Department Erziehungs- und Sozialwissenschaften, University of Cologne, Germany, Gronewaldstr. 2a, 50931, Cologne, Deutschland.
Psychometrika. 2022 Dec;87(4):1214-1237. doi: 10.1007/s11336-022-09841-1. Epub 2022 Feb 5.
Many of the models that have been proposed for response data share the assumptions that define the monotone homogeneity (MH) model. Observable properties that are implied by the MH model allow for these assumptions to be tested. For binary response data, the most restrictive of these properties is called conditional association (CA). All the other properties considered can be considered incomplete tests of CA that alleviate the practical limitations encountered when assessing the MH model assumptions using CA. It is found that the assessment of the MH model assumptions with an incomplete test of CA, rather than CA, is generally associated with a substantial loss of information. We also look at the sensitivity of the observable properties to model violation and discuss the implications of the results. It is argued that more research is required about the extent to which the assumptions and the model specifications influence the inferences made from response data.
许多用于响应数据的模型都共享定义单调同质性 (MH) 模型的假设。MH 模型所隐含的可观察属性允许对这些假设进行检验。对于二项响应数据，这些属性中最严格的称为条件关联 (CA)。其他所有被认为是 CA 的不完全检验的属性都可以缓解在使用 CA 评估 MH 模型假设时遇到的实际限制。结果发现，使用 CA 的不完全检验而不是 CA 来评估 MH 模型假设通常会导致大量信息丢失。我们还研究了可观察属性对模型违反的敏感性，并讨论了结果的含义。有人认为，需要进一步研究假设和模型规格在多大程度上影响从响应数据中得出的推论。
