Mixture simultaneous factor analysis for capturing differences in latent variables between higher level units of multilevel data

K. De Roover, J.K. Vermunt, Marieke E. Timmerman, Eva Ceulemans

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Abstract

Given multivariate data, many research questions pertain to the covariance structure: whether and how the variables (for example, personality measures) covary. Exploratory factor analysis (EFA) is often used to look for latent variables that may explain the covariances among variables; for example, the Big Five personality structure. In case of multilevel data, one may wonder whether or not the same covariance (factor) structure holds for each so-called ‘data block’ (containing data of one higher-level unit). For instance, is the Big Five personality structure found in each country or do cross-cultural differences exist? The well-known multigroup EFA framework falls short in answering such questions, especially for numerous groups/blocks. We introduce mixture simultaneous factor analysis (MSFA), performing a mixture model clustering of data blocks, based on their factor structure. A simulation study shows excellent results with respect to parameter recovery and an empirical example is included to illustrate the value of MSFA.
Original languageEnglish
Pages (from-to)506-523
JournalStructural Equation Modeling
Volume24
Issue number4
DOIs
Publication statusPublished - 6 Mar 2017

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simultaneous analysis
Latent Variables
Factor analysis
Factor Analysis
factor analysis
Exploratory Factor Analysis
Factor Structure
Unit
personality structure
Covariance Structure
Cultural Differences
Question Answering
Multivariate Data
Mixture Model
Recovery
cultural difference
Simulation Study
Clustering
personality
Latent variables

Cite this

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title = "Mixture simultaneous factor analysis for capturing differences in latent variables between higher level units of multilevel data",
abstract = "Given multivariate data, many research questions pertain to the covariance structure: whether and how the variables (for example, personality measures) covary. Exploratory factor analysis (EFA) is often used to look for latent variables that may explain the covariances among variables; for example, the Big Five personality structure. In case of multilevel data, one may wonder whether or not the same covariance (factor) structure holds for each so-called ‘data block’ (containing data of one higher-level unit). For instance, is the Big Five personality structure found in each country or do cross-cultural differences exist? The well-known multigroup EFA framework falls short in answering such questions, especially for numerous groups/blocks. We introduce mixture simultaneous factor analysis (MSFA), performing a mixture model clustering of data blocks, based on their factor structure. A simulation study shows excellent results with respect to parameter recovery and an empirical example is included to illustrate the value of MSFA.",
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Mixture simultaneous factor analysis for capturing differences in latent variables between higher level units of multilevel data. / De Roover, K.; Vermunt, J.K.; Timmerman, Marieke E.; Ceulemans, Eva.

In: Structural Equation Modeling, Vol. 24, No. 4, 06.03.2017, p. 506-523.

Research output: Contribution to journalArticleScientificpeer-review

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AB - Given multivariate data, many research questions pertain to the covariance structure: whether and how the variables (for example, personality measures) covary. Exploratory factor analysis (EFA) is often used to look for latent variables that may explain the covariances among variables; for example, the Big Five personality structure. In case of multilevel data, one may wonder whether or not the same covariance (factor) structure holds for each so-called ‘data block’ (containing data of one higher-level unit). For instance, is the Big Five personality structure found in each country or do cross-cultural differences exist? The well-known multigroup EFA framework falls short in answering such questions, especially for numerous groups/blocks. We introduce mixture simultaneous factor analysis (MSFA), performing a mixture model clustering of data blocks, based on their factor structure. A simulation study shows excellent results with respect to parameter recovery and an empirical example is included to illustrate the value of MSFA.

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