Calibration of Response Data Using MIRT Models With Simple and Mixed Structures

It is common to assume during a statistical analysis of a multiscale assessment that the assessment is composed of several unidimensional subtests or that it has simple structure. Under this assumption, the unidimensional and multidimensional approaches can be used to estimate item parameters. These two approaches are equivalent in parameter estimation if the joint maximum likelihood method is used. However, they are different from each other if the marginal maximum likelihood method is applied. A simulation study is conducted to further compare the unidimensional and multidimensional approaches with the marginal maximum likelihood method. The simulation results indicate that when the number of items is small, the multidimensional approach provides more accurate estimates of item parameters, whereas the unidimensional approach prevails if the number of items in each subtest is large enough. Furthermore, the impact of the violation of the simple structure assumption is also investigated theoretically and numerically. The results demonstrate that when a set of response data does not have a simple structure but is specified as such in calibration, the models will be incorrectly estimated and the correlation coefficients between abilities will be overestimated.