Two classes of dichotomous multidimensional item response theory (MIRT) models, compensatory and noncompensatory, are reviewed. After a review of the literature, it is concluded that relatively little research has been conducted with the noncompensatory class of models. A monte-carlo simulation study was conducted exploring the estimation of a 2-parameter noncompensatory IRT model. The estimation method used was a modification of the Metropolis-Hastings algorithm that used multivariate prior distributions to help determine whether or not a newly sampled value was retained or rejected. Results showed that the noncompensatory model required a sample size of 4,000 people, 6 unidimensional items per dimension, and latent traits that are not highly correlated, for acceptable item parameter estimation using the modified Metropolis method. It is then argued that the noncompensatory model might not warrant further research due to the great requirements for acceptable estimation. The multidimensional interactive IRT model (MIIM) is proposed, which is more flexible than previous multidimensional models and explicitly accounts for correlated latent traits by using an interaction term within the logit. Item response surfaces for the MIIM model can be shaped either like compensatory or noncompensatory IRT model response surfaces.
University of Minnesota Ph.D. dissertation. December 2009. Major: Psychology. Advisor: Dr. David J. Weiss. 1 computer file (PDF); vi, 81 pages, appendices A-D.
Babcock, Benjamin Grant Eugene.
Estimating a noncompensatory IRT model using a modified metropolis algorithm..
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