Priors That Route but Do Not Score: Linking, Prior-Informed Routing, and Fairness in Through-Year Assessment Systems

Through-year assessment systems use interims during the school year to inform, route, or partly replace the spring summative. We treat the system, not the single test, as the unit of analysis. Interims are linked to the summative scale with a latent multivariate normal model that carries each score’s measurement error forward and handles missing interims; the model is estimated by EM with SQUAREM acceleration. Linked projections serve as routing priors in a two-stage multistage test. We evaluate routing accuracy, precision and fairness for late enrollers, low scorers, and students whose growth accelerated after the last interim. Across 100 known-truth replications, linked priors were calibrated (z SD 1.01; 89.9% coverage of 90% intervals). Prior-informed routing raised routing accuracy from 70% to 84%. Using the prior to score as well as to route biased late-growing students by −0.29 logits, whereas routing-only use left them about as biased as a cold start (−0.05 vs −0.07). A through-year projection used in place of the summative matched it in overall accuracy (90.3% vs 89.7%), but wrongly classified 21% of late-growing students as not proficient, versus 6% for the summative. A factorial study of 600 data sets showed that more precise interims strengthen routing but worsen the scoring bias for late-growing students (up to −0.36 logits), and make summative replacement look more accurate overall without reducing its misclassification of that group. We conclude that interim information can defensibly route students but should not score them, and that summative replacement needs subgroup-level evidence. The methods are implemented in the R package throughyear.