A Comparison of Priors When Using Bayesian Regression to Estimate Oral Reading Fluency Slopes

Abstract

Bayesian regression has emerged as a viable alternative for the estimation of curriculum-based measurement (CBM) growth slopes. Preliminary findings suggest such methods may yield improved efficiency relative to other linear estimators and can be embedded into data management programs for high-frequency use. However, additional research is needed, as Bayesian estimators require multiple specifications of the prior distributions. The current study evaluates the accuracy of several combinations of prior values, including three distributions of the residuals, two values of the expected growth rate, and three possible values for the precision of slope when using Bayesian simple linear regression to estimate fluency growth slopes for reading CBM. We also included traditional ordinary least squares (OLS) as a baseline contrast. Findings suggest that the prior specification for the residual distribution had, on average, a trivial effect on the accuracy of the slope. However, specifications for growth rate and precision of slope were influential, and virtually all variants of Bayesian regression evaluated were superior to OLS. Converging evidence from both simulated and observed data now suggests Bayesian methods outperform OLS for estimating CBM growth slopes and should be strongly considered in research and practice.