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Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)

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  • Hao Wu

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  • Michael Browne

Abstract

In this rejoinder we discuss the following aspects of our approach to model discrepancy: the interpretations of the two populations and adventitious error, the choice of inverse Wishart distribution, the perceived danger of justifying a model with bad fit, the relationship among our new approach, Chen’s (J R Stat Soc Ser B, 41:235–248, 1979 ) approach and the existing RMSEA-based approach, and the Pitman drift assumption. Copyright The Psychometric Society 2015

Suggested Citation

  • 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.
  • Handle: RePEc:spr:psycho:v:80:y:2015:i:3:p:619-624
    DOI: 10.1007/s11336-015-9456-y
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    References listed on IDEAS

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    1. Rolf Steyer & Erik Sengewald & Sonja Hahn, 2015. "Some Comments on Wu and Browne," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 608-610, September.
    2. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    4. Albert Satorra, 2015. "A Comment on a Paper by H. Wu and M. W. Browne (2014)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 613-618, September.
    5. A. Shapiro, 2015. "Comments on “Quantifying Adventitious Error in a Covariance Structure as a Random Effect” by Hao Wu and Michael Browne," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 611-612, September.
    6. 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.
    7. Yuan, Ke-Hai & Hayashi, Kentaro & Bentler, Peter M., 2007. "Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1262-1282, July.
    8. 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.
    9. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    10. Chun, So Yeon & Alexander, Shapiro, 2009. "Normal versus Noncentral Chi-square Asymptotics of Misspecified Models," MPRA Paper 17310, University Library of Munich, Germany.
    11. Shapiro, Alexander, 2009. "Asymptotic normality of test statistics under alternative hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 936-945, May.
    12. Le, N. & Sun, L. & Zidek, J. V., 1998. "A note on the existence of maximum likelihood estimates for Gaussian-inverted Wishart models," Statistics & Probability Letters, Elsevier, vol. 40(2), pages 133-137, September.
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