Markov chain Monte Carlo (MCMC) estimation is investigated for multidimensional compensatory and noncompensatory item response models. Simulation analyses are used to evaluate parameter recovery for the multidimensional two-parameter logistic model (M2PL) and the multidimensional latent trait model (MLTM) under varying conditions of sample size (1,000, 3,000), number of items (25, 50), and correlation between abilities (.0, .3, and .6). Results suggest that an MCMC procedure using a Metropolis-Hastings algorithm can recover the parameters of both models but is less successful for the MLTM as the correlation between abilities increases. In general, estimation is more accurate for the M2PL than the MLTM. A Bayes factor criterion for comparing the relative .t of the models to a common data set is investigated using simulated data. Using real data, the M2PL is found to be the superior model for a test of English usage.
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