Explores the asymptotic theory of a method of nonparametric item characteristic curve estimation based on kernel smoothing with the theory of obtaining the proper linear ordering of examinees with respect to their true latent abilities. Results support the usefulness of estimates of the type produced by the TESTGRAF program. (SLD)

H. H. Chang and W. F. Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous item response (IRT) theory models. This paper presents an extension of their results to polytomous IRT models and defines a global information…

Three methods based on the nonparametric item response theory (IRT) of R. J. Mokken for the estimation of the reliability of single dichotomous test items are discussed. Analytical and Monte Carlo studies show that one method, designated "MS," is superior because of smaller bias and smaller sampling variance. (SLD)