Multidimensional item response theory (MIRT) is a statistical test theory that precisely estimates multiple latent skills of learners from the responses in a test. Both compensatory and non-compensatory models have been proposed for MIRT: the former assumes that each skill can complement other skills, whereas the latter assumes they cannot. This non-compensatory assumption is convincing in many tests that measure multiple skills; therefore, applying non-compensatory models to such data is crucial for achieving unbiased and accurate estimation. In contrast to tests, latent skills will change over time in daily learning. To monitor the growth of skills, dynamical extensions of MIRT models have been investigated. However, most of them assumed compensatory models, and a model that can reproduce continuous latent states of skills under the non-compensatory assumption has not been proposed thus far. To enable accurate skill tracing under the non-compensatory assumption, we propose a dynamical extension of non-compensatory MIRT models by combining a linear dynamical system and a non-compensatory model. This results in a complicated posterior of skills, which we approximate with a Gaussian distribution by minimizing the Kullback–Leibler divergence between the approximated posterior and the true posterior. The learning algorithm for the model parameters is derived through Monte Carlo expectation maximization. Simulation studies verify that the proposed method is able to reproduce latent skills accurately, whereas the dynamical compensatory model suffers from significant underestimation errors. Furthermore, experiments on an actual data set demonstrate that our dynamical non-compensatory model can infer practical skill tracing and clarify differences in skill tracing between non-compensatory and compensatory models.

多维项目反应理论 (MIRT) 是一种统计测试理论，可根据测试中的反应精确估计学习者的多项潜在技能。已经为 MIRT 提出了补偿性和非补偿性模型：前者假设每项技能可以补充其他技能，而后者假设它们不能。在许多衡量多种技能的测试中，这种非补偿假设是有说服力的；因此，将非补偿模型应用于此类数据对于实现无偏见和准确的估计至关重要。与测试相反，潜在技能会在日常学习中随时间发生变化。为了监测技能的增长，研究了 MIRT 模型的动态扩展。然而，他们中的大多数人都采用了补偿模型，到目前为止，还没有提出在非补偿假设下可以再现技能连续潜在状态的模型。为了在非补偿性假设下实现准确的技能追踪，我们提出了通过结合线性动力系统和非补偿性模型来动态扩展非补偿性 MIRT 模型。这导致了复杂的技能后验，我们通过最小化近似后验和真实后验之间的 Kullback-Leibler 散度来近似高斯分布。模型参数的学习算法是通过蒙特卡洛期望最大化推导出来的。仿真研究证实，所提出的方法能够准确地重现潜在技能，而动态补偿模型存在严重的低估错误。此外，