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

• Published in: Assessment for effective intervention Vol. 47; no. 4; pp. 234 - 244
• Main Authors: Solomon, Benjamin G., Forsberg, Ole J., Thomas, Monelle, Penna, Brittney, Weisheit, Katherine M.
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.09.2022; SAGE Publications and Hammill Institute on Disabilities; SAGE PUBLICATIONS, INC
• Subjects: Accuracy; Achievement Gains; Bayesian analysis; Bayesian Statistics; Comparative Analysis; Curricula; Curriculum Based Assessment; Elementary School Students; Fluency; Grade 2; Grade 3; Growth rate; Least Squares Statistics; Oral Reading; Reading Achievement; Reading Fluency; Reading Skills; Reading Tests; Specification; Standardized Tests; Values; Variants; progress monitoring; reading/literacy; curriculum-based measurement
• ISSN: 1534-5084; 1938-7458
• DOI: 10.1177/15345084211040219

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.