Most computerized adaptive tests (CAT) have been studied under the framework of unidimensional item response theory. However, many psychological variables are multidimensional and might benefit from using a multidimensional approach to CAT. In addition, a number of psychological variables (e.g., quality of life, depression) can be conceptualized as being consistent with a bifactor model (Holzinger & Swineford, 1937) in which there is a general dimension and some number of subdomains with each item loading on only one of those domains. The present study extended the work on bifactor CAT of Weiss & Gibbons (2007) in comparison to a fully multidimensional bifactor method using multidimensional maximum likelihood [straight theta] estimation and Bayesian [straight theta] estimation for the bifactor model (MBICAT algorithm). Although Weiss and Gibbons applied the bifactor model to CAT (BICAT algorithm), their methods for item selection and scoring were based on unidimensional IRT methods. Therefore, this study investigated a fully multidimensional bifactor CAT algorithm using simulated data. The MBICAT algorithm was compared to two variations of the BICAT algorithm under three different conditions: different numbers of group factors, variations in the group factor discriminations, and trait ([straight theta]) estimation method. A fixed test length was used as the termination criterion for the CATs for Study 1. The accuracy of [theta hat] using the BICAT algorithm and the MBICAT algorithm was evaluated with the correlation between [straight thetas] and [theta hats], the root mean square error (RMSE), and the observed standard error (OSE). Two termination criteria (OSE = 0.50 and 0.55) were used to investigate efficiency of the MBICAT for Study 2. This study demonstrated that the MBICAT algorithm worked well when latent scores on the secondary dimensions were estimated properly. Although the MBICAT algorithm did not improve the accuracy and efficiency of the general factor scores compared to two the BICAT algorithms, MBICAT showed an improvement in the accuracy and efficiency for the group factors. In the two BICAT algorithms, the use of differential entry on the group factors, as in Weiss and Gibbons (2007), did not make a difference compared to initial item at [straight theta] of 0 for both the general factor and group factor scales (Gibbons, et al., 2008) in terms of accuracy and efficiency. [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.]