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3PL model 3PNO model approximate model averaged over items Beguin Bejar Box & Tiao burn-in iterations cloned items cloning model ICM computerized adaptive testing Computerized Testing Report correct response discrimination parameter EAP Estimate equal to v0 examinees First-Level Model French language Gelman Gibbs sampler Glas hyperparameters ICM Approx informative prior item cloning model Item cloning techniques item ip items and replications Law School Admission Likelihood Function Linden in press logit loss of precision MAE refers MCMC chain MCMC procedure mean absolute error model are sampled multilevel item response multivariate normal distribution Newtown normal distribution associated normal prior normal-inverse-Wishart prior normal-ogive number of responses number of simulation number of students Parameter recovery Parameter True MAE parent item parameters point estimates prior distributions procedures for updating random item parameters responding to item response variable School Admission Council second procedure set equal standard normal distribution Updating Item Parameter variance vector xni xni