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Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)

Published online by Cambridge University Press:  01 January 2025

Hao Wu*
Affiliation:
Boston College
Michael W. Browne
Affiliation:
The Ohio State University
*
Correspondence should be made to Hao Wu, Department of Psychology, Boston College, Chestnut Hill, MA 02467, USA. Email: hao.wu.5@bc.edu

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.

Type
Original Paper
Copyright
Copyright © 2014 The Psychometric Society

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References

Chen, C-F. (1979). Bayesian inference for a normal dispersion matrix and its application to stochastic multiple regression analysis. Journal of the Royal Statistical Society, Series B, 41, 235248.CrossRefGoogle Scholar
Chun, S.Y., & Shapiro, A. (2009). Normal versus noncentral Chi square asymptotics of misspecified models. Multivariate Behavioral Research, 44, 803827.CrossRefGoogle ScholarPubMed
Kennedy, M.C., & O’Hagan, A. (2001). Bayesian calibration of computer models. Journal of Royal Statistical Society, Series B, 63(3), 425464.CrossRefGoogle Scholar
Le, N., Sun, L., & Zidek, J.V. (1998). A note on the existence of maximum likelihood estimates for Gaussian-inverted-Wishart models. Statistics and Probability Letters, 40, 133137.CrossRefGoogle Scholar
MacCallum, R. C., & O’Hagan, A., (2015). Advances in modeling model discrepancy: Comments on Wu and Browne (2015). Psychometrika. doi:10.1007/11336-015-9452-2.CrossRefGoogle Scholar
Satorra, A., (2015). A comment on a paper by Wu and Browne (2015). Psychometrika. doi:10.1007/11336-015-9455-z.CrossRefGoogle Scholar
Shapiro, A., (2015). Comments on "Quantifying adventitious error in a covariance structure as a random effect" by Hao Wu and Michael Browne. Psychometrika. doi:10.1007/11336-015-9454-1.CrossRefGoogle Scholar
Shapiro, A. (2009). Asymptotic normality of test statistics under alternative hypotheses. Journal of Multivariate Analysis, 100, 936945.CrossRefGoogle Scholar
Steyer, R., Sengewald, E., & Hahn, S., (2015). Some comments Wu and Browne (2015). Psychometrika. doi:10.1007/11336-015-9453-0.CrossRefGoogle Scholar
Trucano, T.G., Swiler, L.P., Igusa, T., Oberkampf, W.L., & Pilch, M. (2006). Calibration, validation and sensitivity analysis: What’s what. Reliability Engineering and System Safety, 91, 13311357.CrossRefGoogle Scholar
Vuong, Q.H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57, 307333.CrossRefGoogle Scholar
White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, 50, 126.CrossRefGoogle Scholar
Wu, H., (2010). An empirical Bayesian approach to misspecified covariance structures. Dissertation submitted to The Ohio State University.Google Scholar
Wu, H. (2014). Asymptotic distribution in moment structure analysis under a weaker mode of convergence and a weaker Pitman drift assumption. Paper presented to the Joint Statistical Meeting at Boston, MA.Google Scholar
Wu, H., & Browne, M. W., (2015). Quantifying Adventitious Error in a Covariance Structure as a Random Effect. Psychometrika. doi:10.1007/s11336-015-9451-3.CrossRefGoogle Scholar
Wu, H. (under review). Asymptotic distribution under the alternative hypothesis in moment structures with a different asymptotic framework.Google Scholar
Yuan, K-H. (2008). Noncentral chi-square versus normal distributions in describing the likelihood ratio statistic: The univariate case and its multivariate implication. Multivariate Behavioral Research, 43, 109136.CrossRefGoogle ScholarPubMed
Yuan, K-H, Hayashi, K., & Bentler, P.M. (2007). Normal theory likelihood ratio statistic for mean and covariance structure analysis under alternative hypotheses. Journal of Multivariate Analysis, 98, 12621282.CrossRefGoogle Scholar