The Effect of Test Length on the Accuracy of Estimating Ability Parameter in the Two- and Three-Parameter Logistic Models: Comparison by Using the Bayesian Method of Expected Prior Mode and Maximum Likelihood Estimation

Abstract

This study aims to compare the effect of test length on the degree of ability parameter estimation in the two-parameter and three-parameter logistic models, using the Bayesian method of expected prior mode and maximum likelihood. The experimental approach is followed, using the Monte Carlo method of simulation. The study population consists of all subjects with the specified ability level. The study includes random samples of subjects and of items. Results reveal that estimation accuracy of the ability parameter in the two-parameter logistic model according to the maximum likelihood method and the Bayesian method increases with the increase in the number of test items. Results also show that with long and average length tests, the effectiveness is related to the maximum likelihood method and to all conditions of the sample size, whereas in short tests, the Bayesian method of prior mode outperformed in all conditions. Results indicate that the increase of the ability parameter in the three-parameter logistic model increases with the increase of test items number. The Bayesian method outperforms with respect to the accuracy of estimation at all conditions of the sample size, whereas in long tests the maximum likelihood method outperforms at all different conditions.
 
 Received: 17 September 2021 / Accepted: 24 November 2021 / Published: 3 January 2022

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“…If the disturbance term (U i ) is introduced, the log it model becomes (equation (7) ). Variables with a contingency coefficient of less than 0.75 have weak associations, while values greater than 0.75 have strong associations ( Al-Tarawnah and Al-Qahtani, 2022 ). A goodness of fit metric is a review statistic that represents the model's accuracy in observed data ( Magrini, 2022 ).…”