Unbiased Metropolis-Hastings Algorithm With Couplings For Grade Response Models

Item Response Theory(IRT)plays an important role in educational and psychological measurement.It transforms abstract features into measurable and comparable potential variables.With the development of theory,the corresponding parameter estimation methods are also developing rapidly.Under Bayesian framework,Markov chain Monte Carlo(MCMC)method has attracted psychometricians' attention because of its excellent effect in dealing with complex IRT models.In this paper,the unbiased M-H method based on the maximum coupling idea is applied to estimate parameters of the graded response model(GRM).The performance of the proposed method is illustrated and compared with the traditional M-H algorithm via a simulation study.In the simulation study,the influence of test length,number of categories,sample size,burn-in value and number of iterations on the estimation accuracy and efficiency is examined.The results show that increasing burn-in values and iterations will lead to more accurate estimation and higher efficiency.Finally,taking SAT data as an example,the feasibility and effectiveness of unbiased M-H method in real data analysis are illustrated.