Mix-DINA Model Function Development And Comparison With DINA And MS-DINA Model Based On Simulated And Empirical Data

Cognitive diagnostic assessment is on behalf of one of the developmentdirections of modern test theory combined with substantial psychology. However,there still lack enough attention on psychological research results in the area ofcognitive diagnositc assessment. Although many psychological studies have shownthat many cognitive tasks (such as syllogistic reasoning, figure reasoning, etc.) whichcan be solved by more than one strategy, a lot of present studies and practicalapplications on cognitive diagnosis assume that all subjects answer the test utilizingthe same sets of skills as there is only one Q matrix. In fact, for test tasks which canbe solved by multiple strategies, different subjects may use different strategies toanswer the same item and the same subject may also use different strategies to answerdifferent items. Then multiple Q matrix must be used to correspond the specific skillsof subjects which tends to choose different strategy during testing, which makes thetest data very complicated.According to the number of Q matrix and whether strategy shift phenomenonexists, four types of test data can be distinguished, which are single strategy withoutmixture, multiple strategy mixture within person, multiple strategy mixture betweenperson and multiple strategy between and within person. The current study suggeststhat, in mixture test data, the same items’ difficulty may differ for subjects whochoose different strategies. Then, test data generated by MS-DINA without the aboveassumption does not belong to those four types of test data.If DINA or MS-DINA model could fit each type of multiple strategy data or theerror could be ignored, there’s no need to develop new cognitive models. Thenwhether the above two models are applcable to multiple strategy data is examined bysimulation experiment at first. And then learn from the idea of mixture distributionIRT models, Mix-DINA model is defined in detail and model identification isachieved by MCMC algorism. Each type of test data listed aboved is fitted byMix-DINA model to assess its performance. Finally, compared DINA, Mix-DINA andMS-DINA model are compared by examing fitness and diagnosis results in analyzingRaven Advanced Reasoning Test. Key Findings of this dissertation listed below:1) Precision of estimating item parameters and diagnosing subjects’ knowledgestate when using DINA model to fit multiple strategy test data exceptmultiple strategy mixture within person are significantly lower than fitting single strategy without mixture test data. And pattern match rate whenfitting multiple strategy mixture between person and multiple strategymixture data between and within person test data(especially the latter) islower than fitting data generated by MS-DINA model. Then, DINA modelis not applicable for fitting multiple strateg test data.2) When using MS-DINA model to fit two kinds of multiple strategy mixturedata(expecially multiple strategy mixture data between person), there arealso large errors in estimated item parameters and subjects’ knowlege state.Then, MS-DINA model is not applicable for fitting multiple strategymixture data.3) Using self-designed MCMC algorithm and self-programmed R code,Mix-DINA model’s item parameters, subjects’ knowledge state and stategypreference can be estimated accurately. Accuracy of estimating itemparameters and subjects’ knowledge state when using Mix-DINA model tofit multiple strategy mixturebetween and within person data is higher thanmultiple strategy mixutre between person. With the decrease of proportionof subjects using the first strategy, the estimation precision of itemparameters for the first strategy and pattern match rate also decreased,however subjects’ strategy preference classification and estimation of itemparameters for the second strategy increased increased.4) In comparison with MS-DINA, When using Mix-DINA model to fit singlestrategy without mixture and multiple strategy mixture within person testdata, the estimation of item parameters and subjects’ knowledge state ismore precise, and even very close to the results of DINA model. The resultsof using Mix-DINA model to fit data generated by MS-DINA model isbetter than results of using MS-DINA model to fit multiple strategy mixturebetween person and multiple strategy mixture between and within persontest data. It shows that Mix-DINA model can fit many kinds of test databetter than MS-DINA model.5) Multiple strategy Q matrix which contains verbal-analytic and visual-spatialstrategy are constructed for Raven Advanced Progressive Matrix Test. Theempirical data analysis shows that Mix-DINA model fit APM test data best,MS-DINA model follows, and fitness of DINA model is worst. Thatdemonstrates the practical value of Mix-DINA model in empirical dataanalysis.