Several types of parameterizations of attribute correlations in cognitive diagnosis models use the reduced reparameterized unified model. The general approach presumes an unconstrained correlation matrix with K(K - 1)/2 parameters, whereas the higher order approach postulates K parameters, imposing a unidimensional structure on the correlation matrix between the latent skills. This article investigates the differences in performance between the correlational structure parameterizations (a general structure, a higher order single-factor structure, and a baseline uniform distributional approach constraining the attributes to be independent) across a wide variety of simulated multidimensional attribute spaces. Results suggest that the correlational approaches perform equally well with respect to classification and item parameter estimation accuracy, regardless of the violations of the assumptions of the higher order model. Findings suggest the general robustness of the higher order model and the associated estimation procedure. The three approaches are also used to analyze a real-world test; results suggest that such tests can be analyzed effectively by the higher order algorithm. (Contains 3 tables and 1 note.)