Latent and manifest monotonicity in item response models

The monotonicity of item response functions (IRF) is a central feature of m ost parametric and nonparametric item response models. Monotonicity allows items to be interpreted as measuring a trait, and it allows for a general t heory of nonparametric inference for traits. This theory is based on monoto ne likelihood ratio and stochastic ordering properties. Thus, confirming th e monotonicity assumption is essential to applications of nonparametric ite m response models. The results of two methods of evaluating monotonicity ar e presented: regressing individual item scores on the total test score and on the "rest" score, which is obtained by omitting the selected item from t he total test score. It was found that the item-total regressions of some f amiliar dichotomous item response models with monotone IRFs exhibited nonmo notonicities that persist as the test length increased. However, item-rest regressions never exhibited nonmonotonicities under the nonparametric monot one unidimensional item response model. The implications of these results f or exploratory analysis of dichotomous item response data and the applicati on of these results to polytomous item response data are discussed.