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Should "Multiple Imputations" be Treated as "Multiple Indicators"? NAEP

Mislevy, Robert J.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Data Analysis, LISREL, National Assessment of Educational Progress (NAEP), Statistical Analysis


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.

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