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An Intermediate Primer to Estimating Linear Multilevel Models using SAS ® PROC MIXED

This paper expands upon Bell et al.’s (2013) “A Multilevel Model Primer Using SAS ® PROC MIXED” in which we presented an overview of estimating two and three-level linear models via PROC MIXED. However, in our earlier paper, we, for the most part, relied on simple options available in PROC MIXED. In this paper, we present a more advanced look at common PROC MIXED options used in the analysis of social and behavioral science data, as well introduce users to two different SAS macros previously developed for use with PROC MIXED: one to examine model fit (MIXED_FIT; Ene, Smiley, & Bell, 2012) and the other to examine distributional assumptions (MIXED_DX; Bell et al., 2010). Specific statistical options presented in the current paper include (a) PROC MIXED statement options for estimating statistical significance of variance estimates (COVTEST, including problems with using this option) and estimation methods (METHOD =), (b) MODEL statement option for degrees of freedom estimation (DDFM =), and (c) RANDOM statement option for specifying the variance/covariance structure to be used (TYPE =). Given the importance of examining model fit, we also present methods for estimating changes in model fit through an illustration of the SAS macro MIXED_FIT. Likewise, the SAS macro MIXED_DX is introduced to remind users to examine distributional assumptions associated with two-level linear models, including normality and homogeneity of level-1 and level-2 residuals. To maintain continuity with the 2013 introductory PROC MIXED paper, thus, providing users with a set of comprehensive guides for estimating multilevel models using PROC MIXED, we use the same real world data sources that we used in our earlier primer paper (Bell et al., 2013).