This article proposes a class of cognitive diagnosis models (CDMs) for polytomously scored items with different link functions. Many existing polytomous CDMs can be considered as special cases of the proposed class of polytomous CDMs. Simulation studies were carried out to investigate the feasibility of the proposed CDMs and the performance of several information criteria (Akaike’s information criterion [AIC], consistent Akaike’s information criterion [CAIC], and Bayesian information criterion [BIC]) in model selection. The results showed that the parameters of the proposed CDMs could be recovered adequately under varied conditions. In addition, CAIC and BIC had better performance in selecting the most appropriate model than AIC. Finally, a set of real data was analyzed to illustrate the application of the proposed CDMs.

本文针对具有不同链接功能的多得分项目，提出了一类认知诊断模型（CDM）。许多现有的多角CDM可以视为提议的多角CDM类的特例。进行了仿真研究，以研究拟议CDM的可行性以及几种信息标准（Akaike信息标准[AIC]，一致的Akaike信息标准[CAIC]和贝叶斯信息标准[BIC]）的性能。结果表明，所提出的CDM的参数可以在各种条件下得到适当的恢复。此外，与AIC相比，CAIC和BIC在选择最合适的模型方面表现更好。最后，对一组真实数据进行了分析，以说明所提出的CDM的应用。