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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.

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. [ABSTRACT FROM AUTHOR]

This study compared several parameter estimation methods for multi-unidimensional graded response models using their corresponding statistical software programs and packages. Specifically, we compared two marginal maximum likelihood (MML) approaches (Bock-Aitkin expectation-maximum algorithm, adaptive quadrature approach), four fully Bayesian algorithms (Gibbs sampling, Metropolis-Hastings, Hastings-within-Gibbs, blocked Metropolis), and the Metropolis-Hastings Robbins-Monro (MHRM) algorithm via the use of IRTPRO, BMIRT, and MATLAB. Simulation results suggested that, when the intertrait correlation was low, these estimation methods provided similar results. However, if the dimensions were moderately or highly correlated, Hastings-within-Gibbs had an overall better parameter recovery of item discrimination and intertrait correlation parameters. The performances of these estimation methods with different sample sizes and test lengths are also discussed. [ABSTRACT FROM AUTHOR]