Importantly, data generated according to a network or factor model can have the very same variance-covariance structure, despite different underlying, data-generating processes. Consequently, even if a 1-factor model describes the phenotypic data well, this does not guarantee that the 1-factor model is the actual data-generating model. This realization is relevant for univariate GWAS where factor analytic results are often taken as indication that reduction of the multivariate data to sum scores is justified. In reality, however, such reduction is only justified if the data-generating process is a unidimensional factor model, but not if the data-generating process is a network model.
