Application Of Rough Set Theory In Cognitive Diagnosis

Cognitive Diagnosis (CD) is designed to measure specific knowledge structuresand processing skills in students so as to provide information about their cognitivestrengths and weaknesses. In this way, classroom testing is regarded as an ideal areato develop CDs. To cognitive diagnosis really play a role, cognitive diagnosis modelsexisting still have many difficulties to overcome.First, most cognitive diagnosismodels are based on probability models which need a big sample in estimating itemparameters, so it is difficult to integrate into daily teaching for them. Second, timelyfeedback is a necessary condition to play CD remedial teaching function,so far, CDare mainly used in lager-scale examination. In these examinations, more sophisticatedpsychometric procedures are developed and require more complex estimationmethods (e.g., Markov Chain Monte Carlo estimation), thus affecting data processingand, ultimately, reporting times. Many large-scale assessment results are releasedmonths after the tests are administered, and are not useful for promoting teaching.Under the item parameters known conditions, although Cognitive DiagnosticComputerized Adaptive Testing(CD-CAT) can timely feedback results, theestablishment of item bank is expensive, long periodicity, and item exposure andother issues, it is not convenient to popularize.Therefore,it is very necessary to find anew method when item parameters are unknown, examinees are less and feedbacksare timely.We apply a new method–Rough Set Theory(RST) in cognitive diagnosis. It cansolve the size of knowledge granularity caused uncertainty in CD. It requires no apriori knowledge, through the knowledge reduction, induce decision or classificationrules, the object can be classify.This paper aims at the application of rough set theoryin CD. This paper is divided into six parts.Research1is effective research with CDbased on RST, we will verificate the application of RST in CD by designing differentsituations such as different number of reachability matrix, different kinds ofhierarchical structures, different number of cognitive attribute. Research2is themethod of attribute-chunk,it discuss whether attribute-chunk will affect the correctrate. Research3is concerned on RST will be used to study the small sample. Research4is item attribute identification for paper and pen testing, Research5isabout multiple-strategies CD and compared with the existing method. Research6isempirical research.The results show that:(1)In the absence of item parameters, the rough set theory of CD has no business withsample size, fast diagnostic speed and good results.It shows that RST can be appliedto classroom tests.When the number of attributes is less than6,the diagnostic resultsare satisfied,on the other hand,is not.(2)by the method of attribute-chunk, we will premote the Pattern Match Ration(PMR)under the condition of large number of attributes, the number of required items isgreatly reduced.(3) In the item with unknown parameters, using of cognitive diagnosis of rough settheory, the sample size has no significant effect to PMR and the estimated results arestable.(4) Application RST to item attribute identification,when examinee’s PMR is lower,the failure rate is high and the number of attributes is much, item attributeidentification’s PMR is low.(5) RST is used for multiple strategies, results are agree with the existing research.(6) Based on rough set theory, This method can be used to establish the cognitivediagnostic item bank, in which all items only need to provide item attributes and noitem parameters, so the model fitting and equating can be avoided completely,and thecost of the establishment can be significantly saved.The above research,both results are estimated by rough set software,regardless ofsample size and item number,estimated speed is very fast,about10seconds.It showthe powerful advantage of RST CD.