For equating tests that measure several distinct proficiencies, procedures that reflect the multidimensional structure of the data are needed. Although there exist a few equating procedures developed under the multidimensional item response theory (MIRT) framework, there is a need for further research in this area. Therefore, the primary objectives of this dissertation are to consolidate and expand MIRT observed score equating research with a specific focus on the common-item nonequivalent groups (CINEG) design, which requires scale linking. Content areas and item types are two focal points of dimensionality. This dissertation uses two studies with different data types and comparison criteria to address the research objectives. In general, a comparison between unidimensional item response theory (UIRT) and MIRT methods suggested a better performance of the MIRT methods over UIRT. The simple structure (SS) and full MIRT methods showed more accurate equating results compared to UIRT. In terms of calibration methods, concurrent calibration outperformed separate calibration for all equating methods under most of the studied conditions. [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/en-US/products/dissertations/individuals.shtml.]