Goodness-of-fit methods for nonparametric IRT models

This chapter has three sections. The first section introduces the unidimensionalmonotone latent variable model for data collected by means of a test or a questionnaire. The second section discusses the use of goodness-of-fit methods for statistical models, in particular, item response models such as theunidimensional monotone latent variable model. The third section discusses the use of the conditional association property for testing the goodness-of-fit of the unidimensional monotone latent variable model. It is established that conditional association is well suited for assessing the local independence assumption and a procedure is proposed for identifying locally independent sets of items. The procedure is used in a real-data analysis.