Title: On Model-Selection and Applications of Multilevel Models in Survey and Causal Inference
Description: This thesis includes three parts. The overarching theme is how to analyze multilevel structured datasets, particularly in the areas of survey and causal inference. The first part discusses model selection of hierarchical models, in the context of a national political survey. I found that the commonly used model selection criteria based on predictive accuracy, such as cross validation, don't perform very well in the case of political survey and explore the possible causes. The second part centers around a unique data set on the presidential election collected through an online platform. I show that with adequate modeling, meaningful and highly accurate information could be extracted from this highly-biased data set. The third part builds on a formal causal inference framework for group-structured data, such as meta-analysis and multi-site trials. In particular, I develop a Gaussian Process model under this framework and demonstrate additional insights that can be gained compared with traditional parametric models.