Contrasting OLS and Quantile Regression Approaches to Student “Growth” Percentiles

Abstract

Regression methods can locate student test scores in a conditional distribution, given past scores. This article contrasts and clarifies two approaches to describing these locations in terms of readily interpretable percentile ranks or “conditional status percentile ranks.” The first is Betebenner’s quantile regression approach that results in “Student Growth Percentiles.” The second is an ordinary least squares (OLS) regression approach that involves expressing OLS regression residuals as percentile ranks. The study describes the empirical and conceptual similarity of the two metrics in simulated and real-data scenarios. The metrics contrast in their scale-transformation invariance and sample size requirements but are comparable in their dependence on the number of prior years used as conditioning variables. These results support guidelines for selecting the model that best fits the data and have implications for the interpretations of these percentiles ranks as “growth” measures.