The basics of conditioning models: stability of marginal and conditional achievement to model specification

Abstract This study investigates how different conditioning model specifications affect the stability of marginal and subgroup achievement distributions in large-scale assessments. Through both a simulation and an empirical example reflecting typical operational designs, we examine the robustness of these distributions under alternative latent regression models. We compare parameter estimates obtained from generating parameters with aggregated estimates derived from plausible values. Our findings show that marginal and subgroup achievement distributions are consistently stable and well-recovered across several specifications, aligning with established results from linear regression and multiple imputation. These results provide practical guidance for methodological practice and strengthen the interpretation of large-scale assessment outcomes, bridging technical rigor with applied research needs.