R-Squared Measures for Two-Level Hierarchical Linear Models Using SAS

Abstract

The hierarchical linear model (HLM) is the primary tool of multilevel analysis, a set of techniques for examining data with nested sources of variability. The concept of R2 from classical multiple regression analysis cannot be applied directly to HLMs without certain undesirable results. However, multilevel analogues have been formulated. The goal here is to demonstrate a SAS macro that will calculate estimates of these quantities for a two-level HLM that has been fit with SAS's linear mixed modeling procedure, PROC MIXED.