A Statistical Model for Misreported Binary Outcomes in Clustered RCTs of Education Interventions

In education randomized control trials (RCTs), the misreporting of student outcome data could lead to biased estimates of average treatment effects (ATEs) and their standard errors. This article discusses a statistical model that adjusts for misreported binary outcomes for two-level, school-based RCTs, where it is assumed that misreporting could occur for students with truly undesirable outcomes, but not for those with truly desirable outcomes. A latent variable index approach using study baseline data is employed to model both the misreporting and binary outcome decision processes, separately for treatments and controls, using random effects probit models to adjust for school-level clustering. Quasi-Newton maximum likelihood methods are developed to obtain consistent estimates of the ATE parameter and the unobserved misreporting rates. The estimation approach is demonstrated using self-reported arrest data from a large-scale RCT of Job Corps, the nation’s largest residential training program for disadvantaged youths between the ages of 16 and 24.