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Quantifying Adventitious Error in a Covariance Structure as a Random Effect

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  • Hao Wu
  • Michael Browne

Abstract

We present an approach to quantifying errors in covariance structures in which adventitious error, identified as the process underlying the discrepancy between the population and the structured model, is explicitly modeled as a random effect with a distribution, and the dispersion parameter of this distribution to be estimated gives a measure of misspecification. Analytical properties of the resultant procedure are investigated and the measure of misspecification is found to be related to the root mean square error of approximation. An algorithm is developed for numerical implementation of the procedure. The consistency and asymptotic sampling distributions of the estimators are established under a new asymptotic paradigm and an assumption weaker than the standard Pitman drift assumption. Simulations validate the asymptotic sampling distributions and demonstrate the importance of accounting for the variations in the parameter estimates due to adventitious error. Two examples are also given as illustrations. Copyright The Psychometric Society 2015

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  • Hao Wu & Michael Browne, 2015. "Quantifying Adventitious Error in a Covariance Structure as a Random Effect," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 571-600, September.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:3:p:571-600
    DOI: 10.1007/s11336-015-9451-3
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    Cited by:

    1. Alexander Robitzsch, 2023. "Modeling Model Misspecification in Structural Equation Models," Stats, MDPI, vol. 6(2), pages 1-17, June.
    2. Alberto Maydeu-Olivares, 2017. "Assessing the Size of Model Misfit in Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 533-558, September.
    3. Hao Wu & Michael Browne, 2015. "Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 619-624, September.
    4. Robert MacCallum & Anthony O’Hagan, 2015. "Advances in Modeling Model Discrepancy: Comment on Wu and Browne (2015)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 601-607, September.
    5. Keke Lai, 2019. "Creating Misspecified Models in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 781-801, September.
    6. Alexander Robitzsch, 2022. "Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches," Stats, MDPI, vol. 5(3), pages 1-42, July.
    7. So Yeon Chun & Michael W. Browne & Alexander Shapiro, 2018. "Modified Distribution-Free Goodness-of-Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 48-66, March.

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