The purpose of this study is to evaluate the performance of three commonly used model fit indices when measurement invariance is tested in the context of multiple-group CFA analysis with categorical-ordered data. As applied researchers are increasingly aware of the importance of testing measurement invariance, as well as Likert-type scales are frequently used in social and behavioral sciences, specific guidelines are in need for evaluating model fit in this context. To achieve the study goal, two Monte Carlo simulation studies were conducted. Study 1 investigated the sampling variability of fit indices under different levels of invariance. Based on the sampling variability of fit indices, cutoff values for various levels of invariance proposed. Study 2 investigated the influence of several conditions on the sensitivity of fit indices' changes to two commonly used non-invariance levels: metric invariance and scalar invariance. Then, rejection rates based on cutoff values of fit indices proposed were examined in Study 2.Findings indicated that all three fit indices (CFI, RMSEA, SRMR) appeared to be sensitive to lack of invariance in factor thresholds than factor loadings. Different cutoff values may be applied under various conditions with categorial-ordered data. In addition, using cutoff values should be cautious as factors impacted changes in model fit indices differently. Recommendations for the use of model fit indices in the multiple-group CFA invariance context were provided for applied researchers. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]