188宝金博页面版

ArticleTreatment Effects on Ordinal Outcomes: CausalEstimands and Sharp BoundsJiannan LuMicrosoft CorporationPeng DingUniversity of California-BerkeleyTirthankar DasguptaRutgers UniversityAssessing the causal effects of interventions on ordinal outcomes is an impor-tant objective of many educational and behavioral studies. Under the potentialoutcomes framework, we can define causal effects as comparisons between thepotential outcomes under treatment and control. However, unfortunately, theaverage causal effect, often the parameter of interest, is difficult to interpret forordinal outcomes. To address this challenge, we propose to use two causalparameters, which are defined as the probabilities that the treatment is bene-ficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, thetwo aforementioned parameters depend on the association between the poten-tial outcomes and are therefore not identifiable from the observed data withoutadditional assumptions. Echoing recent advances in the econometrics andbiostatistics literature, we present the sharp bounds of the aforementionedcausal parameters for ordinal outcomes, under fixed marginal distributions ofthe potential outcomes. Because the causal estimands and their correspondingsharp bounds are based on the potential outcomes themselves, the proposedframework can be flexibly incorporated into any chosen models of the potentialoutcomes and is directly applicable to randomized experiments, unconfoundedobservational studies, and randomized experiments with noncompliance. Weillustrate our methodology via numerical examples and three real-life appli-cations related to educational and behavioral research.Keywords: linear programming; monotonicity; noncompliance; partial identification;potential outcome; stochastic dominance1. IntroductionIn educational, behavioral, and public health research, a scenario frequentlyencountered is evaluating causal effects of interventions on ordinal (i.e., orderedJournal of Educational and Behavioral Statistics2018, Vol. 43, No. 5, pp. 540–567DOI: 10.3102/1076998618776435Article reuse guidelines: sagepub.com/journals-permissions© 2018 AERA. http://jebs.aera.net540