We describe a Bayesian multidimensional explanatory IRT model, and an associated Markov Chain Monte Carlo (MCMC) estimation procedure and the corresponding development of calibration software, designed for psychometric analyses of large numbers of sparsely-linked persons and items. Such data structures can arise, for example, from adaptive assessments using large banks of automatically generated items with individual test takers receiving a very small proportion of the entire bank. We discuss how our choices for model specification, data structures, and algorithm implementation combine to create a scalable method for explanatory IRT that can support a variety of psychometric operations with sparse data.

翻译：我们描述了一种贝叶斯多维解释性IRT模型、相应的马尔可夫链蒙特卡洛（MCMC）估计程序及配套校准软件的开发。该框架专为大规模稀疏连接被试与项目间的心理测量分析而设计。此类数据结构常见于自适应评估场景——例如使用包含大量自动生成项目的题库，而每位考生仅需作答题库中极小比例的题目。我们论证了模型规范、数据结构与算法实现之间的协同设计，如何共同构建支持稀疏数据下多种心理测量操作的可扩展解释性IRT方法。