When measuring latent constructs, for example, language ability, we use statistical models to specify appropriate relationships between the latent construct and observe responses to test items. These models rely on theoretical assumptions to ensure accurate parameter estimates for valid inferences based on the test results. This dissertation specifically concerned the local independence (LI) assumption (or presence of local dependence (LD) equivalently) in two specific item response theory (IRT) models -- the partial credit model (PCM) and the generalized partial credit model (GPCM). With a primary focus on several commonly used global fit indices (GFIs), this study investigated how parameter estimates in the studied IRT models were affected by varying degrees of LD, whether the studied GFIs were responsive to model misspecifications due to LD, and any insights regarding making reasonable decisions in terms of good-fit models. The results revealed that, first, parameter estimates in both the PCM and GPCM were severely biased, especially the latent trait and item step parameter estimates. The degree of biases increased with higher levels of LD across different model and data conditions. Other general factors, including the test length and number of item response categories, could also impact biases in parameter estimates. Second, all studied GFIs were responsive to model misfit caused by the presence of LD. Specifically, studied GFIs exhibited moderate to strong associations with biases of the latent trait estimates in expected directions. Lastly, based on the performance of the studied GFIs under baseline and LD-induced conditions, the absolute fit indices (RMSEA and SRMSR) appeared to be more informative than the incremental fit indices (CFI and TLI) in assessing the global fit of the PCM and GPCM. This study provides insights into adopting specific decision criteria of good model fit under various model and data conditions, aiming to reduce potential false positive rates while maintaining reasonable true positive rates. [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.]