重参数化多分属性DINA模型的多级评分拓广——基于等级反应模型

多分属性认知诊断模型（CDMs）比传统的二分属性CDMs提供更详细的诊断反馈信息，但现有大部分多分属性CDMs并不具备直接分析多级（或混合）评分数据的功能。本文基于等级反应模型对重参数化多分属性DINA模型进行多级评分拓广，开发一个可处理多级评分数据的等级反应多分属性DINA模型。首先通过实证数据分析呈现新模型的现实可应用性；然后通过模拟研究探究新模型的参数估计返真性。结果表明，新模型满足同时处理多分属性和多级评分数据的现实需求；且具备良好的心理计量学性能，但对测验质量有一定要求（如题目质量较高且测验Qp矩阵具有完备性等）。

A Graded Response Extension of the Reparametrized Polytomous Attributes DINA Model

Many cognitive diagnostic models (CDMs) have been developed in the last few decades, but almost all of them are only adaptive for dichotomous items and/or dichotomous attributes. To make the CDMs better applicable to the actual educational situation, researchers have developed several CDMs for polytomous scoring data and several CDMs for polytomous attributes, respectively. However, there is still a lack of models that can deal with polytomous attributes and polytomous scoring data simultaneously. To this end, a graded response extension of the reparametrized polytomous attributes DINA (GRPa-DINA) model was proposed in this study, which can be treated as a combination of the reparametrized polytomous attributes DINA model (Zhan, Bian, & Wang, 2016) and the polytomous-DINA model (Tu, Cai, Dai, & Ding, 2010). Model parameters in the GRPa-DINA can be estimated via the full Bayesian approach with the Markov chain Monte Carlo (MCMC) method.Firstly, an empirical example was conducted to emphasize the practical value of the proposed model. A math test for the linear equation with one unknown was used and refurbished from binary attributes to polytomous attributes. The data contains the responses of 255 participants to 25 mixed-scoring items, in which, items 1 to 18 are dichotomous, and items 19 to 25 are polytomous items with four categories. An empirical polytomous Q matrix was constructed by several experts. The GRPa-DINA was used to fit the data. The results indicated that (1) the proposed model can be used for empirical data analysis and can provide an estimate of polytomous attribute patterns at the individual level; (2) the overall quality of the test was good, but the slip parameter for some items is high, which may indicate that the current polytomous Q matrix either omits some required attributes or specifies some required attributes at a lower level.Secondly, two simulation studies were conducted to further explore the psychometric characteristics of the proposed model. In the simulation study 1, the polytomous Q matrix in the empirical example was still used, and the estimates of item parameters in the empirical example were treated as the true values of item parameters to generate data. Besides, the sample size in the simulation study 1 was also consistent with that in the empirical example. The results indicated that the recovery of item parameters is good; although the classification accuracy rate of polytomous attributes is low, it is in line with previous research results. One of the main reasons is that the employed polytomous Q matrix is incomplete because of the lack of a polytomous reachability matrix. In the simulation study 2, the performance of the proposed model in an ideal test condition was further explored. A complete polytomous Q matrix with 30 items and 4 attributes were constructed. Two factors were manipulated: the sample size of 500 and 1000, and the item quality of higher and lower. The results indicated that (1) all model parameters can be well recovered; (2) increasing sample size leads to better recovery of item parameters and increasing item quality leads to better recovery of attributes.Overall, the proposed model works well in empirical data analysis and simulation studies and also meets the need for simultaneously analyzing polytomous scoring data and polytomous attributes. However, to ensure the accuracy of model parameter estimation, more and higher quality items and a complete polytomous Q matrix are necessary.