Tree-Based Models for Political Science Data

Political scientists often find themselves analyzing data sets with a large number of observations, a large number of variables, or both. Yet, traditional statistical techniques fail to take full advantage of the opportunities inherent in “big data,” as they are too rigid to recover nonlinearities and do not facilitate the easy exploration of interactions in high-dimensional data sets. In this article, we introduce a family of tree-based nonparametric techniques that may, in some circumstances, be more appropriate than traditional methods for confronting these data challenges. In particular, tree models are very effective for detecting nonlinearities and interactions, even in data sets with many (potentially irrelevant) covariates. We introduce the basic logic of tree-based models, provide an overview of the most prominent methods in the literature, and conduct three analyses that illustrate how the methods can be implemented while highlighting both their advantages and limitations. Replication Materials: The data, code, and any additional materials required to replicate all analyses in this article are available on the American Journal of Political Science Dataverse within the Harvard Dataverse Network at: https://doi.org/10.7910/DVN/8ZJBLI. Social science scholars often work with data sets containing a large number of observations, many potential covariates, or (increasingly) both. Indeed, political scientists now regularly analyze data with levels of complexity unimaginable just two decades ago. Widely used surveys, for instance, interview tens of thousands of respondents about hundreds of topics. Scholars of institutions can quickly assemble data sets with thousands of observations using resources like the Comparative Agendas Project. Moreover, new measurement methods, such as text analysis, have combined with data sources, such as Twitter, to generate databases of almost unmanageable sizes. It is clear that political science, like all areas of the social sciences, will increasingly have access to a deluge of data so vast that it will dwarf everything that has come before. What statistical methods are needed in this datasaturated world? Surely, there is no one correct answer. Yet, just as surely, traditional statistical models are not always equipped to take full advantage of new data sources. Traditional models—largely variants of linear regressions—are ideal for evaluating theories that imply specific functional forms relating outcomes to predictors. In particular, they excel in their ability to leverage assumptions about the data-generating process, or DGP (additivity, linearity in the parameters, homoskedasticity, Jacob M. Montgomery is Associate Professor, Department of Political Science, Washington University in St. Louis, Campus Box 1063, One Brookings Drive, St. Louis, MO 63130 (jacob.montgomery@wustl.edu). Santiago Olivella is Assistant Professor, Department of Political Science, University of North Carolina at Chapel Hill, Hamilton Hall 361, CB 3265, Chapel Hill, NC 27599 (olivella@unc.edu). etc.) to make valid inferences despite inherent data limitations. Although appropriate when testing theories that conform with these assumptions, standard models are often insufficiently flexible to capture nuances in the data—such as complex nonlinear functional forms and deep interactions—when no clear a priori expectations exist. In this article, we introduce a family of tree-based nonparametric techniques from the machine learning literature. We argue that, under specific circumstances, regression and classification tree models are an appropriate standard choice for analyzing high-dimensional data sets. In particular, past research has shown tree-based methods to be very useful for making accurate predictions when the underlying DGP includes nonlinearities, discontinuities, and interactions among many covariates. Further, tree models require few assumptions. Rather than imposing a presumed structure on the DGP, tree-based methods allow the data to “speak for themselves. ” Thus, our goal in this article is to introduce political scientists to this promising family of methods, which are well suited for today’s data analysis demands. In the next sections, we discuss the promise and perils of high-dimensional, “large”-N data sets and introduce the basic logic of tree models. We then provide an overview of the most prominent methods in the literature. American Journal of Political Science, Vol. 62, No. 3, July 2018, Pp. 729–744 C ©2018, Midwest Political Science Association DOI: 10.1111/ajps.12361