Albright JJ Estimating Multilevel Models using SPSS, Stata, and SAS.pdf

Estimating Multilevel Models using SPSS, Stata, and
SAS
Jeremy J. Albright
May 11, 2007
Multilevel data are pervasive in the social sciences. Students may be nested within schools,
voters within districts, or workers within firms, to name a few examples. Statistical meth-
ods that explicitly take into account hierarchically structured data have gained popularity
in recent years, and there now exist several special-purpose statistical programs designed
specifically for estimating multilevel models (. HLM, MLwiN). In addition, the increasing
use of of multilevel models — also known as hierarchical linear and mixed effects models
— has led general purpose packages such as SPSS, Stata, and SAS to introduce their own
procedures for handling nested data.
heless, researchers may face two challenges when attempting to determine the ap-
propriate syntax for estimating multilevel/mixed models using general purpose software.
First, many users from the social e to multilevel modeling with a background
in regression models, whereas much of the software documentation utilizes examples from
experimental disciplines [due to the fact that multilevel modeling methodology evolved out
of ANOVA methods for analyzing experiments with random effects (Searle, Casella, and Mc-
Culloch, 1992)]. Second, notation for multilevel models is often inconsistent across disciplines
(Ferron 1997).
The purpose of this document is to demonstrate how to estimate multilevel models using
SPSS, Stata, and SAS. It first seeks to clarify the vocabulary of multilevel models by defining
what is meant by fixed effects, random effects, and ponents. It pares
the model building notation frequently employed in applications from the social sciences with
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the more general matrix notation found in much of the software documentation. The syntax
for centering variables and estimating multilevel models is then presented for each package.
1 Vocabulary of Mixed and Multilevel Models
Models for