Randomization based sharp bounds and monotonicity for ordinal outcomes in $2^K$ factorial experiments

Statistical Seminar

Organizer：

吴宇楠

Speaker：

杨玥含 教授中央财经大学统计与数学学院

Time：

Fri., 16:00-17:00, April 17, 2026

Venue：

C654, Shuangqing Complex Building A

Title：

Randomization based sharp bounds and monotonicity for ordinal outcomes in $2^K$ factorial experiments

Abstract:

Randomized $2^K$ factorial experiments with ordinal outcomes are common in economics, biomedical research, and behavioral studies, where multiple interventions may jointly affect an ordered response. Within the potential outcomes framework, factorial effects are often defined through linear contrasts of average potential outcomes, but such contrasts can be difficult to interpret when outcome categories have a natural ordering. To address this, we propose a novel framework that generalizes traditional factorial designs to incorporate ordinal outcomes, and define probability-based main and interaction effects. Because these estimands depend on the unobserved joint distribution of potential outcomes, they are generally not point-identified. We derive closed-form bounds through partial identification, relying solely on the observable marginal distributions, without imposing parametric models or distributional assumptions. In particular, we obtain sharp bounds for main effects and valid, typically non-sharp bounds for interaction effects, where excluding $0$ yields a robust conclusion on the interaction direction. Our framework allows the single factor as a special case and is applicable to both binary and multicategory outcomes. Considering the wide application of monotonicity in practice, we derive its testable equivalent form, which can yield tighter identification intervals for the factorial effects. For inference, we construct nonparametric bootstrap confidence intervals and evaluate the finite sample performance of the proposed procedures through simulation and two empirical applications.