Applying The Latent Mixture Modeling To The Multidimensional 3PLM Parameter Estimation

The current study focuses on one of longstanding issues for the multidimensional three-parameter logistic model,the item parameter estimation,and proposes a new algorithm to precisely obtain the estimates of this model,namely,the Bayesian Expectation-Maximization-Maximization based on the Metropolis-Hastings RobbinsMonro(BEMM-MH-RM)algorithm.Compared with the classical Bayesian EM(BAEM)algorithm,the new method replaces the low-efficient Hermite-Gauss quadrature method with Metropolis-Hastings(MH)method to rapidly approximate the high dimension integration,and then replaces Fisher-scoring iteration method with Robbins-Monro method which is particularly adept at handling missing data.In order to successfully gain a more robust estimate,compared with original MH-RM algorithm,by introducing an extra ability-based latent classical variable and calculating its conditional expectation,the new method disassembles and approximates the likelihood function,and then separates the estimation procedure of guessing parameters and other parameters into two independent parts,and then utilizes Maximization step twice for guessing and other parameters,respectively.According to simulation studies and the real data analysis,the advantages of the BEMM-MH-RM algorithm are listed as follows:(1)more accurate estimates,which means it has more powerful capability to maximize the likelihood function;(2)more robust estimates,which means there is no obvious difference for point estimates yielded by the new method between two different types of the guessing prior;(3)more efficient speed,which means the elapsed time of the new methods is far less than other methods due to the technique of vector programming and parallel computing.