Bilişsel Tanı Ve Çok Boyutlu Madde Tepki Kuramı Modellerinin Karşılıklı Uyumlarının İncelenmesi

Abstract

In this study , interchangeable use of cognitive diagnosis models (CDM) and multidimensional item response theory (MIRT) models, which have common features, were investigated . T his study can be considered as a retrofitting study , which concentrates on the accuracy of estimated person parameter s to the ir true level s . To this end, a polytomous attribute CDM, which is referred to as fully - additive model (fA - M) with features close to MIRT , has been proposed. In the study, polytomous generalized deterministic input noisy and gate (pG - DINA) and fA - M models from CDMs and 2PL MIRT models were used. By manipulating the item discrimination index, the ratio of item structure of test , the test length , and the correlat ion between the abilities ; 54 conditions formed for compensatory and non - compensatory cases. Therefore, for each model, a total of 108 data sets were generated under compensatory and non - compensatory approach es. T wo dimension al MIRT structure was organized as two attributes with four levels for CDM cases . Continuous person parameter s in MIRT was categorized using cut - off scores to make it compatible with CDM . Correct classification rates of person parameters by the models were obtained for each dataset. The study was characterized with two sub - questions . The first was concerned with retrofitting CDM to MIRT , which includes the analysis of MIRT data; and the other was concerned with the retrofitting MIRT to CDM by analysis of CD M data. In both sub - questions , the effect of the conditions to results was similar. In conclusion, it was seen that the increase in test length was the strongest factor that led to an increase in person parameter accuracy. The item discrimination index and the ratio of item structure of test followed the test length , respectively. The presence of a positive correlation between the abilit ies had limited positive influence to the accuracy of person parameters when compared to other factors. In the first sub - question involving retrofitti ng CD M, the difference between the results of the analysis of the compensator y and the non - compensatory data wa s very small . x However, in the second sub - question involving the adaptation of the MIRT, it wa s seen that this difference wa s larger and favor ing the compensatory data analysis. When the results are considered in terms of models, as expected , all data types we re estimated with highest accuracy by the true models . In the retrofitting cases , accuracy rates were close to true model estimation accuracy levels when MIRT and pG - DINA data analyzed by fA - M and fA - M data analyzed by MIRT. To obtain cognitive diagnostic information from the MIRT data, fA - M may be a convenient tool if abilities can be transformed into polytomous attributes . Likewise, if continuous ability score is desired from fA - M data, MIRT application is recommended if attributes can be converted into dimensions. In addition to these results, lower correct classification rates were obtained when pG - DINA data were retrofit ted to MIRT, and vice versa. Furthermore, a nalysis of f A - M data with pG - DINA resulted in lower accuracy rate. High classification accuracy rates of fA - M when MIRT and pG - DINA data fitted may be considered as success indicators of the proposed model. Future studies may propose new models using the success probability computation develop ed for fA - M . In this respect, f A - M may lead to a new model family yielding successful estimations for various data sets with high model - data fit.