although one's compliance score cannot be directly observed, the probability of compliance can be estimated by observing the compliance condition from the same strata,  in other words those that share the same covariate profile. the compliance score is treated as a latent pretreatment covariate, which is independent of treatment assignment formula_1. for each unit formula_2, compliance score is denoted as formula_3, where formula_4is the covariate vector for unit formula_5.