Identification of a Semiparametric Item Response Model

We consider the identification of a semiparametric multidimensional fixed effects item response model. Item response models are typically estimated under parametric assumptions about the shape of the item characteristic curves (ICCs), and existing results suggest difficulties in recovering the distribution of individual characteristics under nonparametric assumptions. We show that if the shape of the ICCs are unrestricted, but the shape is common across individuals and items, the individual characteristics are identified. If the shape of the ICCs are allowed to differ over items, the individual characteristics are identified in the multidimensional linear compensatory case but only identified up to a monotonic transformation in the unidimensional case. Our results suggest the development of two new semiparametric estimators for the item response model.