Estimation of Plausible Values Considering Partially Missing Background Information: A Data Augmented MCMC Approach

Abstract

The National Educational Panel Study (NEPS) provides data on the development of competencies across the whole life span. Plausible values as a measure of individual competence are provided by explicitly including background variables that capture individual characteristics in the corresponding Item Response Theory model. Despite tremendous efforts in field work, missing values in the background variables can occur. Adequate estimation routines are needed to reflect the uncertainty stemming from missing values in the background variables with regard to plausible values. We propose an estimation strategy based on Markov Chain Monte Carlo techniques that simultaneously addresses missing values in background variables and estimates parameters characterizing the distribution of plausible values. We evaluate the validity of our approach with respect to statistical accuracy in a simulation study that allows for controlling the mechanism that causes missing data. The results show that the proposed approach is capable of recovering the true regression parameters that describe the relationship between latent competence scores and background variables and thus of recovering the distribution that characterizes plausible values. The approach is illustrated in an example using competence test data on mathematical abilities of Grade-5 students.