| Abstract: | 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. |
