Partitioning variation in multilevel models

In multilevel modelling, the residual variation in a response variable is split into component parts that are attributed to various levels. In applied work, much use is made of the percentage of variation that is attributable to the higher-level sources of variation. Such a measure however only makes sense in simple variance components Normal response models where it is often referred to as the ‘intra-unit correlation’. In this paper we describe how similar measures can be found for both more complex random variation in Normal response models and models with discrete responses. In these cases the variance partitions are dependent on predictors associated with the individual observation. We will compare several computational techniques to compute the variance partitions