The four-parameter logistic (4PL) item response model, which includes an upper asymptote for the correct response probability, has drawn increasing interest due to its suitability for many practical scenarios. This paper proposes a new Gibbs sampling algorithm for estimation of the multidimensional 4PL model based on an efficient data augmentation scheme (DAGS). With the introduction of three continuous latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. Simulation studies are conducted to evaluate the proposed method and several popular alternatives. An empirical data set was analysed using the 4PL model to show its improved performance over the three-parameter and two-parameter logistic models. The proposed estimation scheme is easily accessible to practitioners through the open-source IRTlogit package.

中文翻译：

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通过数据增强方案的多维四参数逻辑项目响应模型的吉布斯采样器

四参数逻辑 (4PL) 项目响应模型（包括正确响应概率的上渐近线）因其适用于许多实际场景而引起了越来越多的兴趣。本文提出了一种新的 Gibbs 采样算法，用于基于有效数据增强方案 (DAGS) 的多维 4PL 模型估计。通过引入三个连续的潜在变量，完整的条件分布是易于处理的，从而可以轻松实现 Gibbs 采样器。进行模拟研究以评估所提出的方法和几种流行的替代方法。使用 4PL 模型分析了一个经验数据集，以显示其相对于三参数和二参数逻辑模型的改进性能。IRTlogit包。