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aberrant adaptive item score assumed binomial distribution CAT research computerized adaptive testing correct answers denote the number detection rate developments in nonparametric different 8 levels different 8 value difficult items easiest items estimated example g and h Guttman model incorrect responses invariant item ordering IRFs item difficulty item g item pool item proportion correct Item Response Functions item response theory item score pattern item selection latent trait Linden logistic models longest run marginal independence maximum Fisher information maximum information given MHM model Mokken & Lewis ngnh Nondecreasing Item Response Nonparametric Checks nonparametric IRT models number correct score number of correct number of runs parameter Parametric IRT Models positive covariances probability distribution proportion correct score put order restrictions response variable response vector Rosenbaum set of items significance probability Sijtsma & Meijer similarly ordered functions simulated stochastic ordering testlet selected testlet-based total number total score Trabin & Weiss variance