The Joint model of two-parameter logistic and response time model for computer-based tests

The purpose of this research is to produce a test measurement model that can explain the realistic conditions of the computer-based test by considering the response time. This research is a measurement model development consisting of two main analyses, such as 1) developing a joint model of two-parameter logistic and response time model and 2) examining the accuracy of the parameter model by using standard deviation and testing model fit by using DIC statistics. The model is implemented on empirical data from the National Selection test results of 1559 New Learners of Madrasah Aliyah Negeri (MAN) Insan Cendekia Ministry of Religion of the Republic of Indonesia in 2019 in the field of Mathematics consisting of 15 items with a time limit of 45 minutes. Estimation of parameter models used the Bayesian MCMC method with R2WinBUGS Software. The results of this research show that the joint model of Two Parameter Logistic and response time model produces a hierarchical structure model with three (3) groups of parameters, i.e., person parameters, item parameters, and rho parameters. Measurement models involving response time can improve the accuracy of model parameters compared with Two Parameter Logistic models that are separated from response time. The empirical data in this research fit better with the joint model of Two Parameter Logistic with response time characterized by a smaller DIC value than the Two Parameter Logistic model separated by response time. Therefore, it proves that the joint model of the Two Parameter Logistic with response time is more suitable to be implemented for computer-based and time-constrained tests