  We present a flexible tool, called General Effect Modelling (GEM), for the
analysis of any multivariate data influenced by one or more qualitative
(categorical) or quantitative (continuous) input variables. The variables can
be design factors or observed values, e.g., age, sex, or income, or they may
represent subgroups of the samples found by data exploration. The first step in
GEM separates the variation in the multivariate data into effect matrices
associated with each of the influencing variables (and possibly interactions
between these) by applying a general linear model. The residuals of the model
are added to each of the effect matrices and the results are called Effect plus
Residual (ER) values. The tables of ER values have the same dimensions as the
original multivariate data. The second step of GEM is a multi- or univariate
exploration of the ER tables to learn more about the multivariate data in
relation to each input variables. The exploration is simplified as it addresses
one input variable at the time, or if preferred, a combination of input
variables. One example is a study to identify molecular fingerprints associated
with a disease that is not influenced by age where individuals at different
ages with and without the disease are included in the experiment. This
situation can be described as an experiment with two input variables: the
targeted disease and the individual age. Through GEM, the effect of age can be
removed, thus focusing further analysis on the targeted disease without the
influence of the confounding effect of age. ER values can also be the combined
effect of several input variables. This publication has three parts: the first
part describes the GEM methodology, Part 2 is a consideration of multivariate
data and the benefits of treating such data by multivariate analysis, with a
focus on omics data, and Part 3 is a case study in Multiple Sclerosis (MS).
