Abstract
Although considerable developments have been added to the cognitive diagnosis modeling literature recently, most have been conducted for dichotomous responses only. This research proposes a general cognitive diagnosis model for polytomous responses—the general polytomous diagnosis model (GPDM), which combines the G-DINA modeling process for dichotomous responses with the item-splitting process for polytomous responses. The polytomous items are specified similar to dichotomous items in the Q-matrix, and the MML estimation is implemented using an EM algorithm. Under the general framework, different saturated forms, and some reduced forms, can be transformed linearly. Model assessment and adjustment under the dichotomous context can be extended to polytomous responses. This simulation study demonstrates the effectiveness of the model when comparing the two response types. The real-data example further illustrates how the proposed model can make a difference in practice.
Highlights
Cognitive diagnosis models (CDMs) have received increasing attention in educational and psychological measurement
The findings reflected the loss of diagnostic information by treating the polytomous responses as dichotomous under the settings used in this study
Considerable developments have been added to the CDM literature recently, most have been conducted for dichotomous responses only
Summary
Cognitive diagnosis models (CDMs) have received increasing attention in educational and psychological measurement. Considerable developments had been added to the CDM literature. In terms of model assessment, various methods or procedures are provided for Q-matrix validation or more general model misfit (e.g., de la Torre, 2008; Chen et al, 2013; Chiu, 2013; de la Torre and Chiu, 2015; Chen, 2017). With these developments, one can find a growing number of CDM applications across different educational and psychological areas. CDM-based measurement can be found in topics such as math (Tatsuoka, 1990), reading (Jang, 2009; Chen and Chen, 2015, 2016), psychological disorder (Templin and Henson, 2006), and situational judgment (García et al, 2014)
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