Using SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models

Abstract

SAS PROC MIXED is a flexible program suitable for fitting multilevel models, hierarchical linear models, and individual growth models. Its position as an integrated program within the SAS statistical package makes it an ideal choice for empirical researchers and applied statisticians seeking to do data reduction, management, and analysis within a single statistical package. Because the program was developed from the perspective of a “mixed” statistical model with both random and fixed effects, its syntax and programming logic may appear unfamiliar to users in education and the social and behavioral sciences who tend to express these models as multilevel or hierarchical models. The purpose of this paper is to help users familiar with fitting multilevel models using other statistical packages (e.g., HLM, MLwiN, MIXREG) add SAS PROC MIXED to their array of analytic options. The paper is written as a step-by-step tutorial that shows how to fit the two most common multilevel models: (a) school effects models, designed for data on individuals nested within naturally occurring hierarchies (e.g., students within classes); and (b) individual growth models, designed for exploring longitudinal data (on individuals) over time. The conclusion discusses how these ideas can be extended straighforwardly to the case of three level models. An appendix presents general strategies for working with multilevel data in SAS and for creating data sets at several levels.