Chapter 10: Handling Measurement Error in Predictors using A Multilevel Latent Variable Plausible Values Approach

We propose a multilevel latent variable plausible values (MLVPV) approach for more appropriately handling measurement error in predictors in multilevel modeling settings in which latent predictors are measured by observed categorical variables. This approach draws substantially from the work of Mislevy, Beaton, Kaplan, and Sheehan (1992), along with key ideas in the multiple imputation literature more generally, and from the Bayesian statistics literature, notably the concept of exchangeability. In this chapter, we outline the MLVPV approach and through an illustrative example using the Early Childhood Longitudinal Study–Kindergarten (ECLS–K) 1998–1999 cohort data, discuss its use in analyzing the relation between teacher instructional practices of interest and student achievement. The MLVPV approach consists of two stages. The first stage entails specifying and imputing sets of values from a multilevel measurement model for the key practice measures that we wish to treat as latent variable predictors in analyses of achievement outcome scores. We employ a fully Bayesian approach implemented in WinBUGS (Lunn, Thomas, Best, & Spiegelhalter, 2000) to estimate and impute values from the first-stage model. The second stage consists of fitting multilevel models to the outcome data employing the imputed instructional practice values as predictor variables. In our analyses, we implement the second stage using the HLM7 software program (Raudenbush, Bryk, & Congdon, 2010).