A comparison of the stability of ability parameter estimation based on the maximum likelihood and Bayesian estimation: A case study of dichotomous scoring test results

This research is related to Item Response Theory (IRT), which is essential for determining the best method for estimating participants' abilities on a test measuring English listening ability. This study aims to (1) determine the characteristics of the test device measuring English listening ability, (2) determine the effect of the length of the test on the stability of the ability estimation using the maximum likelihood (ML) method, (3) determine the effect of test length on the stability of the ability estimation using the Bayes method, and (4) compare the stability of the ability estimate between ML and Bayes. This research is an exploratory descriptive study using a simulation approach. The best model is selected to generate data. The result of the generation is the actual ability (θ) and the participant's response, which is estimated with the maximum likelihood and Bayes, which produces the estimated ability with 10 replications, and is compared with calculating the MSE (mean square error). The method with a smaller MSE is stable and has a better estimation method. The results show that (1) the 2PL model is the best, (2) the length of the test affects the stability of the ability estimation in the ML method and the most stable case when the test contains 46 items, (3) the length of the test affects the stability of the ability estimate in the Bayes method and it is most stable when the test contains 46 items, and (4) the Bayes method is better and more accurate for estimating ability.