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      Shame for disrespecting evidence: the personal consequences of insufficient respect for structural equation model testing

      brief-report

      BMC Medical Research Methodology

      BioMed Central

      Factor analysis, Factor model, Testing, Close fit, Structural equation model, SEM

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          Abstract

          Background

          Inappropriate and unacceptable disregard for structural equation model (SEM) testing can be traced back to: factor-analytic inattention to model testing, misapplication of the Wilkinson task force’s [ Am Psychol 54:594-604, 1999] critique of tests, exaggeration of test biases, and uncomfortably-numerous model failures.

          Discussion

          The arguments for disregarding structural equation model testing are reviewed and found to be misguided or flawed. The fundamental test-supporting observations are: a) that the null hypothesis of the χ 2 structural equation model test is not nil, but notable because it contains substantive theory claims and consequences; and b) that the amount of covariance ill fit cannot be trusted to report the seriousness of model misspecifications. All covariance-based fit indices risk failing to expose model problems because the extent of model misspecification does not reliably correspond to the magnitude of covariance ill fit – seriously causally misspecified models can fit, or almost fit.

          Summary

          The only reasonable research response to evidence of non-chance structural equation model failure is to diagnostically investigate the reasons for failure. Unfortunately, many SEM-based theories and measurement scales will require reassessment if we are to clear the backlogged consequences of previous deficient model testing. Fortunately, it will be easier for researchers to respect evidence pointing toward required reassessments, than to suffer manuscript rejection and shame for disrespecting evidence potentially signaling serious model misspecifications.

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          Most cited references 32

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          Statistical methods in psychology journals: Guidelines and explanations.

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            Ensuring Positiveness of the Scaled Difference Chi-square Test Statistic.

            A scaled difference test statistic [Formula: see text] that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (2001). The statistic [Formula: see text] is asymptotically equivalent to the scaled difference test statistic T̄(d) introduced in Satorra (2000), which requires more involved computations beyond standard output of SEM software. The test statistic [Formula: see text] 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 T̄(d) that avoids negative chi-square values.
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              Testing! testing! one, two, three – Testing the theory in structural equation models!

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                Author and article information

                Contributors
                LHayduk@ualberta.ca
                Journal
                BMC Med Res Methodol
                BMC Med Res Methodol
                BMC Medical Research Methodology
                BioMed Central (London )
                1471-2288
                27 November 2014
                27 November 2014
                2014
                : 14
                : 1
                Affiliations
                Department of Sociology, University of Alberta, Edmonton, Canada
                Article
                1153
                10.1186/1471-2288-14-124
                4297459
                25430437
                bd4dd763-e5f9-4e40-be68-89e81bf272bb
                © Hayduk; licensee BioMed Central Ltd. 2014

                This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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                © The Author(s) 2014

                Medicine

                factor analysis, factor model, testing, close fit, structural equation model, sem

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