Partitioning Variation in Multilevel Models

Abstract

Abstract In multilevel modeling 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, makes sense only in simple variance components, Normal response, models where it is often referred to as the intra-unit correlation. In this article 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 compare several computational techniques to compute the variance partitions.