Structured Families of Linear Models with Orthogonal Base

In statistical inference the structured family of models (s.f.m) are constituted by unit models corresponding to the treatments of a linear model called the base model which can be orthogonal with for instance fixed effects and cross-nesting of factors. On the side the unit models can be for instance multiple linear regressions or log-linear models on the same parameters. Through this approach we can study the influence of the factors of the base model on the linear combinations of unit models parameters. Two applications to real data are presented to illustrate the approach. In these case studies s.f.m. with log-linear unit models are applied to hydrology through the analysis of drought classes transitions for comparing sub-periods of the same time series or to compare sub-regions.