Fernández Daniel, Liu Ivy, Arnold Richard, Nguyen Thuong, Spiess Martin
Institut de Recerca Sant Joan de Déu, Parc Sanitari Sant Joan de Déu, CIBERSAM, Barcelona, Spain.
School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand.
Stat Methods Med Res. 2020 Jun;29(6):1527-1541. doi: 10.1177/0962280219864708. Epub 2019 Jul 30.
This paper presents two new model-based goodness-of-fit tests for the ordered stereotype model applied to an ordinal response variable. The proposed tests are based on the Lipsitz test, which partitions the subjects into groups following the popular Hosmer-Lemeshow test for binary data. The tests construct an alternative model where group effects are added into the null model. If the model fits the data well then the null model is correct, and there should be no group effects. One of the main advantages of the ordered stereotype model is that it allows us to determine a new uneven spacing of the ordinal response categories, dictated by the data. The two proposed tests use this new adjusted spacing. One test uses the form of the original ordered stereotype model, and the other uses an ordinary linear model. We demonstrate the performance of both tests under a variety of scenarios. Finally, the results of the application in three examples are presented.
本文针对应用于有序响应变量的有序刻板印象模型，提出了两种基于模型的新拟合优度检验。所提出的检验基于利普西茨检验，该检验按照针对二元数据的常用霍斯默 - 莱梅肖检验将受试者分成组。这些检验构建了一个替代模型，其中在原假设模型中加入了组效应。如果模型对数据拟合良好，那么原假设模型就是正确的，并且不应存在组效应。有序刻板印象模型的一个主要优点是它使我们能够根据数据确定有序响应类别新的不均匀间距。所提出的两种检验使用了这种新的调整间距。一种检验使用原始有序刻板印象模型的形式，另一种检验使用普通线性模型。我们展示了两种检验在各种情况下的性能。最后，给出了在三个例子中的应用结果。
