Item response theory (IRT) is a statistical paradigm for developingeducational tests and assessing students. IRT, however, currentlylacks an established graphical method for examining model fit for thethree-parameter logistic model, the most flexible and popular IRTmodel in educational testing. A method is presented here to do this.The graph, which is referred to herein as a “bin plot,” is the IRTequivalent of a scatterplot for linear regression. Bin plots display aconventional IRT trace line (with ability on the horizontal axis andprobability correct on the vertical axis). Students are binnedaccording to how well they performed on the entire test, and theproportion of students in each bin who answered the focal questioncorrectly is displayed on the graph as points above or below the traceline. With this arrangement, the difference between each point and thetrace line is the residual for the bin. Confidence intervals can beadded to the observed proportions in order to display uncertainty.Computer simulations were used to test four alternative ways forbinning students. These simulations showed that binning studentsaccording to number of questions they answered correctly on the entiretest works best. Simulations also showed confidence intervals for binplots had coverage probabilities close to nominal values for commontesting scenarios, but that there are scenarios in which confidenceintervals had inflated error rates.
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机译：项目响应理论（IRT）是一个统计的开发范式教育测试和评估学生。然而，IRT目前缺乏用于检查模型适合的既定图形方法三参数逻辑模型，最灵活和最受欢迎的IRT教育测试模型。此处提出了一种方法来执行此操作。在此称为“bin图”的图表是IRT相当于线性回归的散点图。 bin plots显示一个传统的IRT跟踪线（水平轴上的能力和垂直轴上的概率正确）。学生们根据他们在整个测试中进行的程度，以及每个垃圾箱的学生比例谁回答了焦点问题正确地显示在迹线上方或下方的图表上线。通过这种安排，每个点与每个点之间的差异跟踪线是垃圾箱的残余。置信区间可以是添加到观察到的比例以显示不确定性。计算机模拟用于测试四种替代方式分宁学生。这些模拟显示啤酒学生根据他们在整个问题上正确回答的问题数量测试最佳。模拟也为垃圾箱显示了置信区间图具有覆盖概率，接近常见的标称值测试场景，但有有信心的情景间隔有膨胀的误差率。
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