Bayesian Estimation Method Of Three-parameter Logistic Model Based On Pólya–Gamma Distribution

Item Response Theory(IRT)plays an important role in education and psychological measurement.IRT is mainly based on the ability of the subjects and the "probability of correct answer" of the test items.This paper mainly studies the Bayesian estimation of three-parameter Logistic item Response model(3PL).Based on Pólya–Gamma distribution family,Jiang's(2019)proposed Gibbs sampling method for two-parameter Logistic item Response Model(2PL).In this paper,Jiang's(2019)Pólya–Gamma based sampling estimation method is extended to 3PL model,and the estimation effect of the model is studied through Monte Carlo simulation,and the sensitivity of the sampling method to different prior assumptions is discussed.In the simulation experiment,factors such as test length,subject sample and prior distribution are discussed in detail.Finally,two statistics--BIAS and Root Mean Squared Error(RMSE)are reported to test the effect of parameter estimation.Simulation analysis shows that the parameter estimation result based on Pólya–Gamma sampling method is relatively accurate.