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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.
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Abstract

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

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Footnotes

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

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