Allowance for multiple chances to answer constructed response questions is a prevalent feature in computer‐based homework and exams. We consider the use of item response theory in the estimation of item characteristics and student ability when multiple attempts are allowed but no explicit penalty is deducted for extra tries. This is common practice in online formative assessments, where the number of attempts is often unlimited. In these environments, some students may not always answer‐until‐correct, but may rather terminate a response process after one or more incorrect tries. We contrast the cases of graded and sequential item response models, both unidimensional models which do not explicitly account for factors other than ability. These approaches differ not only in terms of log‐odds assumptions but, importantly, in terms of handling incomplete data. We explore the consequences of model misspecification through a simulation study and with four online homework data sets. Our results suggest that model selection is insensitive for complete data, but quite sensitive to whether missing responses are regarded as informative (of inability) or not (e.g., missing at random). Under realistic conditions, a sequential model with similar parametric degrees of freedom to a graded model can account for more response patterns and outperforms the latter in terms of model fit.

中文翻译：

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数据不完整的多次尝试的项目响应模型

在基于计算机的家庭作业和考试中，普遍存在的机会是可以回答构造好的回答问题。当允许多次尝试但未扣除额外尝试的明确惩罚时，我们考虑使用项目反应理论来估计项目特征和学生能力。这是在线形成评估中的常见做法，其中尝试次数通常是无限的。在这种环境下，某些学生可能不一定总是回答正确，而是可能在一次或多次不正确的尝试后终止回答过程。我们对比了分级和顺序项目响应模型的情况，这两种都是一维模型，它们没有明确考虑能力以外的因素。这些方法不仅在对数奇数假设方面有所不同，而且重要的是，在处理不完整数据方面。我们通过模拟研究和四个在线作业数据集来探索模型错误指定的后果。我们的结果表明，模型选择对完整数据不敏感，但是对于是否将缺失的响应视为信息性（无能力）（例如，随机缺失）相当敏感。在实际条件下，参数自由度与渐变模型相似的顺序模型可以说明更多的响应模式，并且在模型拟合方面优于后者。但是对于是否将缺失的响应视为（无能力的）信息（例如，随机缺失）非常敏感。在实际条件下，参数自由度与渐变模型相似的顺序模型可以说明更多的响应模式，并且在模型拟合方面优于后者。但是对于是否将缺失的响应视为（无能力的）信息（例如，随机缺失）非常敏感。在实际条件下，参数自由度与渐变模型相似的顺序模型可以说明更多的响应模式，并且在模型拟合方面优于后者。