Standard Errors, Priors, and Bridge Sampling. A Discussion of Liu et al.

Abstract

Liu, Hu, Cao, Wang, and Chen (2019) present five methods to estimate the marginal likelihood of Item Response Theory (IRT) models and compare the performance on English examination data. On these data they compute the marginal likelihood for the 1PL and 2PL models using five different methods that were extensively described in the methods section of their paper. In this discussion, we will first shortly reflect on the standard errors of the estimates in relation to the number of iterations used. Then the choice of prior distributions and their potential impact is discussed. And finally, we will give results of an additional estimation approach.