In this paper, we show that the marginal distribution of plausible values is a consistent estimator of the true latent variable distribution, and, furthermore, that convergence is monotone in an embedding in which the number of items tends to infinity. We use this result to clarify some of the misconceptions that exist about plausible values, and also show how they can be used in the analyses of educational surveys.

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.