Diagnostic classification assessment (DCA) utilizes latent class models to provide fine-grained information about students’ strengths and weaknesses in the learning process. In the past decades, extensive research has been conducted in the area of DCA and many statistical models based on a probabilistic approach have been proposed. At present, several diagnostic classification models (DCMs) for dichotomous attributes exist, which include the deterministic inputs, noisy “and” gate (DINA; Junker & Sijtsma, 2001); the deterministic inputs, noisy “or” gate (DINO; Templin & Henson, 2006); and the linear logistic model (LLM; Maris, 1999). In contrast, only a few DCMs can be used to deal with the polytomous attributes, such as the model based on the ordered-category attribute coding (OCAC; Karelitz, 2004), and the polytomous generalized DINA (pG-DINA; Chen & de la Torre, 2013).
Polytomous attributes, particularly those defined as part of the test development process, can provide additional diagnostic information. The present research proposes three reparametrized reduced models of pG-DINA (Chen & de la Torre, 2013), which include the reparametrized polytomous attributes DINA (RPa-DINA), the reparametrized polytomous attributes DINO (RPa-DINO), and the reparametrized polytomous attributes LLM (RPa-LLM). Furthermore, to better understand the classification accuracy of the new models, the impact of 6 factors was investigated, namely, the number of polytomous attributes, the highest level of polytomous attributes, the correlations among polytomous attributes, the hierarchical structure, the sample size, and the number of items. Results of the simulation study indicated that:
(1) more polytomous attributes led to lower classification. Their effects, in descending order, were the RPa-LLM, the RPa-DINO, and the RPa-DINA. Less than 5 polytomous attributes used in empirical research is suggested;
(2) for the number of attribute levels, more levels resulted in worse performance. Less than 4 levels within one attribute used in empirical research is suggested;
(3) the higher the correlations among polytomous attributes, the higher the classification accuracy would be;
(4) different hierarchical structure had different influences on the classification accuracy. No matter what structure we had, the performance of RPa-DINA was quite well behaved. However, other 2 models, especially the RPa-DINO, were recommended for the analysis of response data from independent hierarchical structure;
(5) the sample size has little impact on the classification accuracy; and
(6) the number of items was inversely proportional to the classification accuracy.