Multilevel Mixture Factor Models

Varriale, Roberta; Vermunt, Jeroen K.

doi:10.1080/00273171.2012.658337

Cited by 26 publications

(32 citation statements)

References 33 publications

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“…The nine-fold classification was already presented in Vermunt (2008), Palardy and Vermunt (2010) and Varriale and Vermunt (2012), and there are too many modelling options to discuss them all. Therefore, the framework is not discussed extensively again but only shortly presented to be able to place the A3 model from the current article into a broader context.…”

Section: General Frameworkmentioning

confidence: 99%

“…More information about the estimation procedures can be found in Fox and Glas (2001), Goldstein, Bonnet, and Rocher (2007), Vermunt (2008), Fox (2010), Palardy and Vermunt (2010), Muthén and Asparouhov (2011), and Varriale and Vermunt (2012). In the present study, the software package Latent GOLD (Vermunt & Magidson, 2013) was used to estimate the models.…”

Section: General Frameworkmentioning

confidence: 99%

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Micro–Macro Multilevel Analysis for Discrete Data

Bennink

Croon

Vermunt

2013

Sociological Methods & Research

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A multilevel regression model is proposed in which discrete individual-level variables are used as predictors of discrete group-level outcomes. It generalizes the model proposed by Croon and van Veldhoven for analyzing micromacro relations with continuous variables by making use of a specific type of latent class model. A first simulation study shows that this approach performs better than more traditional aggregation and disaggreagtion procedures. A second simulation study shows that the proposed latent variable approach still works well in a more complex model, but that a larger number of level-2 units is needed to retain sufficient power. The more complex model is illustrated with an empirical example in which data from a personal network are used to analyze the interaction effect of being religious and surrounding yourself with married people on the probability of being married.

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Section: General Frameworkmentioning

confidence: 99%

Section: General Frameworkmentioning

confidence: 99%

Micro–Macro Multilevel Analysis for Discrete Data

Bennink

Croon

Vermunt

2013

Sociological Methods & Research

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“…Indeed, CFA imposes an assumed structure of zero loadings on the factors; thus, CFA-based methods can only account for differences in the size of the freely estimated (i.e., nonzero) factor loadings. Specifically, we compare MSFA to (a) a nonmultilevel mixture EFA model, called mixtures of factor analyzers (MoFA; McLachlan & Peel, 2000), and (b) a multilevel mixture EFA model, MLMFA (Varriale & Vermunt, 2012). MoFA performs a mixture clustering of individual observations based on their underlying EFA model.…”

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confidence: 99%

“…More important, subgroups of data blocks might exist that share essentially the same structure and finding these subgroups is substantively interesting. Multilevel mixture factor analysis (MLMFA; Varriale & Vermunt, 2012) performs a mixture clustering of the data blocks based on some parameters of their underlying factor model, but it does not allow the factors themselves to differ across the data blocks.Within the deterministic modeling framework, however, a method exists that clusters data blocks based on their underlying covariance structure and performs a simultaneous component analysis (SCA, which is a multigroup extension of standard principal component analysis [PCA]; Timmerman & Kiers, 2003) per cluster. The so-called clusterwise SCA De Roover, Ceulemans, Timmerman, Nezlek, & Onghena, 2013; has proven its merit in answering questions pertaining to differences and similarities in covariance structures (Brose, De Roover, Ceulemans, & Kuppens, 2015;Krysinska et al, 2014).…”

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confidence: 99%

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confidence: 99%

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Mixture Simultaneous Factor Analysis for Capturing Differences in Latent Variables Between Higher Level Units of Multilevel Data

Roover

Vermunt

Timmerman

et al. 2017

Structural Equation Modeling: A Multidisciplinary Journal

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Given multivariate data, many research questions pertain to the covariance structure: whether and how the variables (e.g., personality measures) covary. Exploratory factor analysis (EFA) is often used to look for latent variables that might explain the covariances among variables; for example, the Big Five personality structure. In the case of multilevel data, one might wonder whether or not the same covariance (factor) structure holds for each so-called data block (containing data of 1 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 or 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.Keywords: factor analysis, latent variables, mixture model clustering, multilevel data Given multivariate data, researchers often wonder whether the variables covary to some extent and in what way. For instance, in personality psychology, there has been a debate about the structure of personality measures (i.e., the Big Five vs. Big Three debate; De Raad et al., 2010). Similarly, emotion psychologists have discussed intensely whether and how emotions as well as norms for experiencing emotions can be meaningfully organized in a lowdimensional space (e.g., Ekman, 1999;Fontaine, Scherer, Roesch, & Ellsworth, 2007;Russell & Barrett, 1999;Stearns, 1994). Factor analysis (Lawley & Maxwell, 1962) is an important tool in these debates as it explains the covariance structure of the variables by means of a few latent variables, called factors. When the researchers have a priori assumptions on the number and nature of the underlying latent variables, confirmatory factor analysis (CFA) is often used, whereas exploratory factor analysis (EFA) is applied when one has no such assumptions.Research questions about the covariance structure get further ramifications when the data have a multilevel structure; for instance, when personality measures are available for inhabitants from different countries. We refer to data organized according to the higher level units (e.g., the countries) as data blocks. For multilevel data, one can wonder whether or not the same structure holds for each data block. For example, is the Big Five personality structure found in each country or not (De Raad et al., 2010) Setiadi, & Markam, 2002;MacKinnon & Keating, 1989;Rodriguez & Church, 2003).When looking for differences and similarities in covariance structures, using EFA is very advantageous because it leaves more room for finding differences than CFA does. For instance, in the emotion norm example (Eid & Diener, 2001), one might very well expect two latent variables to show up in each country corresponding to approved and disap...

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Micro–macro multilevel latent class models with multiple discrete individual-level variables

Bennink

Croon

Kroon

et al. 2016

Adv Data Anal Classif

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An existing micro-macro method for a single individual-level variable is extended to the multivariate situation by presenting two multilevel latent class models in which multiple discrete individual-level variables are used to explain a group-level outcome. As in the univariate case, the individual-level data are summarized at the group-level by constructing a discrete latent variable at the group level and this grouplevel latent variable is used as a predictor for the group-level outcome. In the first extension, that is referred to as the Direct model, the multiple individual-level variables are directly used as indicators for the group-level latent variable. In the second extension, referred to as the Indirect model, the multiple individual-level variables are used to construct an individual-level latent variable that is used as an indicator for the grouplevel latent variable. This implies that the individual-level variables are used indirectly at the group-level. The within-and between components of the (co)varn the individuallevel variables are independent in the Direct model, but dependent in the Indirect model. Both models are discussed and illustrated with an empirical data example.

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Multilevel Mixture Factor Models

Cited by 26 publications

References 33 publications

Micro–Macro Multilevel Analysis for Discrete Data

Micro–Macro Multilevel Analysis for Discrete Data

Mixture Simultaneous Factor Analysis for Capturing Differences in Latent Variables Between Higher Level Units of Multilevel Data

Micro–macro multilevel latent class models with multiple discrete individual-level variables

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