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Ensuring positiveness of the scaled difference chi-square test statistic

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dc.contributor.author Satorra, Albert
dc.contributor.author Bentler, Peter M.
dc.date.accessioned 2021-01-04T09:00:39Z
dc.date.available 2021-01-04T09:00:39Z
dc.date.issued 2010
dc.identifier.citation Satorra A, Bentler PM. Ensuring positiveness of the scaled difference chi-square test statistic. Psychometrika. 2009 Jun 20;75(2):243-8. DOI: 10.1007/s11336-009-9135-y
dc.identifier.issn 0033-3123
dc.identifier.uri http://hdl.handle.net/10230/46120
dc.description.abstract A scaled difference test statistic T~d that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (Psychometrika 66:507–514, 2001). The statistic T~d is asymptotically equivalent to the scaled difference test statistic T¯d introduced in Satorra (Innovations in Multivariate Statistical Analysis: A Festschrift for Heinz Neudecker, pp. 233–247, 2000), which requires more involved computations beyond standard output of SEM software. The test statistic T~d has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the implicit function theorem, this note develops an improved scaling correction leading to a new scaled difference statistic T¯d that avoids negative chi-square values.
dc.description.sponsorship Research supported by grants SEJ2006-13537 and PR2007-0221 from the Spanish Ministry of Science and Technology and by USPHS grants DA00017 and DA01070.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Springer
dc.relation.ispartof Psychometrika. 2009 Jun 20;75(2):243-8
dc.rights © Springer The final publication is available at Springer via http://dx.doi.org/10.1007/s11336-009-9135-y
dc.title Ensuring positiveness of the scaled difference chi-square test statistic
dc.type info:eu-repo/semantics/article
dc.identifier.doi http://dx.doi.org/10.1007/s11336-009-9135-y
dc.subject.keyword Moment-structures
dc.subject.keyword Goodness-of-fit test
dc.subject.keyword Chi-square difference test statistic
dc.subject.keyword Chi-square distribution
dc.subject.keyword Nonnormality
dc.relation.projectID info:eu-repo/grantAgreement/ES/2PN/SEJ2006-13537
dc.relation.projectID info:eu-repo/grantAgreement/ES/2PN/PR2007-0221
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/acceptedVersion

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