The CP model fits seasonal achievement data better than a traditional polynomial growth model on RMSE, AIC, and BIC while reducing residual autocorrelation¶

Claim · All claims
Evidence · 1 study · design r2 · q2
Currency · newest study 2019 · not yet checked against its sources · not reviewed by a person · overdue for a recheck since 2022: tool and model accuracy changes quickly

Subclaims¶

q2 i? For MAP Growth data with marked seasonality, the Compound Polynomial model fit better than a traditional growth curve model based on RMSE, AIC, and BIC and reduced autocorrelation in the residuals. → Soland 2019

Evidence¶

Soland 2019¶

Soland, J. & Thum, Y.M. (2019). School effectiveness, summer loss, and federal accountability: Applying the compound polynomial model in a program evaluation context. The Collaborative for Student Growth at NWEA Working Paper. https://www.nwea.org/research/publication/school-effectiveness-summer-loss-and-federal-accountability-applying-the-compound-polynomialmodel-in-a-program-evaluation-context/

q2 · i? · design · r2

Model-fit comparison in a multilevel analysis of vertically scaled MAP Growth scores from one cohort of students in grades 2-6 in an East Coast state, covering 570 schools. The authors report the CP "fit better based on RMSE, AIC, and BIC statistics" with reduced residual autocorrelation (Appendix Table A3).

"To confirm the superior fit of the CP relative to the traditional growth curve model for these data, we fit both just as Thum and Hauser (2015) and Thum and Matta (2015) did, and found that the CP fit better based on RMSE, AIC, and BIC statistics while also reducing autocorrelation in the residuals"

Discussion¶

Related Claims¶

• Across 90 grade-subject-level conditions, the three-piece piecewise model showed the lowest deviance for 64% of student-level and 78% of school-level models, outperforming both compound polynomial candidates — related
• The 2025 MAP Growth norms adopted a two-year, two-level piecewise mixed-effects design because two consecutive years of data are sufficient for within-year and adjacent-year growth norms — related
• Interim achievement data exhibit distinctly seasonal patterns that few existing statistical models can approximate — a broader claim this one bears on
• Mean achievement in the studied cohort shows a saw-tooth seasonal pattern, with within-year gains followed by summer declines (summer learning loss) — related
• The proposed seasonal growth model combines polynomial terms for year-to-year growth with piecewise terms for within-year gains and losses — a broader claim this one bears on
• Seasonal patterns are discrepant across national data sets — related