Latent and Manifest Monotonicity in Item Response Models

Abstract

The monotonicity of item response functions(IRF) is a central feature of most parametric andnonparametric item response models. Monotonicityallows items to be interpreted as measuring a trait,and it allows for a general theory of nonparametricinference for traits. This theory is based on monotonelikelihood ratio and stochastic ordering properties.Thus, confirming the monotonicity assumption isessential to applications of nonparametric itemresponse models. The results of two methods ofevaluating monotonicity are presented: regressingindividual item scores on the total test score andon the ‘rest’ score, which is obtained by omittingthe selected item from the total test score. It wasfound that the item-total regressions of some familiardichotomous item response models with monotoneIRFs exhibited nonmonotonicities that persist as thetest length increased. However, item-rest regressionsnever exhibited nonmonotonicities under the nonparametricmonotone unidimensional item responsemodel. The implications of these results for exploratoryanalysis of dichotomous item response dataand the application of these results to polytomousitem response data are discussed.