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A Generalized Speed-Accuracy Response Model for Dichotomous Items

机译：二分法的广义速度准确响应模型

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摘要

We propose a generalization of the speed-accuracy response model (SARM) introduced by Maris and van der Maas (Psychometrika 77:615-633, 2012). In these models, the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled. Our generalization is similar to that of the one-parameter logistic (or Rasch) model to the two-parameter logistic (or Birnbaum) model in item response theory. An expectation-maximization (EM) algorithm for estimating model parameters and standard errors was developed. Furthermore, methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score. The presented methods were evaluated in a small simulation study, the results of which indicated good parameter recovery and reasonable type I error rates for the residuals. Finally, the methods were applied to two real data sets. It was found that the two-parameter SARM showed improved fit compared to the one-parameter SARM in both data sets.
机译：我们对Maris和van der Maas（Psychometrika 77:615-633，2012）提出的速度-精度响应模型（SARM）进行了推广。在这些模型中，由评分规则得出的分数被建模，该评分规则综合了项目响应的速度和准确性。我们的推广类似于项目反应理论中的单参数logistic（或Rasch）模型和双参数logistic（或Birnbaum）模型。提出了一种估计模型参数和标准误差的期望最大化（EM）算法。此外，以项目得分函数的广义残差和总得分密度的鞍点近似的形式提供了评估模型拟合的方法。在一项小型模拟研究中对提出的方法进行了评估，结果表明，参数恢复良好，残差的I型错误率合理。最后，将这些方法应用于两个实际数据集。结果发现，在两个数据集中，与单参数SARM相比，双参数SARM显示出更好的拟合。

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