This study investigated the Type I error rate and power of the multivariate extension of the S - [chi][squared] statistic using unidimensional and multidimensional item response theory (UIRT and MIRT, respectively) models as well as full-information bifactor (FI-bifactor) models through simulation. Manipulated factors included test length, sample size, latent trait characteristics such as discrimination pattern and intertrait correlations, and model type misspecification. The nominal Type I error rates were observed under all conditions. The power of the S - [chi][squared] statistic for UIRT models was high for MIRT and FI-bifactor models that were structurally most distinct from the UIRT models but was low otherwise. The power of the S - [chi][squared] statistic to detect misfitting between MIRT and FI-bifactor models was low across all conditions because of the structural similarity of these two models. Finally, information-based indices of relative model-data fit and latent variable correlations were obtained, and these showed expected patterns across conditions. (Contains 1 note and 13 tables and 1 figure.)