The Development Of Q-matrix Estimation Method For Cognitive Diagnosis Test

Nowadays,we are not satisfied with a total score from measurement,but hope to get a informative report.As the core of new generation test theory,cognitive diagnosis(CD)attracts more and more people's attention.Since it can reveal the result form a microscopic perspective,such as individuals' knowledge structures,processing skills and cognitive procedure etc,it would help us to take individualized teaching and promote students ' development.Cognitive diagnosis assessments infer the attribute mastery pattern of respondents by item responses based on Q-matrix.The Q-matrix plays the role of a bridge between items and respondents.Many studies have shown that misspecification of the Q-matrix can affect the accuracy of model parameters and result in the misclassification of respondents.In practice,Q_matrix is established by experts.However,with the application of cognitive diagnosis,more and more researchers found that specification of Q-matrix was very hard.Different experts may provided different Q_matrices.To avoid the subjectivity from experts in Q-matrix specification and ensure the correct of Q_matrix,researchers are trying to look for objective methods.Many researchers have found a number of methods to estimate and validate the Q_matrix.Nevertheless,existing methods need information from parameter and a large amount of computation.To simplify the method of Q-matrix estimation,this article introduces two new Q-matrix estimation methods based on Hamming Distance(HD)and ICC(Item Consistency Criterion).The process of the HD method as follow: Firstly,we infer the attribute mastery pattern of respondents by Hamming Distance.Secondly,we can establish a Expected Response Pattern(ERP)matrix by the relationship between attribute mastery pattern of all respondents and each measurement pattern.Finally,the method measures the distance between all respondents' Observed Response Pattern(ORP)and Expected Response Pattern(ERP)in each measurement pattern,and choose a measurement pattern with the minimum Hamming Distance to items.In this way,we can infer the measurement pattern of items.When there are more than one measurement patterns which are the same minimum Hamming Distance,we take random choose.This method based on some items which were assumed correctly pre-specified.If the measurement pattern of the item A is a subset of the item B.The logic of the ICC method is that it is impossible a person get “0” score on item A,but get “1”on item B.Of course,if item A and item B have same measurement pattern.It is impossible that a person get “1”score on item A,but get “0”on item B(or,the other way around).From this logic we come up with Item Consistency Criterion.In order to improve the effect of ICC method,we come up with ICC-IR method.In order to explore the effect of two methods,we considered different number of participants,different number of base items and different Q-matrix whose attribute number is different.The item parameters and attribute mastery pattern of respondents are obeyed a uniform distribution.The Monte Carlo simulation study and real data study showed that: generally,the Hamming Distance method and ICC-IR method can recover the real Q-matrix with a highrate of success.Relative to the sample size,the number of base items is more important.Furthermore,the two methods are easier to understand and needs less computation.For example,the time taken by program is not more than 30 second under 3 attributes and 8base items condition.The real data study also showed that the Hamming Distance method can estimate the Q_matrix with a high success rate.The results of this study demonstrate that those two methods are easy and preferable methods in Q-matrix Estimation.Compared to the existing methods,those two methods are faster and superior.Besides,without the needs of parameters estimation,those two methods are not affected by the deviation caused by the misfit between model and data.In a word,those two methods are simple and effective in Q-matrix Estimation,what is meaningful to the simplification of cognitive diagnosis.