A tutorial on the analysis of multifactorial designs from one or more data sources using AComDim

To analyze data acquired from experiments based on multifactorial designs, approaches able to decompose and model the main sources of variation in the measurements are particularly useful. Although methods combining analysis of variance (ANOVA) with principal components analysis (PCA) or simultaneous components analysis (SCA), namely, ANOVA-PCA (APCA) and ANOVA-SCA (ASCA), have proven to be efficient to tackle such data structures, they require the construction and interpretation of a model for each experimental factor and interaction. Other methods like parallel factor analysis-SCA (PARAFASCA), ANOVA multiblock orthogonal partial least squares (AMOPLS) and ANOVA-Common Dimensions (AComDim) offer the possibility to have an overall picture of all the sources of variation by means of a single model. Moreover, acquiring data from one or multiple data sources through the same experimental design is becoming more common, and approaches able to cope with such complex data structures are needed. In this tutorial, an explanation of the theory and software implementation of AComDim as well as its usage for the analysis of data acquired from experimental designs is provided. Relying on the multiblock nature of AComDim, an extension to cases where data from multiple sources are acquired on the same samples is proposed.