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Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)

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  • Hao Wu
  • 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. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    2. 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.
    3. 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.
    4. 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.
    5. Chun, So Yeon & Alexander, Shapiro, 2009. "Normal versus Noncentral Chi-square Asymptotics of Misspecified Models," MPRA Paper 17310, University Library of Munich, Germany.
    6. 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.
    7. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    8. 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.
    9. 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.
    10. 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.
    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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