In Huggins-Manley & Han (2017), it was shown that WLSMV global model fit indices used in structural equating modeling practice are sensitive to person parameter estimate RMSE and item difficulty parameter estimate RMSE that results from local dependence in 2-PL IRT models, particularly when conditioning on number of test items and sample size. However, the fit indices were insensitive to RMSE in item discrimination parameter estimates under particular conditions of local independence, causing issues for using them in IRT practice. Huggins-Manley and Han (2017) hypothesized that using these fit indices to evaluate local independence may be more appropriate in Rasch models, but they did not test this hypothesis. The purpose of this study is to evaluate the sensitivity of WLSMV global fit indices to violations of local independence in Rasch models, particularly violations that result in inaccurate person and item parameter estimates. If these fit indices are appropriately sensitive to these assumption concerns of Rasch models, then they would provide practitioners with a simple method for evaluating the degree to which assumption violation is problematic for their data analysis purpose. [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.]