Detecting which variables alter component interpretation across multiple groups: A resampling-based method View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04-01

AUTHORS

Sopiko Gvaladze, Kim De Roover, Francis Tuerlinckx, Eva Ceulemans

ABSTRACT

In psychology, many studies measure the same variables in different groups. In the case of a large number of variables when a strong a priori idea about the underlying latent construct is lacking, researchers often start by reducing the variables to a few principal components in an exploratory way. Herewith, one often wants to evaluate whether the components represent the same construct in the different groups. To this end, it makes sense to remove outlying variables that have significantly different loadings on the extracted components across the groups, hampering equivalent interpretations of the components. Moreover, identifying such outlying variables is important when testing theories about which variables behave similarly or differently across groups. In this article, we first scrutinize the lower bound congruence method (LBCM; De Roover, Timmerman, & Ceulemans in Behavior Research Methods, 49, 216-229, 2017), which was recently proposed for solving the outlying-variable detection problem. LBCM investigates how Tucker's congruence between the loadings of the obtained cluster-loading matrices improves when specific variables are discarded. We show that LBCM has the tendency to output outlying variables that either are false positives or concern very small, and thus practically insignificant, loading differences. To address this issue, we present a new heuristic: the lower and resampled upper bound congruence method (LRUBCM). This method uses a resampling technique to obtain a sampling distribution for the congruence coefficient, under the hypothesis that no outlying variable is present. In a simulation study, we show that LRUBCM outperforms LBCM. Finally, we illustrate the use of the method by means of empirical data. More... »

PAGES

1-28

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.3758/s13428-019-01222-4

DOI

http://dx.doi.org/10.3758/s13428-019-01222-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1113175512

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/30937846


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41 schema:description In psychology, many studies measure the same variables in different groups. In the case of a large number of variables when a strong a priori idea about the underlying latent construct is lacking, researchers often start by reducing the variables to a few principal components in an exploratory way. Herewith, one often wants to evaluate whether the components represent the same construct in the different groups. To this end, it makes sense to remove outlying variables that have significantly different loadings on the extracted components across the groups, hampering equivalent interpretations of the components. Moreover, identifying such outlying variables is important when testing theories about which variables behave similarly or differently across groups. In this article, we first scrutinize the lower bound congruence method (LBCM; De Roover, Timmerman, & Ceulemans in Behavior Research Methods, 49, 216-229, 2017), which was recently proposed for solving the outlying-variable detection problem. LBCM investigates how Tucker's congruence between the loadings of the obtained cluster-loading matrices improves when specific variables are discarded. We show that LBCM has the tendency to output outlying variables that either are false positives or concern very small, and thus practically insignificant, loading differences. To address this issue, we present a new heuristic: the lower and resampled upper bound congruence method (LRUBCM). This method uses a resampling technique to obtain a sampling distribution for the congruence coefficient, under the hypothesis that no outlying variable is present. In a simulation study, we show that LRUBCM outperforms LBCM. Finally, we illustrate the use of the method by means of empirical data.
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