Shim Hyejin, Bonifay Wes, Wiedermann Wolfgang
University of Missouri, 5 C Hill Hall, Columbia, MO, 65211, USA.
Missouri Prevention Science Institute, Columbia, MO, USA.
Behav Res Methods. 2025 May 19;57(6):176. doi: 10.3758/s13428-025-02700-8.
Application of the four-parameter logistic model (4PLM) in item response theory (IRT) research is contentious due to the complexities of estimating the asymptotes that correspond to upper and lower asymptote effects. We introduce the cauchit IRT model (i.e., a model that utilizes a link function based on the Cauchy distribution) as a compelling parsimonious alternative to the 4PLM. Through comprehensive simulation studies and real-data analysis, we determine that the cauchit model, distinguished by its symmetric error distribution and pronounced tails, provides a streamlined solution, because the tail-pronounced symmetric error distribution captures key features of the 4PLM with only one item parameter. The 4PLM requires large sample sizes (e.g., N > 5000), medium item difficulty, and high discrimination when both upper and lower asymptote effects are present. In contrast, we show that the cauchit model works well with drastically smaller sample sizes (e.g., N = 100). Our study further discusses the versatility of the cauchit model, underscoring its adaptability, especially in small sample research situations.
由于估计与上下渐近线效应相对应的渐近线存在复杂性，四参数逻辑模型（4PLM）在项目反应理论（IRT）研究中的应用存在争议。我们引入柯西IRT模型（即一种基于柯西分布使用链接函数的模型）作为4PLM的一种引人注目的简约替代方案。通过全面的模拟研究和实际数据分析，我们确定，以其对称误差分布和明显尾部为特征的柯西模型提供了一种简化的解决方案，因为尾部明显的对称误差分布仅用一个项目参数就捕捉到了4PLM的关键特征。当同时存在上下渐近线效应时，4PLM需要大样本量（例如，N > 5000）、中等项目难度和高区分度。相比之下，我们表明柯西模型在样本量小得多（例如，N = 100）的情况下也能很好地工作。我们的研究进一步讨论了柯西模型的通用性，强调了其适应性，特别是在小样本研究情况下。
