Most research on confirmatory factor analysis using information-based fit indices (Akaike information criterion [AIC], Bayesian information criteria [BIC], bias-corrected AIC [AICc], and consistent AIC [CAIC]) has used a structural equation modeling framework. Minimal research has been done concerning application of these indices to item response models, especially within the framework of multidimensional Rasch analysis with an emphasis of the role of between-dimension correlation on index accuracy. We investigated how sample size, between-dimension correlation, model-to-data misfit, and test length affect the accuracy of these indices in model recovery in dichotomous data using a multidimensional Rasch analysis simulation methodology. Results reveal that, at higher values of between-dimension correlation, AIC indicated the correct two-dimension generating structure slightly more often than the BIC or CAIC. The results also demonstrated that violations of the Rasch model assumptions are magnified at higher between-dimension correlations. We recommend that practitioners working with highly correlated multidimensional data use moderate length (roughly 40 items) instruments and minimize data-to-model misfit in the choice of model used for confirmatory factor analysis (multidimensional random coefficient multinomial logit or other multidimensional item response theory models). (Contains 4 tables and 2 figures.)