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Evaluating Cluster-Level Factor Models with lavaan and Mplus

Research Institute of Child Development and Education, University of Amsterdam, 1012 WX Amsterdam, The Netherlands
Department of Data Analysis, Ghent University, B-9000 Ghent, Belgium
Author to whom correspondence should be addressed.
Academic Editor: Alexander Robitzsch
Psych 2021, 3(2), 134-152;
Received: 29 April 2021 / Revised: 25 May 2021 / Accepted: 26 May 2021 / Published: 31 May 2021
Background: Researchers frequently use the responses of individuals in clusters to measure cluster-level constructs. Examples are the use of student evaluations to measure teaching quality, or the use of employee ratings of organizational climate. In earlier research, Stapleton and Johnson (2019) provided advice for measuring cluster-level constructs based on a simulation study with inadvertently confounded design factors. We extended their simulation study using both Mplus and lavaan to reveal how their conclusions were dependent on their study conditions. Methods: We generated data sets from the so-called configural model and the simultaneous shared-and-configural model, both with and without nonzero residual variances at the cluster level. We fitted models to these data sets using different maximum likelihood estimation algorithms. Results: Stapleton and Johnson’s results were highly contingent on their confounded design factors. Convergence rates could be very different across algorithms, depending on whether between-level residual variances were zero in the population or in the fitted model. We discovered a worrying convergence issue with the default settings in Mplus, resulting in seemingly converged solutions that are actually not. Rejection rates of the normal-theory test statistic were as expected, while rejection rates of the scaled test statistic were seriously inflated in several conditions. Conclusions: The defaults in Mplus carry specific risks that are easily checked but not well advertised. Our results also shine a different light on earlier advice on the use of measurement models for shared factors. View Full-Text
Keywords: multilevel SEM; cluster-level constructs; maximum likelihood estimation multilevel SEM; cluster-level constructs; maximum likelihood estimation
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MDPI and ACS Style

Jak, S.; Jorgensen, T.D.; Rosseel, Y. Evaluating Cluster-Level Factor Models with lavaan and Mplus. Psych 2021, 3, 134-152.

AMA Style

Jak S, Jorgensen TD, Rosseel Y. Evaluating Cluster-Level Factor Models with lavaan and Mplus. Psych. 2021; 3(2):134-152.

Chicago/Turabian Style

Jak, Suzanne, Terrence D. Jorgensen, and Yves Rosseel. 2021. "Evaluating Cluster-Level Factor Models with lavaan and Mplus" Psych 3, no. 2: 134-152.

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