Predictive Inference Using Latent Variables with Covariates∗

Plausible Values (PVs) are a standard multiple imputation tool for analysis of large education survey data that measures latent proficiency variables. When latent profi-ciency is the dependent variable, we reconsider the standard institutionally-generated PV methodology and find it applies with greater generality than shown previously. When latent proficiency is an independent variable, we show that the standard institu-tional PV methodology produces biased inference because the institutional conditioning model places restrictions on the form of the secondary analysts ’ model. We offer an alternative approach that avoids these biases based on the mixed effects structural equations (MESE) model of Schofield (2008)