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dc.contributor.authorGrønneberg, Steffen
dc.contributor.authorMoss, Jonas
dc.contributor.authorFoldnes, Njål
dc.date.accessioned2022-02-01T13:04:51Z
dc.date.available2022-02-01T13:04:51Z
dc.date.created2020-11-27T10:38:24Z
dc.date.issued2020
dc.identifier.citationPsychometrika, volume 85, pages:1028–1051 (2020)en_US
dc.identifier.issn0033-3123
dc.identifier.urihttps://hdl.handle.net/11250/2976285
dc.description.abstractThe tetrachoric correlation is a popular measure of association for binary data and estimates the correlation of an underlying normal latent vector. However, when the underlying vector is not normal, the tetrachoric correlation will be different from the underlying correlation. Since assuming underlying normality is often done on pragmatic and not substantial grounds, the estimated tetrachoric correlation may therefore be quite different from the true underlying correlation that is modeled in structural equation modeling. This motivates studying the range of latent correlations that are compatible with given binary data, when the distribution of the latent vector is partly or completely unknown. We show that nothing can be said about the latent correlations unless we know more than what can be derived from the data. We identify an interval constituting all latent correlations compatible with observed data when the marginals of the latent variables are known. Also, we quantify how partial knowledge of the dependence structure of the latent variables affect the range of compatible latent correlations. Implications for tests of underlying normality are briefly discussed.en_US
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.titlePartial identification of latent correlations with binary dataen_US
dc.typeJournal articleen_US
dc.typePeer revieweden_US
dc.description.versionacceptedVersionen_US
dc.rights.holderSpringeren_US
dc.source.pagenumber1028–1051en_US
dc.source.volume85en_US
dc.source.journalPsychometrikaen_US
dc.identifier.doi10.1007/s11336-020-09737-y
dc.identifier.cristin1853279
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode2


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