The linear mixed model used by variancePartition has three distinct advantages compared to ANOVA. First, by placing a Gaussian prior on variables modeled as random effects, the linear mixed model more accurately estimates the fraction of variance explained. Even as the number of categories in a discrete variable increases, the linear mixed model still produces accurate estimates because the prior shrinks the estimate for each category towards the zero. Conversely, the fixed effects ANOVA is fit with a linear regression model using ordinary least squares. This method is known to suffer from overfitting and over-estimates the variance fractions for variables with many categories. These properties are well established [31, 38, 39] and are consistent with our simulation study (Additional file 1).
