique is still robust even when we work with missing observations.