A Nonparametric Approach Of Q-Matrix Modification For Polytomous Situations

With the development of educational examination reform at home and abroad,the diagnostic function of educational examination has been paid more and more attention.In this context,the cognitive diagnostic assessment to assess the cognitive structure of students has been constantly mentioned,and related studies have become increasingly prominent,among which "Q matrix definition" is an important branch of research.At present,there are few researches on the definition of Q matrix in the multi-grade scoring situation,and the existing correction methods of Q matrix are all parametric methods.The parametric method requires a large sample size and a long running time,which is not consistent with the current situation of small sample size and limited time in daily teaching.The non-parametric method can meet the above practical requirements,so it is more reasonable to propose the non-parametric method of Q matrix correction under the multi-grade scoring situation.Therefore,this study intends to develop Q-matrix correction for multi-grade Scoring situations using Scoring by Attributive-Manhattan Distance(SA-MD)and Scoring by Attribution-Polytomous Item Consistency Criterion(SA-PICC).This paper is divided into three studies: Study 1 analyzes the change of subjects' scores in the multi-grade scoring situation when Q matrix is defined incorrectly,and constructs two Q matrix correction methods of SA-MD and SA-PICC.In study 2,through simulation study,the modification effects of the two methods under a variety of factors were discussed,including: state distribution of subjects' knowledge,sample size,number of test attributes,error rate of Q matrix,and average number of item attributes.The study 3 uses empirical data to further verify the validity of the two methods in the empirical study.The main conclusions of this study are as follows:(1)It is feasible to construct PICC index reasonably.In theory,MD and PICC can be used to modify Q matrix of multi-grade scoring.(2)In a variety of situations,SA-MD has better correction effect;When the average number of attributes is small,SA-PICC has better correction effect;SA-MD is more robust than SA-PICC.(3)SA-MD and SA-PICC are feasible and necessary in practice.(4)when the average number of attributes of the item is small,EDD should be avoided to distinguish the mastery mode of the subjects.EDD will reduce the accuracy of the subjects.