Comparison of Item Parameters and Model Fit from Item Response Theory Applications: A Monte Carlo Study

Abstract

The purpose of this study is to identify and compare NIRT, PIRT and MIRT across different sample sizes, test length and correlation between dimensions in a two dimensional simple structures. Data sets in various conditions have been simulated. These conditions are sample size (100, 500, 1000 and 5000), test length (5, 15 and 25) and correlation between dimensions (0.00, 0.25 and 0.50). From each experimental design, within the frame of Monte Carlo study, the findings have been obtained through 20 replications. For the item parameters and model data fit for the items, standard errors and significance values have been calculated. Having analyzed the findings of the research, with the increase of sample sizes and test length, it is also found out that the model data fit for the test has increased as well. It can be stated that tests consisting of less items fit better to MIRT models. In all simulation designs, model data fit for the items are calculated with quite low errors in NIRT. When the chi-square, infit and outfit values obtained for PIRT have been analyzed, it has been revealed that along with the increase of sample sizes and test length, all three coefficients exhibit better model fit. In NIRT, the standard errors belonging to Hi and p parameters tend to decrease with the increase of sample sizes and test length. In PIRT, a parameters tend to decrease when the sample sizes and test length increase.