Latent and manifest monotonicity in item response models

The monotonicity of item response functions (IRF) is a central feature of most parametric and nonparametric item response models. Monotonicity allows items to be interpreted as measuring a trait, and it allows for a general theory of nonparametric inference for traits. This theory is based on monotone likelihood ratio and stochastic ordering properties. Thus, confirming the monotonicity assumption is essential to applications of nonparametric item response models. The results of two methods of evaluating monotonicity are presented: regressing individual item scores on the total test score and on the "rest " score, which is obtained by omitting the selected item from the total test score. It was found that the item-total regressions of some familia