Abstract: The value of diagnostic assessment lies in its ability to reveal each student’s specific cognitive strengths and weaknesses and further helps design effective interventions for individual student. Leighton et al.（2004） proposed a cognitive diagnostic model called Attribute Hierarchy Method (AHM), which is based on the assumption that test items can be described by a hierarchically-ordered set of attributes. Attributes are defined as basis cognitive processes or skills required to solve test items correctly. Examinees’ attribute pattern can be estimated by classifying each observed response pattern into one of the expected response patterns, which can be clearly explained by the presence or absence of the attributes without any errors or “slip”. So far, AHM was has only been introduced based on dichotomous IRT models, where items used in classroom assessments or performance assessments usually involve open-ended or constructed responses., and there is an assumption that an item can be answered correctly if and only if all the attributes involved in the item can be answered correctly. It means that missing one attribute is equivalent to missing all required attributes.
Since accurate diagnosis requires a rich description of examinee test performance, and polytomous models can give more information for score than the dichotomous model, an extension of AHM for based on a particular polytomous model ¾ graded response model (GRM), is proposed, and a new classification method is introduced in this paper. Four kinds of attribute hierarchies were separately used as the basis for the simulation. For each of the four attribute hierarchies, a sample of 5000 expected item response vectors was generated to approximate a normal distribution, Given that samples only consist of expected response patterns which are free from slips, the observed item response patterns were generated by randomly adding slips to each of the expected response patterns. In this study, the percentage of random errors was manipulated to be 2％, 5％,10％ and 15％, respectively, of the total number of item response in order to examine whether the percentage of random errors has an impact on the accuracy of classification methods. In order to generate 5％ random errors, for example, a uniform probability of 0.05 was employed to randomly add slips. For each item, if random number less than 0.025, then the score of item subtract 1 provided the original score is not zero; if random number higher than 0.925, then the score of the item adds 1 whenever the original score is not full. Ability parameters and item parameters can be estimated using ANOTE 1.60.
Simulation results showed that the classification rate for LL is only slightly better than that of Method A, but clearly outperforms that of Method B. In addition, polytomous extension of AHM is better than the polytomous extension of the Fusion Model proposed by Bolt et al.（2004）in terms of the classification accuracy and simplicity.

Key words: attribute hierarchy method, graded response model, logarithm likelihood ratio