CHull as an alternative to AIC and BIC in the context of mixtures of factor analyzers

Mixture analysis is commonly used for clustering objects on the basis of multivariate data. When the data contain a large number of variables, regular mixture analysis may become problematic, because a large number of parameters need to be estimated for each cluster. To tackle this problem, the mixt...

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Bibliographic Details
Published in:Behavior research methods 2013-09, Vol.45 (3), p.782-791
Main Authors: Bulteel, Kirsten, Wilderjans, Tom F., Tuerlinckx, Francis, Ceulemans, Eva
Format: Article
Language:English
Subjects:
Bayes Theorem
Bayesian analysis
Behavioral Science and Psychology
Cluster Analysis
Cognitive Psychology
Consumer Behavior
Economic models
Factor Analysis, Statistical
Models, Psychological
Models, Statistical
Multivariate Analysis
Parameter estimation
Psychology
Studies
Uncertainty
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Summary:Mixture analysis is commonly used for clustering objects on the basis of multivariate data. When the data contain a large number of variables, regular mixture analysis may become problematic, because a large number of parameters need to be estimated for each cluster. To tackle this problem, the mixtures-of-factor-analyzers (MFA) model was proposed, which combines clustering with exploratory factor analysis. MFA model selection is rather intricate, as both the number of clusters and the number of underlying factors have to be determined. To this end, the Akaike (AIC) and Bayesian (BIC) information criteria are often used. AIC and BIC try to identify a model that optimally balances model fit and model complexity. In this article, the CHull (Ceulemans & Kiers, 2006 ) method, which also balances model fit and complexity, is presented as an interesting alternative model selection strategy for MFA. In an extensive simulation study, the performances of AIC, BIC, and CHull were compared. AIC performs poorly and systematically selects overly complex models, whereas BIC performs slightly better than CHull when considering the best model only. However, when taking model selection uncertainty into account by looking at the first three models retained, CHull outperforms BIC. This especially holds in more complex, and thus more realistic, situations (e.g., more clusters, factors, noise in the data, and overlap among clusters).
ISSN:1554-3528
1554-351X
1554-3528
DOI:10.3758/s13428-012-0293-y