Missing data in value-added modeling of teacher effects

TL;DR

This study extends value-added models for student achievement data to account for non-random missing data, finding that such missing data assumptions have minimal impact on estimated teacher effects due to data characteristics.

Contribution

It introduces methods allowing for non-random missing data in value-added models and demonstrates their application to real district data.

Findings

Allowing for non-random missing data has little effect on teacher effect estimates.

Estimated teacher effects are robust despite different missing data assumptions.

Scores from students with incomplete data are downweighted, reducing bias.

Abstract

The increasing availability of longitudinal student achievement data has heightened interest among researchers, educators and policy makers in using these data to evaluate educational inputs, as well as for school and possibly teacher accountability. Researchers have developed elaborate "value-added models" of these longitudinal data to estimate the effects of educational inputs (e.g., teachers or schools) on student achievement while using prior achievement to adjust for nonrandom assignment of students to schools and classes. A challenge to such modeling efforts is the extensive numbers of students with incomplete records and the tendency for those students to be lower achieving. These conditions create the potential for results to be sensitive to violations of the assumption that data are missing at random, which is commonly used when estimating model parameters. The current study extends recent value-added modeling approaches for longitudinal student achievement data Lockwood et al. [J. Educ. Behav. Statist. 32 (2007) 125--150] to allow data to be missing not at random via random effects selection and pattern mixture models, and applies those methods to data from a large urban school district to estimate effects of elementary school mathematics teachers. We find that allowing the data to be missing not at random has little impact on estimated teacher effects. The robustness of estimated teacher effects to the missing data assumptions appears to result from both the relatively small impact of model specification on estimated student effects compared with the large variability in teacher effects and the downweighting of scores from students with incomplete data.