Robust Regression for Slope Estimation in Curriculum-Based Measurement Progress Monitoring

Abstract

Although ordinary least-squares (OLS) regression has been identified as a preferred method to calculate rates of improvement for individual students during curriculum-based measurement (CBM) progress monitoring, OLS slope estimates are sensitive to the presence of extreme values. Robust estimators have been developed that are less biased by extreme values; however, the performance of robust estimators in the short data streams typical of CBM progress monitoring is unknown. The purpose of the current study was to investigate bias and efficiency relative to OLS for several robust slope estimators on simulated CBM progress monitoring data. Data were generated at several combinations of series lengths (i.e., 7, 12, and 24 data points) and percentages of extreme value contamination (i.e., 0%, 15%, and 30% of data points). Results indicated that the robust slope estimates were substantially more efficient than OLS in the presence of extreme values. Potential uses of robust slope estimates for calculating students’ rates of improvement in CBM progress monitoring are discussed.