Adjusting the Adjusted χ2/df Ratio Statistic for Dichotomous Item Response Theory Analyses
Adjusting the Adjusted χ2/df Ratio Statistic for Dichotomous Item Response Theory Analyses
复制标题
调整二分项目响应理论分析的调整后 χ2/df 比率统计量
DOI：
10.1177/0013164411416976
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发表时间：
2012
影响因子：
2.7
通讯作者：
F. Drasgow
中科院分区：
文献类型：
--
作者：
L. Tay;F. Drasgow
两项蒙特卡罗模拟研究考察了Drasgow及其同事提出的均值校正χ2/df统计量的有效性，并且由于该方法存在问题，开发了一种评估项目反应理论模型拟合优度的新方法。以前曾建议，使用交叉验证数据集，调整后的平均χ2/df值大于3表明存在严重的不匹配。作者使用模拟来检验不同测试长度（15,30,45）和样本量（500,1,000,1,500,5,000）的临界值。将单参数、二参数和三参数logistic模型拟合到不同logistic模型模拟的数据中，包括一维模型和多维模型。一般来说，固定的截止值不足以确定项目反应理论模型数据的拟合。因此，作者提出使用参数自举法来研究错拟合并评估其性能。这种新方法产生了适当的I型错误率，并且具有很大的能力来检测模拟条件下的不匹配。在第三项研究中，作者应用参数自举方法对LSAT数据进行分析，以确定哪种二同质项目反应理论模型产生最佳拟合。讨论了均值校正χ2/df统计量的未来应用。
Two Monte Carlo simulation studies investigated the effectiveness of the mean adjusted χ2/df statistic proposed by Drasgow and colleagues and, because of problems with the method, a new approach for assessing the goodness of fit of an item response theory model was developed. It has been previously recommended that mean adjusted χ2/df values greater than 3 using a cross-validation data set indicate substantial misfit. The authors used simulations to examine this critical value across different test lengths (15, 30, 45) and sample sizes (500, 1,000, 1,500, 5,000). The one-, two- and three-parameter logistic models were fitted to data simulated from different logistic models, including unidimensional and multidimensional models. In general, a fixed cutoff value was insufficient to ascertain item response theory model–data fit. Consequently, the authors propose the use of the parametric bootstrap to investigate misfit and evaluated its performance. This new approach produced appropriate Type I error rates and had substantial power to detect misfit across simulated conditions. In a third study, the authors applied the parametric bootstrap approach to LSAT data to determine which dichomotous item response theory model produced the best fit. Future applications of the mean adjusted χ2/df statistic are discussed.