Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-07T14:24:17.374Z Has data issue: false hasContentIssue false

Advances in Modeling Model Discrepancy: Comment on Wu and Browne (2015)

Published online by Cambridge University Press:  01 January 2025

Robert C. MacCallum*
Affiliation:
University of North Carolina at Chapel Hill
Anthony O’Hagan
Affiliation:
University of Sheffield
*
Correspondence should be made to Robert C. MacCallum, Department of Psychology, University of North Carolina at Chapel Hill, Davie Hall CB# 3270, Chapel Hill, NC 27599-3270 USA. Email: rcm@email.unc.edu

Abstract

Wu and Browne (Psychometrika, 79, 2015) have proposed an innovative approach to modeling discrepancy between a covariance structure model and the population that the model is intended to represent. Their contribution is related to ongoing developments in the field of Uncertainty Quantification (UQ) on modeling and quantifying effects of model discrepancy. We provide an overview of basic principles of UQ and some relevant developments and we examine the Wu–Browne work in that context. We view the Wu–Browne contribution as a seminal development providing a foundation for further work on the critical problem of model discrepancy in statistical modeling in psychological research.

Type
Original Paper
Copyright
Copyright © 2014 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Briggs, N.E., & MacCallum, R.C. (2003). Recovery of weak common factors by maximum likelihood and ordinary least squares estimation. Multivariate Behavioral Research, 38, 2556.CrossRefGoogle ScholarPubMed
Browne, M.W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In Bollen, K.A., & Long, J.S. (Eds.), Testing structural equation models (pp. 136162). Newbury Park, CA: Sage.Google Scholar
Brynjarsdóttir, J., & O’Hagan, A., (2014). Learning about physical parameters: The importance of model discrepancy. Inverse Problems, 30(11), 114007. doi:10.1088/0266-5611/30/11/114007.CrossRefGoogle Scholar
Cudeck, R., & Browne, M.W. (1992). Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value. Psychometrika, 57, 357369.CrossRefGoogle Scholar
Cudeck, R., & Henly, S.J. (1991). Model selection in covariance structures analysis and the "problem" of sample size: A clarification. Psychological Bulletin, 109, 512519.CrossRefGoogle ScholarPubMed
Kennedy, M. C., & O’Hagan, A., (2001). Bayesian calibration of computer models. Journal of the Royal Statistical Society B, 63, 425–464.CrossRefGoogle Scholar
MacCallum, R.C. (2003). Working with imperfect models. Multivariate Behavioral Research, 38, 113139.CrossRefGoogle ScholarPubMed
MacCallum, R.C., Browne, M.W., & Cai, L. (2007). Factor analysis models as approximations. In Cudeck, R., & MacCallum, R.C. (Eds.), Factor analysis at 100: Historical developments and future directions (pp. 153175). Mahwah, NJ: Erlbaum.Google Scholar
MacCallum, R.C., & Tucker, L.R. (1991). Representing sources of error in the common factor model: Implications for theory and practice. Psychological Bulletin, 109, 502511.CrossRefGoogle Scholar
MacCallum, R.C., Tucker, L.R., & Briggs, N.E. (2001). An alternative perspective on parameter estimation in factor analysis and related methods. In Cudeck, R., du Toit, S., & Sörbom, D. (Eds.), Structural equation modeling: Present and future (pp. 3957). Lincolnwood, IL: SSI.Google Scholar
MacCallum, R.C., Widaman, K.F., Preacher, K.J., & Hong, S. (2001). Sample size in factor analysis: The role of model error. Multivariate Behavioral Research, 36, 611637.CrossRefGoogle ScholarPubMed
Steiger, J. H., & Lind, J. M., (1980). Statistically-based tests for the number of common factors. Paper presented at Psychometric Society Meeting, Iowa City, Iowa.Google Scholar
Thurstone, L.L. (1947). Multiple factor analysis. Chicago: University of Chicago Press.Google 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
Tucker, L.R., Koopman, R.F., & Linn, R.L. (1969). Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrika, 34, 421459.CrossRefGoogle 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