Item response theory (IRT) has gained an increasing popularity in large-scale educational and psychological testing situations because of its theoretical advantages over classical test theory. Unidimensional graded response models (GRMs) are useful when polytomous response items are designed to measure a unified latent trait. They are limited in practical instances where the test structure is not readily available or items are not necessarily measuring the same underlying trait. To overcome the problem, this dissertation proposes a multi-unidimensional normal ogive GRM under the fully Bayesian framework via the use of Markov chain Monte Carlo (MCMC). The performance of the proposed model was evaluated using the Monte Carlo simulations. It was further compared with conventional GRMs under simulated and real test situations. Results from simulation studies as well as a real data example suggest that (1) the proposed MCMC method for the proposed model provides fairly accurate and efficient parameter estimates, including correlations between latent dimensions, (2) compared with the conventional IRT models, the proposed model consistently performs well, if not better as far as the model-data fit is concerned. Therefore, the proposed multi-unidimensional model offers generosity, flexibility, and a better way to represent test situations when the latent dimensionality is not a priori clear or more than one latent trait is involved. In addition, the proposed model is not limited to tests in educational and psychological measurement. Instead, it can be applied to other disciplines, such as business and medicine, where Likert-type items are adopted in an instrument. [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.]