Abstract:

This research aimed to identify the effects of independent variables as sample size, sample distribution, the number of items in the test, and the number of response categories of items in the test on the estimations of Graded Response Model (GRM) under Parametric Item Response Theory (PIRT) and by Monotone Homogeneity Model (MHM) under Non-Parametric Item Response Theory (NIRT) for polytomously scored items. To this goal, the research was performed as a fundamental study in which 192 simulation conditions were designed by the combination of sample size, sample distribution, the number of items, and the number of categories of items. Estimates by GRM and MHM were examined under different levels of sample size (N= 100, 250, 500, 1000), sample distribution (normal, skewed), the number of items (10, 20, 40, 80), and the number of categories of items (3, 5, 7) conditions, by respectively calculating model-data fit, reliability values, standard errors of parameters. As a result of the research, it was found that since the values used to evaluate model-data fit were influenced by the increase of variable while calculating model-data fit and since they cannot be interpreted alone, it is difficult to compare and generalize the results. The practical calculation of model data fit, which can be interpreted without the need for another value, in MHM provides superiority over GRM. Another research result is that the reliability values give similar results for both models. The standard errors of the MHM parameter estimates is lower than the GRM estimates under small sample and few items conditions and the standard errors of the MHM parameter estimates are close to each other in all conditions.

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