Many popular global model-data fit indices (GFIs), such as Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residuals (SRMSR) are proposed and widely used in the context of structural equation modeling (SEM) with continuous data. The proposed cutoffs of those indices are for continuous data, which are not directly applicable to categorical data (Xu et al., 2017; Xia, 2016; Maydeu-Olivares & Joe, 2014; Yu, 2002). Furthermore, the existing GFIs are developed and have been used with a limited information estimation approach, while a full information estimation approach is the most widely used estimation method in item response theory (IRT). Not many GFIs are available for categorical data when the full information IRT estimation is conducted (Maydeu-Olivares & Joe, 2014). When there is an effect of guessing, as far as previous literature was searched, there is no GFI that demonstrates good performance in detecting the model-data fit for the comparative evaluation of the two-parameter logistic (2PL) and the three-parameter logistic (3PL) models. In addition, there is a lack of studies that conduct a systematic full evaluation of those popular GFIs in the unidimensional IRT (UIRT) and multidimensional IRT (MIRT) modeling (Maydeu-Olivares & Joe, 2014; Xu et al., 2017). This study proposes descriptive GFIs using squared or absolute (raw or standardized) item response residuals from the whole item response data when an IRT model is estimated with the full information estimation. This study also compares the performances of the newly proposed GFIs with the existing GFIs in UIRT and MIRT modeling, especially the sensitivity of the indices in detecting the 2PL and the 3PL model fitting when data are contaminated with examinee guessing. As a secondary interest, Akaike's Information Criterion (AIC), Bayesian Information Criterion (BIC), and M2 test are also included in the comparisons. The newly proposed RI.R2s, residual variation reduction index based on the absolute residual summary for standardized residuals, showed the best performance in distinguishing the 3PL and the 2PL model fitting in unidimensional and multidimensional data, which contained test-taker guessing. [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.]