The increasing availability of longitudinal student achievement data has heightened interest among researchers, educators, and policymakers 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 and 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, an assumption that is commonly used when estimating model parameters. The current study extends recent value-added modeling approaches for longitudinal student achievement data developed by Lockwood et al. to allow data to be missing not at random via random effects selection and pattern mixture models, and we apply these 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 assumption 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.
Posted here with permission from The Annals of Applied Statistics, 2011, Vol. 5, No. 2A, pp. 773-797. Copyright © 2011 Institute of Mathematical Statistics.