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Decomposing variables into between and within components are often required in multilevel analysis. This method of decomposition should not ignore possible unreliability of an observed group mean (i.e., arithmetic mean) that is due to small cluster sizes and can lead to substantially biased estimates. Adjustment procedures that allow unbiased estimation have been defined and implemented in software for a two-level model. This study shows how to implement a two-stage adjustment procedure in a three-level design. A simulation study showed that the adjustment procedure provides unbiased estimates. To demonstrate how the adjustment procedure can change results in a real data context, an illustration is provided using a set up in which 355 Level-1 units are nested in 93 Level-2 and 19 Level-3 units.

Best Linear Unbiased Prediction of Latent Means in Three-Level Data