Previous work on the effects of dimensionality on parameter estimation was extended from dichotomous models to the polytomous graded response (GR) model. A multidimensional GR model was developed to generate data in one-, two-, and three-dimensions, with two- and three-dimensional conditions varying in their interdimensional associations. Test length (15 and 30 items) and the ratio of sample size to the number of item parameters to estimate were also investigated, using sample sizes of 375 and 750 for the short test and 750 and 1,500 for the longer test. Results show that for unidimensional data a sample size ratio of 5:1 provided reasonably accurate estimation, and that increasing the sample size did not have a significant impact on the accuracy of item parameter estimation. Regardless of data dimensionality, the difficulty parameters were well-estimated, and for the multidimensional data the correlations between estimated item discrimination and the average and the sum of the dimensional discrimination were greater than the correlations between the estimated item discrimination and individual dimensional discriminations. Fidelity coefficients between the mean ability and the ability estimate were greater than those between the ability estimate and the latent traits. The impact of equating on accuracy indices in a multidimensional context was discussed. Seven tables and 16 graphs present analysis data. (Author/SLD)