Comparative Analysis Of Bayesian Estimation Methods For Four-parameter Logistic Model

The Four Parameter Logistic Model(Four Parameter Logistic Model,4PLM)parameter estimation efficiency and accuracy is the subject of research by many statisticians.4PLM adds an upper asymptote that is less than 1 on the basis of3 PLM.The significance is that it is possible for subjects with higher abilities to answer wrongly with a certain probability,that is,some questions may be missed,so that the probability of correct answer is less than 1,that is The error parameter needs to be introduced.Since 4PLM is a non-convex function,the classic estimation algorithm cannot obtain the global optimal solution,so this paper uses the Markov Chain Monte Carlo(MCMC)method based on Gibbs sampling algorithm in OpenBUGS program and EM in mirt program The algorithm(Expectation Maximization algorithm,EM)and the NUTS algorithm(No-U-Turn Sampler,NUTS)in the Stan program estimate the parameters of 4PLM,and compare and analyze the estimated results.Finally,by introducing the principles of the algorithms implemented by the three programs,this paper discusses the applicable scope of the algorithms in the three software.For multi-dimensional models or higher-order models and other models with complex and large parameters,the NUTS algorithm of the Stan program and the MH-RM of the mirt program The algorithm(Metropolis-Hastings Robbins-Monro hybrid,MH-RM)may be more suitable.