Visualizing Democracy Using Covariate-Adjusted Principal Curves
 

Abstract: A common task in data analysis in social science is to quantify and visually present the potentially non-linear relationship between a set of variables that lack a clear causal or temporal ordering. Principal curves provide one solution by drawing a single smooth curve that runs through the middle of the entire distribution of the data. However, it is often the case that the relationship between the variables differs based on known moderators. Therefore, allowing the curve to vary based on those covariates is crucial to accurately representing the underlying relationship. We propose “covariate-adjusted principal curves” to allow for an arbitrary number of moderators to affect the shape of the curve. Our method extends classic methods for fitting principal curves (e.g. splines) to their covariate-adjusted analogues (e.g. varying-coefficient models).
Our motivating application is the empirical study of democracy. Using an influential existing study, we demonstrate that the relationship between two major dimensions of democracy (contestation and participation) has changed dramatically over the past two centuries---even when adjusting for other moderators such as colonial history and national income. Existing techniques for quantifying the changing relationship, e.g. correlations based on splitting the data into discrete time periods, falls short at illustrating this shift.

Bio: Max Goplerud is an Assistant Professor of Political Science. His primary research creates new methods to facilitate political science research by leveraging the intersection of Bayesian methods and machine learning. These methods are focused on topics such as heterogeneous effects, hierarchical models, and ideal point estimation. He also is interested in understanding legislative behavior using text-as-data in a comparative context including studies on Europe, the United States, and Japan. He received his PhD from the Department of Government at Harvard University in 2020.

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