Heister Hannah, Doebler Philipp, Frick Susanne
University of Groningen, Groningen, Netherlands.
Technische Universität Dortmund, Dortmund, Germany.
Educ Psychol Meas. 2025 May 30:00131644251335586. doi: 10.1177/00131644251335586.
Thurstonian item response theory (Thurstonian IRT) is a well-established approach to latent trait estimation with forced choice data of arbitrary block lengths. In the forced choice format, test takers rank statements within each block. This rank is coded with binary variables. Since each rank is awarded exactly once per block, stochastic dependencies arise, for example, when options A and B have ranks 1 and 3, C must have rank 2 in a block of length 3. Although the original implementation of the Thurstonian IRT model can recover parameters well, it is not completely true to the mathematical model and Thurstone's law of comparative judgment, as impossible binary answer patterns have a positive probability. We refer to this problem as stochastic dependencies and it is due to unconstrained item intercepts. In addition, there are redundant binary comparisons resulting in what we call logical dependencies, for example, if within a block and , then must follow and a binary variable for is not needed. Since current Markov Chain Monte Carlo approaches to Bayesian computation are flexible and at the same time promise correct small sample inference, we investigate an alternative Bayesian implementation of the Thurstonian IRT model considering both stochastic and logical dependencies. We show analytically that the same parameters maximize the posterior likelihood, regardless of the presence or absence of redundant binary comparisons. A comparative simulation reveals a large reduction in computational effort for the alternative implementation, which is due to respecting both dependencies. Therefore, this investigation suggests that when fitting the Thurstonian IRT model, all dependencies should be considered.
瑟斯顿项目反应理论（Thurstonian IRT）是一种成熟的方法，用于通过任意块长度的强制选择数据来估计潜在特质。在强制选择格式中，应试者对每个块内的陈述进行排序。此排序用二元变量编码。由于每个块中每个排名仅被授予一次，因此会出现随机依赖性，例如，当选项A和B的排名分别为1和3时，在长度为3的块中，C的排名必须为2。尽管瑟斯顿IRT模型的原始实现能够很好地恢复参数，但它并不完全符合数学模型和瑟斯顿比较判断定律，因为不可能的二元答案模式具有正概率。我们将此问题称为随机依赖性，它是由于项目截距未受约束所致。此外，存在冗余的二元比较，导致我们所谓的逻辑依赖性，例如，如果在一个块中 且 ，那么 必然成立，因此不需要 的二元变量。由于当前用于贝叶斯计算的马尔可夫链蒙特卡罗方法灵活且同时保证正确的小样本推断，我们研究了考虑随机和逻辑依赖性的瑟斯顿IRT模型的替代贝叶斯实现。我们通过分析表明，无论是否存在冗余二元比较，相同的参数都会使后验似然最大化。一项比较模拟显示，替代实现的计算量大幅减少，这是由于考虑了两种依赖性。因此，这项研究表明，在拟合瑟斯顿IRT模型时，应考虑所有依赖性。
