Multidimensional Item Response Theory (MIRT) has been widely used in educational and psychological assessments. It estimates multiple constructs simultaneously and models the correlations among latent constructs. While it provides more accurate results, the unidimensional IRT model is still dominant in real applications. One major reason is that the parameter estimation is still challenging because of intractable multidimensional integrals of the likelihood, especially in high dimensions. Several algorithms have been proposed to address the issue, such as adaptive Gaussian quadrature methods, Laplace approximations, and stochastic methods. However, the state-of-the-art algorithms are still time-consuming, especially when the number of latent traits exceeds 5. Recently, the Gaussian variational Expectation Maximization (GVEM) algorithm (Cho et al., 2021) was proposed as an alternative for further improving computational efficiency and estimation accuracy. The general framework allows the closed-form solutions for the expectation-maximization process by introducing a variational lower bound of the likelihood function. Although prior studies have demonstrated the superiority of the GVEM algorithm over the widely used Metropolis-Hastings Robbins-Monro algorithm (MH-RM) under various conditions, its performance across diverse practical contexts remains relatively unexplored. For instance, there is an immense need for further investigation into the robustness of the GVEM framework across various missing data scenarios. Additionally, efforts should be directed towards devising methods for estimating standard errors within the GVEM framework. Moreover, the development of an R package to facilitate the application of the GVEM algorithm would significantly augment its accessibility and utility. The purpose of this dissertation is to extend the applicability of the GVEM algorithm and investigate its performance in diverse scenarios. In the second chapter, a modified GVEM algorithm was proposed by adding the bootstrap bias correction step and denoted it as GVEM-BS. A series of simulation studies and real data analysis were conducted to compare GVEM-BS to MH-RM in terms of estimation precision under different missing data scenarios and assessment designs. The results demonstrated the robustness and precision of GVEMBS in the context of high missing proportions, especially for missing at completely random conditions. When applying the two methods to different assessment designs, both GVEM-BS and MH-RM yielded comparable results. In the third chapter, an updated supplemented expectation maximization (USEM) method and a bootstrap method were proposed for GVEM-based SE estimation. These two methods were compared in terms of SE recovery accuracy. The simulation results demonstrated that the GVEM algorithm with bootstrap and item priors (GVEM-BSP) outperformed the other methods, exhibiting less bias and relative bias for SE estimates under most conditions. Although the GVEM with USEM (GVEM-USEM) was the computationally most efficient method, it yielded an upward bias for SE estimates. In the fourth chapter, an R package, VEMIRT, was introduced by offering users efficient computational tools tailored for high-dimensional data under the GVEM framework. This package facilitates both exploratory and confirmatory analyses through the utilization of GVEM models. Additionally, it enables users to compute standard errors of item parameters and implement corrections such as bootstrap sampling and importance sampling, thereby enhancing the accuracy of estimations. [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.]