Participants in achievement tests or psychometric scales can be naturally divided into various sub-groups such as gender, race, social economic status, school district, etc. In order to make meaningful comparison between groups, each item in the test/scale should measure the same underlying construct for participants came from different groups. The increasing implementation of cross-national assessments have raised the question about how to evaluate measurement invariance across a large number of groups. This study compared two relatively new methods--the CFA alignment optimization and the random item effects model--on evaluating measurement invariance. The impact of following factors on the performance of each method were assessed: the proportion of DIF items, type of group mean ability, number of groups, group size, DIF size, and type of DIF. The simulation study demonstrated that both methods performed well in conditions with large number of groups, while they were significantly different from each other. When group size was large and the group mean abilities were equal, both methods would lead to highly accurate parameter estimates, and highly accurate DIF detection rate can be achieved by the alignment method. [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://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]