误用补偿模型会低估高技能者，还可能在原点附近高估技能。
Misspecifying non-compensatory as compensatory IRT: analysis of estimated skills and variance
- 通过理论分析揭示非补偿模型误设为补偿模型的机制。
- 发现高技能者被严重低估，且原点附近存在技能高估现象。
- 首次系统分析参数估计方差在模型误设下的变化情况。
多维项目反应理论是一种基于测试结果来估计学习者潜在能力与题目难度的统计模型。文献中提出了补偿与非补偿两种模型。以往研究发现，当非补偿模型被误设为补偿模型时，高技能者的技能估计会出现显著低估。然而，这一现象背后的机制尚未完全阐明，也未明确是否存在高估问题以及参数估计方差是否受影响。本文通过理论方法，全面探讨模型误设带来的低估与高估效应。除已知的高技能者低估外，我们新发现：在原点附近存在技能高估现象。此外，我们进一步分析了模型误设情况下估计参数的渐近方差与正确建模时的差异，揭示了误设对估计精度的影响。
原文摘要 · Abstract (English)
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.
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