Investigation of the effect of different ability distributions on item parameter estimation under two-parameter logistics model

Tests consisting of dichotomously scored items are frequently used in education and psychology. These tests, which can be used with logistic models under item response theory, have some features that make the estimation more accurate when estimating item parameters but groups in which tests are applied may not always provide these features. The aim of this study is to analyze the effects of various features of the data set on the accuracy of the parameter estimates in the analysis of a data set consisting of dichotomously scored items with a 2 parameter logistic (2 PL) model. This study is important because it will explain how the ability parameters obtained from dichotomously scored tests have not normal distribution and the sample size will affect the accuracy of parameter estimates. For the purpose of the study, item parameters for a test with skewness coefficients 2,00, 1,00, 0,00, -1,00 and -2,00 and with sample sizes of 250, 500, 1,000 and 2,000 and a length of 30 items were produced in the R programming language and RStudio software. 100 replications were performed for each data set produced and the estimations of the item parameters were performed with the help of the marginal maximum likelihood (MML) estimation method in the mirt pack using the R programming language in the RStudio software. To evaluate parameter estimation accuracy, root mean squared error (RMSE) and Bias statistics were used. The results of the study showed that RMSE values for parameters a increased when the skewness coefficients increased by absolute value and Bias values moved away from zero, and that almost identical RMSE and Bias values were obtained when the skewness coefficients for parameters b increased by absolute value. When the sample sizes increased, it was observed that RMSE values decreases in all distributions for the a parameters and the Bias values were almost the same, for the b parameters, the RMSE values decreases as the sample size increased, and the Bias values sometimes approached to zero compared to the skewness coefficient. When the results obtained from the normal distribution are compared with the results obtained from the distributions with other skewness coefficients, it is seen that it produces the smallest RMSE and the Bias values closest to zero.