Abstract: Abstract Cognitive Diagnostic Assessment models has defined attributes as binary until Karelitz (2004) proposed an Ordered Category Attribute Coding (OCAC) framework. This approach assumes that there are Mk steps before an examinee mastering the highest level of a polytomous attribute. It can provide more diagnostic information for researchers. Karelitz (2004) and Peida Zhan, Yufang Bian and Lijun Wang (2016) suppose that a polytomous attribute’s (Lk+1) levels similar to Lk binary attributes which partly satisfied linear hierarchy. The purpose of this study is to prove the relationship between them by comparing the estimation accuracies of the polytomous attribute model and the binary attribute model. In this study, Pa-DINA was chosen to represent the polytomous attribute model, and DINA was chosen to represent polytomous attribute model. The independent variables are: sample size(500/1000), test length(30/50), the number of polytomous attribute(3/5), the highest level of polytomous attribute(2/3). Therefore, there are 16(2×2×2×2) experimental conditions. The dependent variables are: estimation accuracies of attribute parameters (ACCR and PCCR) and noise parameters (bias and RMSE). The steps of this study are as follows: 1) produced a group of data by Pa-DINA with R under every experimental conditions; 2) used the data and Pa-DINA to estimate the parameters of polytomous attribute model; 3) converted polytomous attributes into binary attributes; 4) used the same group of data and DINA to estimate the parameters of binary attribute model; 5) computed Pa-DINA and DINA’s estimation accuracies (ACCR and PCCR); 6) compared Pa-DINA and DINA’s estimation accuracies separately. The results indicate that: 1) The attribute parameters’ estimation accuracies of two models are about equal when the number of polytomous attribute is no more than 3. 2) The attribute parameters’ estimation accuracies of two models tend to be unequal when the number of polytomous attributes is increased to 5. 3) Among all independent variables, only when the number of polytomous attribute grows from 3 to 5, the decrement of attribute parameters’ estimation accuracies of Pa-DINA are smaller than DINA’s, and the decrement of PCCR is remarkably bigger than the decrement of ACCR. 4) In Pa-DINA , the estimation accuracy of si is lower than gi which is about equal to the high estimation accuracies of two noise parameters in DINA. This study proves that, to some extent, the relationship between polytomous attribute and binary attribute is as mentioned above indeed. And they are more dissimilar with the increasing of the number of polytomous attribute. In the field of education and psychometrics, researchers are suggested to use polytomous attribute model to estimate parameters directly if experts believe it is unnecessary to convert polytomous attributes into binary attributes in a study. In order to get more accurate results when data analysts have no alternative but to transform polytomous attributes into binary attributes, this study suggests giving priority to Zhan’s thought of equivalent conversion.

Key words: Cognitive Diagnostic, CDMs, Polytomous Attribute, Attribute Hierarchy, DINA

摘要： 摘 要：Karelitz（2004）和詹沛达等（2016）认为1个多分属性内部(Lk+1)个水平的关系相当于Lk个部分满足线型层级关系的二分属性。本研究的目的是通过比较多分属性模型和二分属性模型的判准率，从而验证多分属性和二分属性间是否存在以上关系。结果表明：当属性个数较少时，两个模型的模式判准率相当，随着属性个数增加，多分属性模型的模式判准率高于二分属性模型的模式判准率。结论：在一定程度上，多分属性和二分属性之间确实存在以上关系，但两者并非完全等价，二者间的差异随着属性个数增加更加明显。

关键词: 认知诊断, 认知诊断模型, 多分属性, 属性层级, DINA