A continuous item response model using a censored normal distribution

This study proposes an item response theory (IRT) model for bounded continuous data: the censored normal response model (CNRM). This model has a structure similar to the Tobit models, which makes it possible to take into account the ceiling and floor effects on item responses. The CNRM is formulated as a special case of the generalized normal ogive framework, which unifies several existing models. A parameter estimation method using the EM algorithm is shown and is applied to simulated and real data. The results suggest that the CNRM provides a computationally efficient and highly interpretable alternative to Molenaar et al.’s (2022) zero-and-one inflated approach.