Comparison of Priors in Bayesian Estimation of 1-PL (One-Parameter Logistic) Item Response Models

• In Event: Issues of Rasch Dimensionality, Scaling, and Fit

Abstract

Efficient and accurate parameter estimation has remained an important issue in item response theory (IRT). Although marginal maximum likelihood (MML) estimation has been a de facto standard, recent advances in computational statistics have made Bayesian methods more accessible. But the use of priors has been inconsistent in Bayesian estimation of IRT models. The present study investigates the impact of prior choice on parameter estimation for 1-PL model and compares the accuracy of estimation for MCMC, variational Bayesian, and MML methods. The study also compares the parameter recovery for Bayesian and MML in skewed data and small samples. Results show that priors should be chosen carefully to obtain reasonable estimates and Bayesian techniques recover parameters better than MML for non-normal data.

Authors

• Prathiba Natesan, University of North Texas

• Ratna Nandakumar, University of Delaware

• Tom Minka, Microsoft Research

• Xiaoyu Qian

• Jonathan D. Rubright, American Institute of Certified Public Accountants