  Nonparametric item response models provide a flexible framework in
psychological and educational measurements. Douglas (2001) established
asymptotic identifiability for a class of models with nonparametric response
functions for long assessments. Nevertheless, the model class examined in
Douglas (2001) excludes several popular parametric item response models. This
limitation can hinder the applications in which nonparametric and parametric
models are compared, such as evaluating model goodness-of-fit. To address this
issue, We consider an extended nonparametric model class that encompasses most
parametric models and establish asymptotic identifiability. The results bridge
the parametric and nonparametric item response models and provide a solid
theoretical foundation for the applications of nonparametric item response
models for assessments with many items.
