This study examined whether cutoffs in fit indices suggested for traditional formats with maximum likelihood estimators can be utilized to assess model fit and to test measurement invariance when a multiple group confirmatory factor analysis was employed for the Thurstonian item response theory (IRT) model. Regarding the performance of the evaluation criteria, detection of measurement non-invariance and Type I error rates were examined. The impact of measurement non-invariance on estimated scores in the Thurstonian IRT model was also examined through accuracy and efficiency in score estimation. The fit indices used for the evaluation of model fit performed well. Among six cutoffs for changes in model fit indices, only ΔCFI > .01 and ΔNCI > .02 detected metric non-invariance when the medium magnitude of non-invariance occurred and none of the cutoffs performed well to detect scalar non-invariance. Based on the generated sampling distributions of fit index differences, this study suggested ΔCFI > .001 and ΔNCI > .004 for scalar non-invariance and ΔCFI > .007 for metric non-invariance. Considering Type I error rate control and detection rates of measurement non-invariance, ΔCFI was recommended for measurement non-invariance tests for forced-choice format data. Challenges in measurement non-invariance tests in the Thurstonian IRT model were discussed along with the direction for future research to enhance the utility of forced-choice formats in test development for cross-cultural and international settings.

中文翻译：

---

Thurstonian IRT模型中的测量不变性检验的拟合指标。

这项研究检验了在Thurstonian项目响应理论（IRT）模型中采用多组确认因子分析时，是否可以利用建议的具有最大似然估计量的传统格式的拟合指数中的临界值来评估模型拟合和测试度量不变性。关于评估标准的性能，检查了测量不变性和I型错误率的检测。还通过分数估算的准确性和效率检查了测量不变性对Thurstonian IRT模型中估算分数的影响。用于评估模型拟合的拟合指数表现良好。在模型拟合指数变化的六个临界值中，只有ΔCFI> .01和ΔNCI>。当发生中等程度的不变性时，02检测到度量不变性，并且没有一个阈值可以很好地检测标量不变性。根据生成的拟合指数差异的采样分布，本研究建议标量不变性的ΔCFI> .001和ΔNCI> .004，而度量公制的ΔCFI> .007。考虑到I型错误率控制和测量不变性的检测率，建议将ΔCFI用于强制选择格式数据的测量不变性测试。讨论了Thurstonian IRT模型中测量不变性测试的挑战以及未来研究的方向，以增强强制选择格式在跨文化和国际环境下的测试开发中的效用。根据生成的拟合指数差异的采样分布，本研究建议标量不变性的ΔCFI> .001和ΔNCI> .004，而度量公制的ΔCFI> .007。考虑到I型错误率控制和测量不变性的检测率，建议将ΔCFI用于强制选择格式数据的测量不变性测试。讨论了Thurstonian IRT模型中测量不变性测试的挑战以及未来研究的方向，以增强强制选择格式在跨文化和国际环境下的测试开发中的效用。根据生成的拟合指数差异的采样分布，本研究建议标量不变性的ΔCFI> .001和ΔNCI> .004，而度量公制的ΔCFI> .007。考虑到I型错误率控制和测量不变性的检测率，建议将ΔCFI用于强制选择格式数据的测量不变性测试。讨论了Thurstonian IRT模型中测量不变性测试的挑战以及未来研究的方向，以增强强制选择格式在跨文化和国际环境下的测试开发中的效用。考虑到I型错误率控制和测量不变性的检测率，建议将ΔCFI用于强制选择格式数据的测量不变性测试。讨论了Thurstonian IRT模型中测量不变性测试的挑战以及未来研究的方向，以增强强制选择格式在跨文化和国际环境下的测试开发中的效用。考虑到I型错误率控制和测量不变性的检测率，建议将ΔCFI用于强制选择格式数据的测量不变性测试。讨论了Thurstonian IRT模型中测量不变性测试的挑战以及未来研究的方向，以增强强制选择格式在跨文化和国际环境下的测试开发中的效用。