How to perform multiblock component analysis in practice

Roover, Kim De; Ceulemans, Eva; Timmerman, Marieke E.

doi:10.3758/s13428-011-0129-1

Cited by 55 publications

(48 citation statements)

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“…In simulations of different clustering techniques, it appears that retrieving the optimal clustering becomes harder when the number of clusters increases and when (many) small clusters exist (e.g., Milligan & Cooper, 1985;Schepers et al, 2008). Furthermore, we expect that when the number of underlying factors becomes larger (Lorenzo-Seva et al, 2011), when the data contain a large amount of noise (Ceulemans & Kiers, 2006), and when the clusters overlap more in mean level or covariance structure (De Roover, Ceulemans, & Timmerman, 2012), model selection performance will decrease and the differences between the model selection methods under study will become more pronounced (see, e.g., Schepers et al, 2008).…”

Section: Research Questionsmentioning

confidence: 99%

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

et al. 2013

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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).Keywords Mixture analysis . Model selection . AIC . BIC . CHullIn the behavioral sciences, researchers often cluster multivariate (i.e., object-by-variable) data in order to capture the heterogeneity that is present in the population. The resulting clusters can differ with regard to their level and/ or covariance structure. A first example pertains to the case in which a number of children are scored on certain psychopathological symptoms. The aim then is to discern different groups and to describe the differences between the groups in terms of the strength of the symptoms and/ or of their linear covariation. A second example is a consumer psychologist who wants to identify different groups of consumers on the basis of their appraisals of a wide range of food products.A commonly used clustering method is mixture analysis (McLachlan & Peel, 2000). In this method, each cluster is described by a different multivariate distribution, and every object belongs to each cluster with a particular probability. As a result, the full data follow a mixture of multivariate distributions. In practice, because of their computational simplicity, multivariate normal distributions are often assumed (McLachlan, Peel, & Bean, 2003), implying that each cluster is characterized by a mean vector and a covariance matrix.When the number of variables increases, such a mixture of multivariate normals may become problematic, in that a large number of variance and covariance parameters need to be estimated for each cluster [i.e., for J variables, J(J + 1)/2 variances and covariances need to be determined]. This problem is aggr...

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Section: Research Questionsmentioning

confidence: 99%

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

et al. 2013

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“…Moreover, the data are multivariate in that all level one units are measured on multiple variables. In the remainder, following De Roover, Ceulemans and Timmerman (2012), we will denote the level two units by Bdata blocksâ nd the level one units by Bobservations.M any research questions regarding two-level multivariate data pertain to the associations between the variables, which need not be the same across all data levels. In case the variables fall apart in predictor (i.e., independent) and criterion (i.e., dependent) variables, multilevel regression models (Snijders & Bosker, 1999) may be adopted to properly model these different associations.…”

Section: Introductionmentioning

confidence: 99%

MultiLevel simultaneous component analysis: A computational shortcut and software package

et al. 2015

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MultiLevel Simultaneous Component Analysis (MLSCA) is a data-analytical technique for multivariate two-level data. MLSCA sheds light on the associations between the variables at both levels by specifying separate submodels for each level. Each submodel consists of a component model. Although MLSCA has already been successfully applied in diverse areas within and outside the behavioral sciences, its use is hampered by two issues. First, as MLSCA solutions are fitted by means of iterative algorithms, analyzing large data sets (i.e., data sets with many level one units) may take a lot of computation time. Second, easily accessible software for estimating MLSCA models is lacking so far. In this paper, we address both issues. Specifically, we discuss a computational shortcut for MLSCA fitting. Moreover, we present the MLSCA package, which was built in MATLAB, but is also available in a version that can be used on any Windows computer, without having MATLAB installed.

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“…Finally, we explored the quality of the outlying-variable detection when too many clusters are used, because determining the appropriate number of clusters may be hard in empirical practice. When using too few clusters, performance will almost always be bad, due to the loss of information (i.e., the merging of clusters leads to mixing of the component structures; see De Roover et al, 2012b); therefore, we do not investigate this empirically. Note that, in contrast to previous clusterwise SCA simulations, we chose not to vary the numbers of data blocks, the numbers of rows per data block, and the cluster sizes, because we expect them to impact outlying-variable detection mostly indirectly, through the goodness of recovery of the clustering and the loading structures.…”

Section: Simulation Study Problemmentioning

confidence: 99%

“…First, there are variants with equality restrictions across groups on the component variances and/or the correlations between the component scores (De Roover et al, 2012b;De Roover, Timmerman, Van Mechelen & Ceulemans, 2013c). Imposing these restrictions may lead to loading differences that are irrelevant for outlyingness.…”

Section: Clusterwise Scamentioning

confidence: 99%

“…To make these decisions in a more systematic and objective way, we propose and evaluate two formal detection heuristics. These heuristics are based on clusterwise simultaneous component analysis (clusterwise SCA;De Roover et al, 2012b). Clusterwise SCA was introduced to simplify the daunting task of finding between-group differences in component structures when the number of groups is large.…”

Section: Introductionmentioning

confidence: 99%

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How to detect which variables are causing differences in component structure among different groups

Roover¹,

Timmerman

Ceulemans³

2015

Behav Res

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When comparing the component structures of a multitude of variables across different groups, the conclusion often is that the component structures are very similar in general and differ in a few variables only. Detecting such Boutlying variables^is substantively interesting. Conversely, it can help to determine what is common across the groups. This article proposes and evaluates two formal detection heuristics to determine which variables are outlying, in a systematic and objective way. The heuristics are based on clusterwise simultaneous component analysis, which was recently presented as a useful tool for capturing the similarities and differences in component structures across groups. The heuristics are evaluated in a simulation study and illustrated using crosscultural data on values.

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How to perform multiblock component analysis in practice

Cited by 55 publications

References 48 publications

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

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

MultiLevel simultaneous component analysis: A computational shortcut and software package

How to detect which variables are causing differences in component structure among different groups

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