标题： 将非补偿性误认为补偿性IRT：估计技能和方差的分析 显示英文标题

标题： Misspecifying non-compensatory as compensatory IRT: analysis of estimated skills and variance

摘要： 多维项目反应理论是一种统计测试理论，用于根据测试结果估计学习者的潜在技能和问题的难度水平。 文献中已经提出了补偿模型和非补偿模型。 先前的研究表明，当非补偿模型被错误指定为补偿模型时，会显著低估较高技能。 然而，这一现象背后的机制尚未完全阐明。 尚不清楚是否也会发生高估，并且关于估计参数的方差是否存在相关问题仍不明确。 在本文中，我们旨在通过理论方法全面理解高估和低估现象。 除了之前发现的技能低估之外，我们新发现技能高估发生在原点附近。 此外，我们研究了在考虑模型误设的情况下，估计参数的渐近方差与未考虑模型误设时的差异程度。 显示英文摘要

摘要： Multidimensional item response theory is a statistical test theory used to estimate the latent skills of learners and the difficulty levels of problems based on test results. Both compensatory and non-compensatory models have been proposed in the literature. Previous studies have revealed the substantial underestimation of higher skills when the non-compensatory model is misspecified as the compensatory model. However, the underlying mechanism behind this phenomenon has not been fully elucidated. It remains unclear whether overestimation also occurs and whether issues arise regarding the variance of the estimated parameters. In this paper, we aim to provide a comprehensive understanding of both underestimation and overestimation through a theoretical approach. In addition to the previously identified underestimation of the skills, we newly discover that the overestimation of skills occurs around the origin. Furthermore, we investigate the extent to which the asymptotic variance of the estimated parameters differs when considering model misspecification compared to when it is not taken into account.