| Efforts to apply Markov Chain Monte Carlo (MCMC) methods to three-parameter linear logistic multidimensional IRT models are addressed using the Metropolis-Hastings algorithm within Gibbs approach. Bayesian modal estimators of both item and proficiency parameters are obtained in a simultaneous process rather than a separate parameter estimation procedure. It is shown that it is effective by blocking individual item discrimination and proficiency dimensional parameters and treating them without reference to other item and proficiency parameters. Both simple and complex structures of item dimensions are included. In addition, various proficiency dimensional structures are considered for three and five dimensional cases, respectively. The effects of four potential factors on model parameter estimation are investigated. Simulation studies are conducted across different designs for one-, three-, and five-dimensional cases. Results show that the parameter estimators based on MCMC are accurate in terms of correlation and root mean square errors. Numeric examples for the estimates of the standard errors demonstrate that the estimation is statistically stable and accurate. |
