Accuracy Of Estimating Item Parameters And Individual' Ability Of Three-Parameter Item Response Theory Model Using Joint Maximum Likelihood Estimation Method In Light Of Sample Size And Test Length

Abstract

The current study aimed to reveal the accuracy of estimating the parameters of the items and the ability of Individual of the three-parameter item response theory (3PL) model using Joint Maximum Likelihood Estimation (JMLE) method according to the sample size and test length. To achieve this, Response data (100, 250, 500, 1000) were generated on tests consisting of (20, 40, 60) items, and the R programming language package (R-4.1.0) was used to estimate item parameters (difficulty, discrimination, guessing). For Individual’ abilities, the JMLE method was used. The correlation coefficient indicator demonstrated that as the sample size and length of the test increased, the value of the correlation coefficient between the expected value and the estimated value of the item's parameters increased. The findings also showed that by increasing the sample size and length of the test, the value of the root mean square error index (RMSEA) fell, indicating that the estimated value of the item parameters and the person's ability was reduced. The study suggested comparing the accuracy of calculating item and person ability using the marginal maximum likelihood approach and the joint maximum likelihood method.