COMPARISON OF UNIDIMENSIONAL AND MULTIDIMENSIONAL APPROACHES TO IRT PARAMETER ESTIMATION

It is common to assume during statistical analysis of a multiscale assessment that the assessment has simple structure or that it is composed of several unidimensional subtests. Under this assumption, both the unidimensional and multidimensional approaches can be used to estimate item parameters. This paper theoretically demonstrates that these two approaches are the same if the joint maximum likelihood method is used to estimate parameters. However, they are different from each other if the marginal maximum likelihood method is applied. A simulation study is then conducted in this paper to further compare the unidimensional and multidimensional approaches with 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, while the unidimensional approach prevails if the test length is long enough. Further, the impact of violation of the simple structure assumption is also investigated. Specifically the correlation coefficient between subscales will be highly overestimated when the simple structure assumption is violated.