Multiblock redundancy analysis from a user's perspective. Application in veterinary epidemiology

Abstract

For the purpose of exploring and modelling the relationships between a dataset Y and several datasets (X₁, …, X_K) measured on the same individuals, multiblock Partial Least Squares is a regression technique which is widely used, particularly in chemometrics. In the same vein, an extension of Redundancy Analysis to the multiblock setting is proposed. It is designed to handle the specificity of complex veterinary epidemiological data. These data usually consist of a large number of explanatory variables organized in meaningful blocks and a dataset to be predicted, e.g. the expression of a complex animal disease described by several variables. Some appropriate indices are also proposed, associated with different interpretation levels, i.e. variable, block and component. These indices are linked to the criterion to be maximized and therefore are directly related to the solution of the maximization problem under consideration.