Advanced Multivariate Analysis

The course begins with a review of core concepts in quantitative analysis, including Monte Carlo simulation, the logic of inference, and the assumptions and diagnostics of linear regression models. It then extends the linear model to include categorical predictors, interactions, and conditional hypotheses, before introducing Generalized Linear Models such as logistic regression for binary outcomes, Poisson and Negative Binomial models for count data, and models for proportions. Attention is then given to model comparison and predictive validation. The second part of the course focuses on advanced approaches, covering multilevel and hierarchical models (random intercepts, random slopes, and cross-classified structures), longitudinal and panel data analysis, and applications in political and social science. The final part of the course introduces Bayesian methods, including Bayesian multilevel modeling. The course concludes with frontier topics such as text-as-data methods, regularization and penalized regression (ridge, LASSO, elastic net), nonparametric and semi-parametric methods (kernel regression and generalized additive models), and an bridge to machine learning approaches relevant for social science applications.