Hostname: page-component-77c78cf97d-lmk9j Total loading time: 0 Render date: 2026-04-24T23:29:01.920Z Has data issue: false hasContentIssue false
  • English
  • Français

Should “Multiple Imputations” be Treated as “Multiple Indicators”?

Published online by Cambridge University Press:  01 January 2025

Robert J. Mislevy
Robert J. Mislevy*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Robert J. Mislevy, Educational Testing Service, Princeton, NJ 08541.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Rubin's “multiple imputation” approach to missing data creates synthetic data sets, in which each missing variable is replaced by a draw from its predictive distribution, conditional on the observed data. By construction, analyses of such filled-in data sets as if the imputations were true values have the correct expectations for population parameters. In a recent paper, Mislevy showed how this approach can be applied to estimate the distributions of latent variables from complex samples. Multiple imputations for a latent variable bear a surface similarity to classical “multiple indicators” of a latent variable, as might be addressed in structural equation modelling or hierarchical modelling of successive stages of random sampling. This note demonstrates with a simple example why analyzing “multiple imputations” as if they were “multiple indicators” does not generally yield correct results; they must instead be analyzed by means concordant with their construction.

Keywords

multiple imputationmultiple indicatorsNational Assessment of Educational Progressplausible values

Information

Type
Notes And Comments
Information
Psychometrika , Volume 58 , Issue 1 , March 1993 , pp. 79 - 85
Copyright
Copyright © 1993 The Psychometric Society

Footnotes

I am grateful to Frank Jenkins, John Mazzeo, Kentaro Yamamoto, and Rebecca Zwick for comments on earlier versions of this paper.

References

Beaton, A. E. (1987). The NAEP 1983/84 technical report, Princeton: Educational Testing Service.Google Scholar
Beaton, A. E. (1988). The NAEP 1985/86 technical report, Princeton: Educational Testing Service.Google Scholar
Goldstein, H. (1987). Multilevel models in educational and social research, London: Griffin, NY: Oxford University Press.Google Scholar
Johnson, E. G., Zwick, R. (1990). The NAEP 1987/88 technical report, Princeton: Educational Testing Service.Google Scholar
Jöreskog, K. G., Sörbom, D. (1989). LISREL 7: User's reference guide, Mooresville, IN: Scientific Software.Google Scholar
Mislevy, R. J. (1991). Randomization-based inference about latent variables from complex samples. Psychometrika, 56, 177–196.CrossRefGoogle Scholar
Mislevy, R. J., Beaton, A. E., Kaplan, B., Sheehan, K. M. (1992). Estimating population characteristics from sparse matrix samples of item responses. Journal of Educational Measurement, 29, 133–161.CrossRefGoogle Scholar
Muthén, B. (1988). LISCOMP [computer program], Mooresville, IN: Scientific Software.Google Scholar
Rubin, D. B. (1977). Formalizing subjective notions about the effect of nonrespondents in sample surveys. Journal of the American Statistical Association, 72, 538–543.CrossRefGoogle Scholar
Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys, New York: Wiley.CrossRefGoogle Scholar