Second, the linear mixed model can decompose variance into multiple components in situations where the fixed effects ANOVA cannot be applied because the design matrix is degenerate (i.e. singular). This situation is very common for the types of question of relevant to complex gene expression studies. For example, sex and ancestry are invariant properties of an individual, so jointly analyzing variation across these 3 dimensions of variation involves a degenerate design matrix. In cases like these, the linear mixed model can accurately estimate the desired variance fractions (Additional file 1), while ANOVA will fail to estimate any of these values because the parameters are not identifiable. Thus ANOVA is inadequate for the type of analysis we performed here with variancePartition using linear mixed model.
