Investigation of measurement invariance (MI) commonly assumes correct specification of dimensionality across multiple groups. Although research shows that violation of the dimensionality assumption can cause bias in model parameter estimation for single-group analyses, little research on this issue has been conducted for multiple-group analyses. We conduct studies at the population and sample levels to explore the effects of mismatch in dimensionality between data and analysis models with multiple-group analyses. Datasets are generated using a bifactor model with different factor structures and are analyzed with single-factor models to assess misspecification effects on MI and latent mean differences. The results of this investigation are important in that single-factor models hypothesized in MI studies inevitably are oversimplifications and ignore small group factors.