Current recommended cutoffs for determining measurement invariance have typically derived from simulation studies that have focused on multigroup confirmatory factor analysis, often using continuous data. These cutoffs may be inappropriate for ordered categorical data in a longitudinal setting. This study conducts two Monte Carlo studies that evaluate the performance of four popular model fit indices used to determine measurement invariance. The comparative fit index (CFI), Tucker-Lewis Index (TLI), and root mean square error of approximation (RMSEA) were all found to be inconsistent across various simulation conditions as well as invariance tests, and thus were not recommended for use in longitudinal measurement invariance testing. The standardized root mean square residual (SRMR) was the most consistent and robust fit index across simulation conditions, and thus we recommended using [greater than or equal to] 0.01 as a cutoff for determining longitudinal measurement invariance with ordered categorical indicators. [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.]