Using SAS PROC MIXED to fit multilevel models, hierarchical models, and individual growth models

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 d ata reduction, management, and analysis within a single statistical package . Because the program was developed from the perspective of a "mixed" stati stical model with both random and fixed effects, its syntax and programming logic may appear unfamiliar to users in education and the social and behav ioral sciences,oho tend to express these models as multilevel or hierarchic al models. The purpose of this paper is to help users familiar with fitting multilevel models using other statistical packages (e.g., HLM, MLwiN, MIXR EG) add SAS PROC MIXED to their array of analytic options. The paper is wri tten as a step-by-step tutorial that shows how to fit the two most common m ultilevel models: (a) school effects models, designed for data on individua ls nested within naturally occurring hierarchies (e.g., students within cla sses); and (b) individual growth models, designed for exploring longitudina l data (on individuals) over rime. The conclusion discusses how these ideas can be extended straighforwardly to the case of three level models. An app endix presents general strategies for working with multilevel data in SAS a nd for creating data sets at several levels.