Date of Graduation
12-2022
Document Type
Thesis
Degree Name
Master of Science in Statistics and Analytics (MS)
Degree Level
Graduate
Department
Statistics and Analytics
Advisor/Mentor
Giovanni G. Petris
Committee Member
Ronna Turner
Second Committee Member
Avishek Chakraborty
Keywords
Item response theory, Unidimensionality
Abstract
In this research, the performance of two popular estimators, Maximum Likelihood Estimator(MLE) and Bayesian Expected a Posteriori (EAP) is studied and compared in estimating the latent ability score in an Item Response Theory (IRT) model. The 2-Parameter Logistic (2PL) IRT model which is characterized by difficulty and discrimination item parameters is used to estimate the latent ability scores. Several datasets are generated for variety of sample size and item length values. The Monte-Carlo simulation is used to analyze the performance of the estimators. Results show that MLE produces reliable results with low root mean square error (RMSE) across all datasets. On the other hand, EAP estimator produces variable RMSE values for the datasets with different sample size and item length values. The affect of these two characteristics of the datasets along with the discrimination item parameter are studied extensively on the performance of EAP estimator. Analyzing the results of EAP shows, in overall, EAP estimator yields less RMSE by increasing the sample size. Finally, the performance of the two estimators on estimating the latent ability scores is compared with each other. Results shows that the MLE produces closer estimations to true values than EAP estimator cross all datasets.
Citation
Taji, S. (2022). MLE and EAP Methods for Estimating Ability Scores for Data of Varying Sample Size and Item Length. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/4740