Examination of different determination of Q-Matrix in cognitive diagnosis models under different ability levels and distribution conditions

With this research, it is aimed to compare the different determination of the Q-matrix under the G-DINA Model under varying conditions. For this purpose, firstly, Q-matrices determined based on expert opinion and exploratory factor analytical method were compared with the classifications made on the population data set by applying validation process to these Q-matrices. Then, by using validation processes proposed for these Q-matrices, classifications made with Q-matrices with different set of attributes in lower and higher ability groups were examined. Finally, the classifications made on the groups providing distribution that differ from normal and non-normal distribution (coefficient of skewness 0.5, 0.75, 1, 1.25, 1.5 and 2) were compared. The classifications made were compared with model fit indices, item parameter estimates (guess and slip parameters) and classification accuracies. The population of this research consists of 4292 sixth grade students participating in the post-test application in the TUBITAK Project No 115K531, titled "A Recommended Model to Increase Success Level of Turkey in Mathematics in International Wide Scale Exams: Effectiveness of the Cognitive Diagnosis Based Tracking Model". Nine groups of 500 student, who were drawn from population is the samples of the study. These samples were obtained in accordance with the nine conditions considered within the scope of the research. Considering the Q-matrix determined based on expert opinion in the classifications made on the population, the highest classification accuracy and the most appropriate parameter estimation at the test level were obtained with the Q-matrix determined as a result of the acceptance of the modifications suggested by the validation method, in addition to the Mesa plot examinations, and the acceptance of the appropriate ones. When the Q-matrix determined by factor analysis was considered, it was seen that the number of modifications suggested by the validation method was quite low and therefore the validation method was not required. It has been observed that Q-matrices whose attribute sets are determined differently in lower and upper skill groups make classifications with different accuracy, and similarly, it has been observed that model data fit and parameter estimates also differ. In general, when non-routine problem solving skills and reading comprehension skills were added to Q-matrices as attributes, it was observed that the classifications on the lower and the upper group were affected differently. However, when the coefficient of skewness increases, it has been observed that the findings obtained are negatively affected in terms of classification accuracy, model fit and parameter estimation, especially when the coefficient of skewness is above 1.25, it provides an unacceptable classification. In the light of the findings obtained from this study, suggestions for determining the appropriate Q-matrix for situations that may be encountered in Cognitive Diagnosis Model applications are presented.