Educational Measurement: Issues and Practice xxx 2014, Vol. 00, No. 0, pp. 1–11 Covariate Measurement Error Correction for Student Growth Percentiles Using the SIMEX Method Yi Shang, John Carroll University, Adam VanIwaarden, University of Colorado at Boul- der, and Damian W. Betebenner, Center for Assessment In this study, we examined the impact of covariate measurement error (ME) on the estimation of quantile regression and student growth percentiles (SGPs), and find that SGPs tend to be overestimated among students with higher prior achievement and underestimated among those with lower prior achievement, a problem we describe as ME endogeneity in this article. We proceeded to assess the effect of covariate ME correction on SGP estimation at two levels—the individual (student) and the aggregate (classroom). Our ME correction approach was limited to the simulation-extrapolation method known as SIMEX. For both the individual and aggregate SGP, we find SIMEX effective in bias reduction. Further, because SIMEX is especially effective in reducing SGP bias for students with very high or very low prior achievement, it significantly weakens the ME endogeneity. SIMEX is also effective in reducing the MSE of aggregate SGP, provided that the students are sorted to some extent on their latent prior achievement. Our empirical study confirms the pattern of the simulation results: SIMEX mainly affects the mean SGP of classes in the highest and lowest quintiles of the prior score distribution, and significantly lowers the correlation between class SGP and prior achievement. Keywords: measurement error, quantile regression, SIMEX, student growth percentiles E ducational accountability systems currently rely upon annually administered standardized tests to track stu- dent academic performance, and to make inferences about academic growth at the individual and aggregate level. Two of the most popular models adopted for this purpose are value- added models (Ballou, Sanders, & Wright, 2004; Braun, 2005; McCaffrey, Lockwood, Koretz, Louis, & Hamilton, 2004) and student growth percentiles (SGP; Betebenner, 2009). The for- mer is based on a classical regression model which estimates the conditional mean of a test outcome variable given some set of covariates. Teacher or school effects can be estimated directly in this type of model as fixed or random effects. In contrast, the computation of SGPs is based up on a quan- tile regression (QR) model which estimates many different conditional quantiles (i.e., the 25th percentile, the 50th per- centile, the 65th percentile, etc.) of a test outcome variable given some set of covariates. Growth percentiles of individual students are derived from the QR results, and can then be aggregated to form descriptive growth percentiles of teach- ers and schools. In both classical and QR models, error-prone standardized test scores are used as covariates. This vio- lates a fundamental assumption common to both models that Yi Shang, Department of Education and School Psychology, John Carroll University, 1 John Carroll Blvd., AD 313, University Heights, OH 44118; yshang@jcu.edu. Adam VanIwaarden, University of Colorado Boulder, CO; vani- waarden@colorado.edu. Damian W. Betebenner, Center for Assessment, PO Box 351, Dover, NH; dbetebenner@nciea.org. the error term of the model is independent of any covariate (cf. Fuller, 2006). When a regression covariate is measured with error, mea- surement error (ME) combines with the regression residual to form a composite model residual. The error-prone covariate is then correlated with the model residual since it is corre- lated with its own ME (Lord & Novick, 1968). The correlation is a symptom of what is known as endogeneity, and it not only causes bias in the estimated coefficient of the error-prone co- variate, but can also affect all other coefficients in the model (Fuller, 2006; Gleser, Carroll, & Gallo, 1987). While there is an extensive literature about the endogeneity problem in classical regression and its implications for value-added and other related models (see, e.g., Battauz, Bellio, & Gori, 2011; Fuller, 2006; Goldstein, 2011; Koedel, Leatherman, & Parsons, 2012; Lockwood & McCaffrey, 2014), the issue has not at- tracted as much attention in the context of QR (Chesher, 2001; Schennach, 2008; Wei & Carroll, 2009). Even less is under- stood about the ramifications of covariate ME in the computa- tion of SGPs at the individual level or at an aggregated level. Shang (2012) investigated the covariate ME problem in linear QR and the potential of the simulation-extrapolation (SIMEX) method as a remedy. Shang demonstrates that co- variate ME biases the estimation of linear QR coefficients. It follows that the SGPs derived from linear QR will also be bi- ased, and the bias is positively correlated with students’ prior achievement, which raises serious fairness concerns. Shang’s simulation study demonstrated the effectiveness of SIMEX in reducing the bias in linear QR coefficients in the scenarios of both homoscedastic and heteroscedastic ME. It cannot be C  2014 by the National Council on Measurement in Education 1