Most research on confirmatory factor analysis using global fit indices (AIC, BIC, AICc, and CAIC) has been in the structural equation modeling framework. Little research has been done concerning application of these indices to item response models, especially within the framework of multidimensional Rasch analysis. The results of two simulations studies that investigated how sample size, between-dimension correlation, and test length affect the accuracy of these indices in model recovery using a multidimensional Rasch analysis are described in this dissertation. The first study analyzed dichotomous data, with model-to-data misfit as an additional independent variable. The second study analyzed polytomous data, with rating scale structure as an additional independent variable. The interaction effect between global fit index and between-dimension correlation had very large effect sizes in both studies. At higher values of between-dimension correlation, AIC indicated the correct two-dimension generating structure slightly more often than does the BIC or CAIC. The correlation by test length interaction had an odds ratio indicating practical importance in the polytomous study but not the dichotomous study. The combination of shorter tests and higher correlations resulted in a difficult-to-detect distinction being modeled with less statistical information. The correlation by index interaction in the dichotomous study had an odds ratio indicating practical importance. As expected, the results demonstrated that violations of the Rasch model assumptions are magnified at higher between-dimension correlations. Recommendations for practitioners working with highly correlated multidimensional data include creating moderate length (roughly 40 items) instruments, minimizing data-to-model misfit in the choice of model used for confirmatory factor analysis (MRCMLM or other MIRT models), and making decisions based on multiple global indices instead of depending on one index in particular.