Abstract: Multidimensional item response theory (MIRT) is a well known theory which combines the advantages of the factor analysis theory and the item response theory. The current study developed a parameter estimation method of MIRT model with MCMC algorithm, and discussed its application on psychology tests. Monte Carlo method was used to explore the feasibility of MCMC algorithm and to examine the estimation precision as well as the properties of three parameter logistic MIRT models. Besides, this study employed MIRT model to analyze Raven’s Advanced Progressive Matrices test (RAPMT).
Three findings were presented: (1) The estimation precision of the self-developed program of three parameter logistic MIRT model was comparable with those reported by western studies, which demonstrated the validity of the self-developed program; (2) Along with the sample size and the number of item sample increased, the estimation precision and the robustness of MIRT parameter increased; but along with the number of the test dimension increased (e.g. from 3 to 5), the estimation precision and the robustness of MIRT parameter decreased; (3) When applied the MIRT into the analysis of the RAPMT: (a) Most of the discrimination of the test items were very high. (b) The ability scores of the five dimensions of in the RAPMT were ranked ascendingly as CR, PP, FA, D3 and D2. Compare to the unidimensional item response theory (UIRT), the ability scores of each dimensions reported by MIRT provided more abundant and valuable information for cognitive diagnosis. (c) The correlations between the five dimensions in the RAPMT were on the low to moderate levels.

Key words: item response theory, multidimensional item response theory, MCMC algorithm, Psychology tests, Item Characteristic Surface