Hierarchical data is often observed in education data. Analyzing such data with Multilevel Modeling becomes crucial to understanding the relationship at the individual and group levels. However, one of the most significant problems with this kind of data is small sample sizes and very low Intraclass Correlations. The multivariate Latent Covariate Model is often accepted as the gold standard for analyzing hierarchically structured data. However, previous studies showed that this model did not work very well under the abovementioned conditions. This dissertation aimed to address two research questions around this situation. The first research question intended to show how the Multilevel Latent Covariate Model worked under these conditions via a simulation study and a real data application. The second research question suggested six new candidate models as an alternative to the Multilevel Latent Covariate Model. The performances of all candidate models were assessed using the same simulation study and the real data application. Raw bias, Root Mean Squared Error, Standard Error Ratio, Type 1 error rate, and Power were used to compare the feasibility of the candidate models while analyzing the multilevel data with low intraclass correlation and very small level-1 sample sizes. The results showed that the alternative candidate models outperformed the gold standard. [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.]