In general, the estimated item parameters are treated as fixed when item response theory (IRT) models were used for analyzing response date. Thus, the accuracy of estimated item parameters is very important. Under the simple structure assumption, the estimated item parameters were equivalent when unidimensional and multidimensional approaches were used and the joint maximum likelihood estimation (JMLE) was used. They are different for these two approaches when the marginal maximum likelihood estimation (MMLE) was used. Thus, the first purpose of this study was demonstrated that the estimated item parameters form the two approaches when MMLE was used. The result shows that when the number of items is small, the estimated parameters from multidimensional approach were more accurate than those from unidimensional approach; otherwise, it was reverse. The second purpose was to illustrate that the multidimensional approach was more appropriated then when violation of simple structure assumption was exist.
Comments & Questions
1. Whether the simulation results can be generated to multidimensional approach when the number of dimensions is larger than 2?
2. It seems that the calculations of RMSE of the discrimination and difficulty parameters were include items calibrated with 3PL and 2PL. If the calculation of the ARMSE will be influenced by items calibrated from different models?