Use of cutoff values for model fit indices to assess dimensionality of binary data representing scores on multiple-choice items is a popular approach among researchers and practitioners, and the commonly used cutoff values are based on simulation studies that used as the generating model factor analysis models, which are compensatory models without modeling guessing. Consequently, it remains unknown how those cutoff values for model fit indices would perform when (a) guessing exists in data, and (b) data follow a noncompensatory multidimensional structure. In this paper, we conducted a comprehensive simulation study to investigate how guessing affected the statistical power of commonly used cutoff values for RMSEA, CFA, and TLI (RMSEA > 0.05; CFA < 0.95; TLI < 0.95) to detect violation of unidimensionality of binary data with both compensatory and noncompensatory models. The results indicated that when data were generated with compensatory models, increase of guessing values resulted in the systematic decrease of the power of RMSEA, CFA, and TLI to detect multidimensionality and in some conditions, a small increase of guessing value can result in dramatic decrease of their statistical power. It was also found that when data were generated with noncompensatory models, use of cutoff values of RMSEA, CFA, and TLI for unidimensionality assessment had unacceptably low statistical power, and while change of guessing magnitude could considerably change their statistical power, such changes were not systematic as in the compensatory models.