The impact of the Item Response Theory (IRT) model on the accuracy of test score equating

Abstract

The aim of the current study was to investigate the impact of the Item Response Theory (IRT) model on the accuracy of test score equating. The focus was on the effect of the two-parameter logistic (2PL) model and the three-parameter logistic (3PL) model, using the Loyd & Hoover mean/mean equating method (1980). To achieve the study's aim, simulated data were generated using the (Wingen3) software for 4 test forms. Two test forms were based on the 2PL model and the other two on the 3PL model, with 10 common items between each pair of test forms. All the data generation was repeated 30 times.
Data were analyzed using the R software through the Mirt and Sirt packages to verify the assumptions of the IRT model. Subsequently, the individual and item parameters were estimated using the PARSCLE software, and equating was performed using the IRTEQ software with the mean/mean method. To evaluate the accuracy of equating, the Root Mean Square Error (RMSE) was used. The results showed that the lowest errors occurred when equating was performed using the 2PL model, with an RMSE value of (0.591). When equating was performed according to the 3PL model, the RMSE value was 1.044, indicating that it is more accurate than the mean/mean method in equating test scores according to the 3PL model.
Through an independent two-sample t-test, it was revealed that the differences were statistically significant, with a significance level of (0.000).