Do principal components matter? Robustness of achievement and subgroup estimates to conditioning model specification

Large-scale assessments (LSAs) such as PISA, TIMSS, and NAEP rely on conditioning models with principal components from background questionnaires to estimate achievement distributions. Recent expansions in conditioning models have reduced the variance accounted for in background data, raising concerns about population and subpopulation estimates. Using simulation and PISA 2022 U.S. data, we examined marginal achievement distributions and secondary regression coefficients across conditioning models that ranged from empty to relatively comprehensive. Marginal distributions were highly stable under the measurement conditions studied. Regression coefficients were generally stable, although sparse conditioning produced appreciable attenuation for several simulated mathematics coefficients. In the simulation, every student responded to items in all three domains, and the measurement model had precision typical of modern LSAs. The empirical mathematics scale was also highly reliable. These features reduce reliance on the conditioning prior and help explain the observed results. Accordingly, our findings apply to high-reliability settings with substantial direct response information; weaker measurement, fewer items, or no direct responses in a domain may increase sensitivity to conditioning-model specification. The results suggest that reductions in background-variable variance accounted for can have limited consequences under these conditions and identify assessment design and measurement precision as important boundaries.