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<p>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.</p>

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A continuous item response model using a censored normal distribution

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月17日

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  • Atsushi Minamimoto,
  • Taisei Wakai,
  • Kensuke Okada

摘要

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.