MBPCA-OS: an exploratory multiblock method for variables of different measurement levels. Application to study the immune response to SARS-CoV-2 infection and vaccination

Studying a large number of variables measured on the same observations and organized in blocks - denoted multiblock data - is becoming standard in several domains especially in biology. To explore the relationships between all these variables - at the block- and the variable-level - several exploratory multiblock methods were proposed. However, most of them are only designed for numeric variables. In reality, some data sets contain variables of different measurement levels (i.e., numeric, nominal, ordinal). In this article, we focus on exploratory multiblock methods that handle variables at their appropriate measurement level. Multi-Block Principal Component Analysis with Optimal Scaling (MBPCA-OS) is proposed and applied to multiblock data from the CURIE-O-SA French cohort. In this study, variables are of different measurement levels and organized in four blocks. The objective is to study the immune responses according to the SARS-CoV-2 infection and vaccination statuses, the symptoms and the participant's characteristics.