Analysis of experimental design with multivariate response: A contribution using multiblock techniques

In many application areas, experimental approaches both involve an experimental design that determines changes in the studying factors and an untargeted analytical method (IR, LC-MS, NMR,…) used to characterize the samples by a large number of variables. This leads to a resulting data set which can be structured in blocks with respect to the different levels of the experimental factors. Among the methods that have been developed to address this situation, the ANOVA-Simultaneous Component Analysis (ASCA) is the only one which proposes the use of a multiblock technique to date. Nevertheless, other possibilities are achievable. Therefore in this article, we propose 1) to adopt another way of defining and organizing the blocks from the initial matrix and 2) to apply Multiple Co-inertia Analysis (MCoA) a multiblock method different from Simultaneous Component Analysis to manage this new scenario. The complementarities of our proposal with ASCA are demonstrated on a case study related to cheese processing.