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A Note on Comparing the Estimates of Models for Cluster-Correlated or Longitudinal Data with Binary or Ordinal Outcomes

Published online by Cambridge University Press:  01 January 2025

Daniel J. Bauer
Daniel J. Bauer*
Affiliation:
University of North Carolina at Chapel Hill
*
Requests for reprints should be sent to Daniel J. Bauer, Department of Psychology, University of North Carolina, Chapel Hill, NC 27599-3270, USA. E-mail: dbauer@email.unc.edu
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Abstract

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for binary or ordered-categorical outcomes, however, comparisons between such models are impeded by the implicit rescaling of the model estimates that takes place with the inclusion of new predictors and/or random effects. This paper presents an approach for putting the estimates on a common scale to facilitate relative comparisons between models fit to binary or ordinal outcomes. The approach is developed for both population-average and unit-specific models.

Keywords

categorical datamixed modelmultilevel modelordinalbinary
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 1 , March 2009 , pp. 97 - 105
Copyright
Copyright © 2008 The Psychometric Society

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References

Fielding, A. (2004). Scaling for residual variance components of ordered category responses in generalised linear mixed multilevel models. Quality & Quantity, 38, 425–433.CrossRefGoogle Scholar
Goodman, L.A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55, 708–713.CrossRefGoogle Scholar
Liang, K.-Y., Zeger, S.L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22.CrossRefGoogle Scholar
McCullagh, P., Nelder, J.A. (1989). Generalized linear models, (2nd ed.). Boca Raton: Chapman & Hall.CrossRefGoogle Scholar
McCulloch, C.E., Searle, S.R. (2001). Generalized, linear, and mixed models, New York: Wiley.Google Scholar
Neuhaus, J.M., Jewell, N.P. (1993). A geometric approach to assess bias due to omitted covariates in generalized linear models. Biometrika, 80, 807–815.CrossRefGoogle Scholar
Raudenbush, S.W., Bryk, A.S. (2002). Hierarchical linear models: Applications and data analysis methods, (2nd ed.). Newbury Park: Sage.Google Scholar
Shrout, P.E., Bolger, N. (2002). Mediation in experimental and nonexperimental studies: new procedures and recommendations. Psychological Methods, 7, 422–445.CrossRefGoogle ScholarPubMed
Snijders, T.A.B., Bosker, R.J. (1994). Modeled variance in two-level models. Sociological Methods & Research, 22, 342–363.CrossRefGoogle Scholar
Snijders, T.A.B., Bosker, R.J. (1999). Multilevel analysis, Thousand Oaks: Sage.Google Scholar
Winship, C., Mare, R.D. (1983). Structural equations and path analysis for discrete data. American Journal of Sociology, 89, 54–110.CrossRefGoogle Scholar
Winship, C., Mare, R.D. (1984). Regression models with ordinal variables. American Sociological Review, 49, 512–525.CrossRefGoogle Scholar