Principles and practice of scaled difference chi-square testing

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• dc.contributor.author Bryant, Fred B.
• dc.contributor.author Satorra, Albert
• dc.date.accessioned 2020-12-22T09:20:41Z
• dc.date.available 2020-12-22T09:20:41Z
• dc.date.issued 2012
• dc.description.abstract We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra–Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction factor (c), depending on the particular structural equation modeling software used. Because of how LISREL 8 defines the SB scaled chi-square, LISREL users should compute c for each model by dividing the model's normal theory weighted least-squares (NTWLS) chi-square by its SB chi-square, to recover c accurately with both tests. EQS and Mplus users, in contrast, should divide the model's maximum likelihood (ML) chi-square by its SB chi-square to recover c. Because ML estimation does not minimize the NTWLS chi-square, however, it can produce a negative difference in nested NTWLS chi-square values. Thus, we recommend the standard practice of testing the scaled difference in ML chi-square values for models M 1 and M 0 (after properly recovering c for each model), to avoid an inadmissible test numerator. We illustrate the difference in computations across software programs for the original and new scaled tests and provide LISREL, EQS, and Mplus syntax in both single- and multiple-group form for specifying the model M 10 that is involved in the new test.en
• dc.description.sponsorship This research was supported in part by a grant SEJ2006-13537 from the Spanish Ministry of Science and Technology (to Albert Satorra).
• dc.format.mimetype application/pdf
• dc.identifier.citation Bryant FB, Satorra A. Principles and practice of scaled difference chi-square testing. Structural Equation Modeling. 2012 Jul 31;19(3):372-98. DOI: 10.1080/10705511.2012.687671
• dc.identifier.doi http://dx.doi.org/10.1080/10705511.2012.687671
• dc.identifier.issn 1070-5511
• dc.identifier.uri http://hdl.handle.net/10230/46110
• dc.language.iso eng
• dc.publisher Taylor & Francis
• dc.relation.ispartof Structural Equation Modeling. 2012 Jul 31;19(3):372-98
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PN/SEJ2006-13537
• dc.rights © This is an Accepted Manuscript of an article published by Taylor & Francis in Structural Equation Modeling on 2012 Jul 31, available online: http://www.tandfonline.com/10.1080/10705511.2012.687671
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Chi-square difference test statisticen
• dc.subject.keyword Goodness-of-fit testen
• dc.subject.keyword Moment structuresen
• dc.subject.keyword Nonnormalityen
• dc.subject.keyword Scaled chi-squareen
• dc.title Principles and practice of scaled difference chi-square testingen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion