Examining multidimensional structure in view of unidimensional and multidimensional graded response model

The aim of this study is to compare estimated item and ability parameters and the model-data fit indexes of multidimensional and polytomous item data based on unidimensional and multidimensional Graded Response Model (GRM). Simulative and real data sets were utilized. All data sets were simple-structured and three-dimensional, but different sample sizes (250, 500, 1500), number of items (15, 30, 60), and correlation levels between dimensions (0.20, 0.50, 0.80) were designated. The real data set used for the study was collected by using Fear Experiences Questionnaire. Unidimensional modeling was utilized to analyze total items (UGRM-t) and each sub-dimension separately (UGRM-a). Then, the results from UGRM and MGRM were compared. It was concluded that between UGRM-t and MGRM, the correlation between a parameters increased as correlation between subdimensions increased. UGRM-a model produced highly correlated a parameters with MGRM. In terms of c parameters, unidimensional and multidimensional models had high and significant correlations with each other. As the sample size increased, the error values of the item parameters decreased. When the sample size was kept constant, the error values decreased as the correlation between the dimensions increased. Ability parameters had high correlations with MGRM and UGRM-a under all conditions. When the error amounts in ability estimation were examined, it was concluded that the multidimensional model predicted with less error as the number of items and sample size increased. Results from the real data set and simulative data set were similar. In all data conditions, MGRM had better fit with the data.