| Cognitive diagnosis is of widespread concern by the researchers because it can reveal each student’s specific cognitive strengths and weaknesses and further help design effective interventions for individual students. As the core of a new generation of test theory, cognitive diagnosis already has rich research results. To obtain more information on the examinees, cognitive model and test identification of Q matrix is one of the most basic and most critical parts, but the results on how to amend Q matrix and cognitive model are still very limited. Q matrix should represent cognitive model accurately. To define the cognitive model or the equivalent to determine Q matrix, of course, need for expert knowledge, but it is not enough, also need to make inferred and refinement through the observed response data. Therefore, the granular computing and formal concept analysis is introduced in this study, through the refinement and generalization of the attribute to modify the expert cognitive model and Q matrix.To determine a cognitive model and test Q matrix(briefly, Qt) whether be amended, this article complements the existing theory of attribute structure evaluation, supplements the definition of HCI and expands a new person-fit index NHCI, and carries out simulation experiments to compare these two indices of performance in different situations. In order to discover frequent patterns more effectively, this thesis uses NHCI to delete abnormal examinees of different numeration representation system converting diagnostic test. It also employs the concept lattice to represent the relationship among the examinee, item and attribute. On this basis, in order to fix the Q matrix and cognitive models of different numeration representation system converting diagnostic test, the attributes of the diagnostic test are refined and generalized, and association rules between attributes are derived in this thesis.In summary, the results of this thesis indicate:(1)With the research of person-fit index in diagnostic test, the first step should be investigate Qt matrix, to check whether the arrangement is reasonable, whether it contains reachability matrix (R matrix). Only that the R matrix to be derived from Qt is a sufficient. If Qt is not inspected first, the entire test may be invalid. Even if the person-fit index of the test substantially high, it can not ensure that the response of examinee is consistent with attribute structure, because Qt does not provide the platform for all examinees to show their true states of knowledge. The study of the HCI index conducted by Cui and Leighton (2009) did not pay attention to this point. Therefore, the investigation of the Q matrix is the first and most basic fundamental step to use person-fit work in cognitive diagnosis. And simulation experiment 1 shows that the higher theoretic construct validity of Q matrix, the lower of the examinees misfit level. So, before the model evaluation, inspection of the theoretic construct validity of this test is necessary. And for discrete structures, the difference between NHCI minus HCI (briefly d) rises with theoretic construct validity declines, which imply that the combination of the old and the new indicators is valuable. This paper makes mathematical definition well for some imperfections on the definition of HCI, to avoid to certain examinees can not be calculated on the value of HCI.HCI count one kind of misfit and neglect another kind of misfit degree, so the extension HCI index is proposed to consider a more comprehensive index, named as NHCI.(2) To compare the detection capabilities of HCI and NHCI, we follow Cui and Leighton (2009) conducte a simulation method 2. The results show that HCI and NHCI have their own advantages. For the creative misfit, NHCI is better than the HCI; for the random misfit, HCI holds an advantage; for the model misfit, in the case of high discrimination, HCI is better, in the case of high discrimination, NHCI performance better.(3)HCI can provide the examinees misfit degree with hierarchical structure. However, the reasons of misfit is unclear, it lacks of specific point. This is largely due to the indicator having not provided the possibility an examinee belongs to a specific attributes mode. With this in mind, with combination of HCI, NHCI and pattern classification, the values of HCI and NHCI are calculated and analyzed for each mode. For the creative misfit, NHCI detective ability is superior to HCI, and both can be for random misfit.(4) The concept lattice is used to represent the relationship among the examinee, item and attribute.(5) In order to discover frequent patterns more effectively, NHCI is used to delete abnormal examinees of different numeration representation system converting diagnostic test. 40 examinees are deleted from 152 examinees.(6) Diagnostic test of different numeration representation system converting is evaluated, the results show that theoretic construct validity is 0.894, both HCI and NHCI, mean of examinees are not exceed 0.3, and DINA model parameters s and g are higher. It can be seen the cognitive structure and data is not fit good, it is possible that the structure is irrational. The regression analysis shows the regression coefficient is not significant, all the attributes are not significant except A7, adjusted R2 statistic is 0.252. Therefore, it is necessary to carry notation Qt and cognitive structure be amended.(7) The data of different numeration representation system converting diagnostic test is analyzed. Given the support parameter be set, association rules between items are extracted in order to determine attribute refinement and generalization plan and to change the granularity of the original attributes. The changed cognitive model is proposed and evaluated. The results show that the mean of examinees’HCI and NHCI upgraded a lot, the mean of DINA g parameters decreased to 0.21, lower than the original 0.3. Significantly regress with attribute and item difficulty parameters, adjusted R2 statistic increase from 0.252 to 0.894, all attributes are significant regression coefficients. Updated model is much better than the original model.(8) The attributes of the diagnostic test item 16 are found wrong and then recalibrated. The results show that both mean of examinees’HCI and NHCI increase. Key words: Cognitive diagnosis;Granular Computing;Formal Concept Analysis;Cognitive model;Qt matrix. |
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