Comparison of DINA and fusion models on item parameters, posterior probabilities and latent class predictions in cognitive diagnostic models

This thesis is in the scope of "A Recommended Model to Increase Success Level of Turkey in Mathematics in International Wide Scale Exams. Effectiveness of the Cognitive Diagnosis Based Tracking Model." TUBITAK number 115K531 project's research problems. In a test, developed and analyzed with Cognitive Diagnostic Models, instead of the total score, an assessment is made to determine which skills are present and which don't. In this sense, tests developed with Cognitive Diagnostic Models are effective in determining the needs of the students rather than serving only the evaluation process. There are many models developed in this field. In this thesis, DINA and Fusion models, which are more common in Cognitive Diagnostic Models and which have software support, used. DINA model is an latent class analysis that resembles dual ability models. DINA model aims to reveal the latent attribute of the responder's that is under its observed ability. Two item parameters, s and g parameters, are obtained from the model. The most important difference of the DINA model from other CDMs is that it sees an individual in the null class who doesn't have only one of the attributes required for an item. The Fusion model, which is not as strict as the DINA in making decisions about the student, provides information in two ways: providing detailed information about the cognitive profile of the respondents and parameters about the test and diagnostic capacity of the items. In the Fusion model, item parameters are obtained in the form of rik*, πi* and ci as well as ability parameters. In the thesis, apart from the statistical structures of the two Cognitive Diagnostic Models chosen, a study was carried out based on their predictions. As a result of the analyzes, it was concluded that the DINA and Fusion model parameters (rs = -0,382; P > 0,05), and the posterior predictions of both models didn't differ. In the next stage, although the model fit and item parameters were similar, it was observed that the estimation of the latent classes changed through models and only 54.94% of the students were assigned to the same class with both models.