On insensitivity of the chi-square model test to nonlinear misspecification in structural equation models

Mostra el registre complet Registre parcial de l'ítem

• dc.contributor.author Mooijaart, Ab
• dc.contributor.author Satorra, Albert
• dc.date.accessioned 2021-01-04T09:00:46Z
• dc.date.available 2021-01-04T09:00:46Z
• dc.date.issued 2009
• dc.description.abstract In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of misspecifications, but even the theoretical (chi-square) distribution of the test is not distorted when severe interaction term misspecification is present in the postulated model. We explain this phenomenon by exploiting results on asymptotic robustness in structural equation models. The importance of this paper is to warn against the conclusion that if a proposed linear model fits the data well according to the chi-quare goodness-of-fit test, then the underlying model is linear indeed; it will be shown that the underlying model may, in fact, be severely nonlinear. In addition, the present paper shows that such insensitivity to nonlinear terms is only a particular instance of a more general problem, namely, the incapacity of the classical chi-square goodness-of-fit test to detect deviations from zero correlation among exogenous regressors (either being them observable, or latent) when the structural part of the model is just saturated.en
• dc.description.sponsorship Research of the second author is supported by the grants SEJ2006-13537 and PR2007-0221 from the Spanish Ministry of Science and Technology.
• dc.format.mimetype application/pdf
• dc.identifier.citation Mooijaart A, Satorra A. On insensitivity of the chi-square model test to nonlinear misspecification in structural equation models. Psychometrika. 2009 Mar 17;74(3):443-55. DOI: 10.1007/s11336-009-9112-5
• dc.identifier.doi http://dx.doi.org/10.1007/s11336-009-9112-5
• dc.identifier.issn 0033-3123
• dc.identifier.uri http://hdl.handle.net/10230/46122
• dc.language.iso eng
• dc.publisher Springer
• dc.relation.ispartof Psychometrika. 2009 Mar 17;74(3):443-55
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PN/SEJ2006-13537
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PN/PR2007-0221
• dc.rights This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Structural equation modelingen
• dc.subject.keyword Testing model fiten
• dc.subject.keyword Nonlinear relationsen
• dc.subject.keyword Interaction termsen
• dc.subject.keyword Equivalent modelsen
• dc.subject.keyword Asymptotic robustnessen
• dc.subject.keyword Saturated modelen
• dc.title On insensitivity of the chi-square model test to nonlinear misspecification in structural equation modelsen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion