On the Performance of Maximum
Likelihood Versus Means and Variance
Adjusted Weighted Least Squares
Estimation in CFA
André Beauducel
Mannheim University
Philipp Yorck Herzberg
Technical University Dresden
The simulation study compared maximum likelihood (ML) estimation with
weighted least squares means and variance adjusted (WLSMV) estimation. The sim-
ulation study was based on confirmatory factor analyses with 1, 2, 4, and 8 factors,
based on 250, 500, 750, and 1,000 cases, and on 5, 10, 20, and 40 variables with 2, 3,
4, 5, and 6 categories. There was no model misspecification. The most important re-
sults were that with 2 and 3 categories the rejection rates of the WLSMV chi-square
test corresponded much more to the expected rejection rates according to an alpha
level of .05 than the rejection rates of the ML chi-square test. The magnitude of the
loadings was more precisely estimated by means of WLSMV when the variables had
only 2 or 3 categories. The sample size for WLSMV estimation needed not to be
larger than the sample size for ML estimation.
Maximum likelihood (ML) estimation is most commonly used in confirmatory
factor analysis (CFA) and structural equation modeling (SEM). ML estimation as-
sumes that the observed variables follow the multivariate normal distribution.
However, many data in psychological research are ordinal data or do not follow the
multivariate normal distribution. One approach for analyzing ordinal data is
weighted least squares (WLS) estimation, which assumes that the observed ordinal
STRUCTURAL EQUATION MODELING, 13(2), 186–203
Copyright © 2006, Lawrence Erlbaum Associates, Inc.
Correspondence should be addressed to Dr. André Beauducel, Department of Psychology II,
Mannheim University, Schloss, Ehrenhof Ost, 68131 Mannheim, Germany. E-mail: beauducel@
tnt.psychologie.uni-mannheim.de