This dissertation compares the parameter estimates obtained from two item response theory (IRT) models: the 1-PL IRT model and the MC1-PL IRT model. Several scenarios were explored in which both unidimensional and multidimensional item-level and personal-level data were used to generate the item responses. The Monte Carlo simulations mirrored the real-life application of the two correlated dimensions of Necessary Operations and Calculations in the basic mathematics domain. In all scenarios, the MC1-PL IRT model showed greater precision in the recovery of the true underlying item difficulty values and person theta values along each primary dimension as well as along a second general order factor. The fit statistics that are generally applied to the 1-PL IRT model were not sensitive to the multidimensional item-level structure, reinforcing the requisite assumption of unidimensionality when applying the 1-PL IRT model.
College and Department
David O. McKay School of Education; Instructional Psychology and Technology
BYU ScholarsArchive Citation
Spencer, Steven Gerry, "The Strength of Multidimensional Item Response Theory in Exploring Construct Space that is Multidimensional and Correlated" (2004). All Theses and Dissertations. 224.
Item Response Theory, Dimensionality, Multidimensional, Goodness of Fit, Fit statistics