Many educational testing programs require different test forms with minimal or no item overlap. At the same time, the test forms should be parallel in terms of their statistical and content-related properties. A well-established method to assemble parallel test forms is to apply combinatorial optimization using mixed-integer linear programming (MILP). Using this approach, in the unidimensional case, Fisher information (FI) is commonly used as the statistical target to obtain parallelism. In the multidimensional case, however, FI is a multidimensional matrix, which complicates its use as a statistical target. Previous research addressing this problem focused on item selection criteria for multidimensional computerized adaptive testing (MCAT). Yet these selection criteria are not directly transferable to the assembly of linear parallel test forms. To bridge this gap the authors derive different statistical targets, based on either FI or the Kullback–Leibler (KL) divergence, that can be applied in MILP models to assemble multidimensional parallel test forms. Using simulated item pools and an item pool based on empirical items, the proposed statistical targets are compared and evaluated. Promising results with respect to the KL-based statistical targets are presented and discussed.

中文翻译：

---

使用混合整数线性规划的多维测试程序集：Kullback–Leibler信息的应用

许多教育性测试计划要求使用不同的测试形式，且项目重叠最少或没有。同时，测试表格的统计和内容相关属性应平行。组装并行测试表格的公认方法是使用混合整数线性规划（MILP）进行组合优化。使用这种方法，在一维情况下，通常将Fisher信息（FI）用作获得并行性的统计目标。但是，在多维情况下，FI是多维矩阵，这使它作为统计目标的使用变得复杂。先前针对此问题的研究集中在多维计算机自适应测试（MCAT）的项目选择标准上。然而，这些选择标准不能直接转移到线性平行测试表格的组装中。为了弥合这一差距，作者基于FI或Kullback-Leibler（KL）差异得出了不同的统计目标，这些统计目标可用于MILP模型中以组装多维并行测试表格。使用模拟项目库和基于经验项目的项目库，比较和评估建议的统计目标。提出并讨论了有关基于KL的统计目标的有希望的结果。