Reliability estimation for single dichotomous items based on Mokken’s IRT model

Item reliability is of special interest for Mokken’s nonparametric item response theory, and is useful for the evaluation of item quality in nonparametric test construction research. It is also of interest for non-parametric person-fit analysis. Three methods for the estimation of the reliability of single dichotomous items are discussed. All methods are based on the assumptions of nondecreasing and nonintersecting item response functions. Based on analytical and monte carlo studies, it is concluded that one method is supe-rior to the other two, because it has a smaller bias and a smaller sampling variance. This method also demon-strated some robustness under violation of the condi-tion of nonintersecting item response functions. Index terms: item reliability, item response theory, Mokken model, nonparametric item response models, test construction. In practice, total scores on a test are more im-portant than scores on individual items. In test con-struction, however, item quality must be assessed to select appropriate items that together will con-stitute a useful test. For example, in classical test theory (Lord & Novick, 1968) item statistics, such as the proportion correct and the corrected item-total correlation, are used for this purpose. In logis-tic item response theory (IRT; e.g., Lord, 1980) items can be evaluated on the basis of their difficulty, dis-crimination, and pseudoguessing level. Moreover, the item information function (Lord, 1980, p. 72) can be used to assess measurement precision of a single item. The nonparametric Mokken approac