In educational and psychological research, the logit and probit links are often used to fit the binary item response data. The appropriateness and importance of the choice of links within the item response theory (IRT) framework has not been investigated yet. In this paper, we present a family of IRT models with generalized logit links, which include the traditional logistic and normal ogive models as special cases. This family of models are flexible enough not only to adjust the item characteristic curve tail probability by two shape parameters but also to allow us to fit the same link or different links to different items within the IRT model framework. In addition, the proposed models are implemented in the Stan software to sample from the posterior distributions. Using readily available Stan outputs, the four Bayesian model selection criteria are computed for guiding the choice of the links within the IRT model framework. Extensive simulation studies are conducted to examine the empirical performance of the proposed models and the model fittings in terms of “in-sample” and “out-of-sample” predictions based on the deviance. Finally, a detailed analysis of the real reading assessment data is carried out to illustrate the proposed methodology.

中文翻译：

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具有灵活广义 Logit 链接的贝叶斯项目响应理论模型

在教育和心理学研究中，logit 和 probit 链接经常用于拟合二元项目响应数据。项目反应理论（IRT）框架内链接选择的适当性和重要性尚未得到研究。在本文中，我们提出了一系列具有广义 Logit 链接的 IRT 模型，其中包括作为特殊情况的传统 Logistic 模型和正态 ogive 模型。该模型系列足够灵活，不仅可以通过两个形状参数调整项目特征曲线尾部概率，而且还允许我们在 IRT 模型框架内将相同链接或不同链接拟合到不同项目。此外，所提出的模型在 Stan 软件中实现，以从后验分布中采样。使用现成的 Stan 输出，计算四个贝叶斯模型选择标准以指导 IRT 模型框架内的链接选择。进行了广泛的模拟研究，以检查所提出的模型的实证性能以及基于偏差的“样本内”和“样本外”预测的模型拟合。最后，对真实阅读评估数据进行详细分析，以说明所提出的方法。