Predictive Inference Using Latent Variables with Covariates

Plausible values (PVs) are a standard multiple imputation tool for analysis of large education survey data, which measures latent proficiency variables. When latent proficiency 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 institutional 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 model of Schofield (Modeling measurement error when using cognitive test scores in social science research. Doctoral dissertation. Department of Statistics and Heinz College of Public Policy. Pittsburgh, PA: Carnegie Mellon University, 2008).