Limited-information fit measures appear to be promising in assessing the goodness-of-fit of dichotomous response cognitive diagnosis models (CDMs), but their performance has not been examined for polytomous response CDMs. This study investigates the performance of the Mord statistic and standardized root mean square residual (SRMSR) for an ordinal response CDM—the sequential generalized deterministic inputs, noisy “and” gate model. Simulation studies showed that the Mord statistic had well-calibrated Type I error rates, but the correct detection rates were influenced by various factors such as item quality, sample size, and the number of response categories. In addition, the SRMSR was also influenced by many factors and the common practice of comparing the SRMSR against a prespecified cut-off (e.g., .05) may not be appropriate. A set of real data was analyzed as well to illustrate the use of Mord statistic and SRMSR in practice.

中文翻译：

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使用有限信息量度评估顺序G-DINA模型的拟合度。

信息量有限的拟合方法在评估二分反应认知诊断模型（CDM）的拟合优度方面似乎很有希望，但是尚未对多反应CDM的性能进行检验。本研究调查了序数响应CDM（顺序广义确定性输入，噪声“和”门模型）的Mord统计量和标准化均方根（SRMSR）的性能。仿真研究表明，Mord统计信息的I型错误率得到了很好的校准，但是正确的检出率受各种因素的影响，例如物品质量，样本量和响应类别的数量。此外，SRMSR还受到许多因素的影响，将SRMSR与预先设定的临界值（例如.05）进行比较的常用做法可能不合适。