Measurement Error Adjustment Using the SIMEX Method: An Application to Student Growth Percentiles

Abstract

Growth models are used extensively in the context of educational accountability to evaluate student-, class-, and school-level growth. However, when error-prone test scores are used as independent variables or right-hand-side controls, the estimation of such growth models can be substantially biased. This article introduces a simulation-extrapolation (SIMEX) method that corrects measurement error induced bias. The SIMEX method is applied to quantile regression, which is the basis of Student Growth Percentile, a descriptive growth model adopted in a number of states to diagnose and project student growth. A simulation study is conducted to demonstrate the performance of the SIMEX method in reducing bias and mean squared error in quantile regression with a mismeasured predictor. One of the simulation cases is based on longitudinal state assessment data. The analysis shows that measurement error differentially biases growth percentile results for students at different achievement levels and that the SIMEX method corrects such biases and closely reproduces conditional distributions of current test scores given past true scores. The potential applications and limitations of the method are discussed at the end of this paper with suggestions for further studies.