Inferring biadditive models within the Bayesian paradigm
2012
Josse, Julie | Denis, Jean-Baptiste
So called biadditive models (most commonly known as Ammi models for additive main effect and multiplicative interaction) are frequently used to interpret the main traits of two ways data, for instance for the interpretation of genotype by environment interactions. Linked with PCA technics, they provide efficient empirical descriptions of matrix structures. The use of Bayesian approaches in statistical analysis in increasing for many statistical models due to the new computer capacities and the existence of specialized algorithms to draw into posterior distributions. Some work was already presented to deal with biadditive models in a Bayesian way. Here, we consider the point, proposing a new solution directly on the overparam eterized model which allows one the use of standard softwares, for instance bugs implementations. We first give a detailed presentation of our proposal and then apply it to a real data set coming from the litterature, focusing on the interpretation. In the appendix, the proposal to deal with overparameterized models is developped for any type of models.
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