Comparison of PARAFASCA, AComDim, and AMOPLS approaches in the multivariate GLM modelling of multi-factorial designs

Abstract

Data tables from experimental designs with multiple response variables and a large number of responses with respect to the number of observations are becoming more common, particularly in the omics and chemometrics fields. Traditional multivariate modelling approaches are not suitable for this type of data and more complex approaches like ANOVA Simultaneous Component Analysis (ASCA) and ANOVA Principal Component Analysis (APCA) have been developed to analyse them. They combine a matrix decomposition based on an ANOVA model with a multivariate step, Principal Component Analysis (PCA), which is applied to each decomposed matrix.This article compares ASCA and APCA to three other and less known techniques combining ANOVA and a multivariate step: PArallel Factor - Simultaneous Component Analysis (PARAFASCA), ANOVA Common Dimensions (AComDim), and ANOVA Multi-block Orthogonal Partial Least Squares (AMOPLS). The main advantages of these three methods are their ability to explore in a single and global procedure all (or a part) of the model effects, extract automatically the most important ones, interpret them visually and quantify their respective importance and significance. Theses approaches are presented in a common framework to make their comparison easier, some enhancements are introduced and they are also extended to unbalanced experimental designs thanks to a GLM version of the matrix decomposition.The three methods are applied to a 1H NMR data set with a three-factor unbalanced experimental design. Quantitative and visual results are compared for the three techniques and show that they are all suitable for the analysis of a complex model, but differ in the type of outputs and the ease of interpretation of the results. This opens perspectives for the analysis of even more complex data, including models with random or quantitative effects.