Accuracy of Bayesian method estimating for a person’s ability and item parameters - two-parameter logistical model (2-PL) of different sample sizes

Abstract

This study aimed to show the accuracy of estimating the Bayesian method in estimating item parameters and person’s ability parameter under any circumstances relating to the sample size, Four levels of the sample were used: 1500,500, 200,100 by making a comparison between the Bayesian method of estimation that is used in the software (WinBUGS V1.4) and the maximum likelihood-is the usual to estimate parameters -way by (Bilog-MG3) software according to a two-parameter logistic (2-PL) model in the item response theory (IRT) models -dichotomous response, Experimental data were generated using WinGen v.3 software, and the item parameters and ability were estimated according to the two methods(Bayesian, maximum likelihood). The results of the estimation accuracy of the Bayesian method were reached in light of the circumstances use of the sample size variable by evaluating the Root Mean Squared Error (RMSE) index of the arithmetic mean, and the relative efficiency (RE) index and the results showed the advantage of the Bayesian method of estimation in small samples, and this was confirmed by the results of (t-test) to compare the correlation coefficients at the two methods of estimation between the generated values and estimated values of the parameters for each method, where parameters showed The correlation of the Bayesian method is a statistically significant difference at (α= 0.05