Methodology

Columbia University has played a unique role in the development of the subfield of political methodology. The landmark quantitative study of voting behavior by Paul F. Lazarsfeld and colleagues took place at Columbia. The effort to collect and make available congressional roll call vote data for quantitative analysis--one of the most important data sets in the discipline of political science--began at Columbia.

The long tradition of quantitative methods at Columbia has been balanced with an equally influential tradition of qualitative research, particularly with respect to area studies. Starting in the 1990's, the Department of Political Science undertook a concerted effort to advance its strengths in the rapidly developing subfield of political methodology. This effort has resulted in the formation of a group of notable faculty who have been central figures in the subfield. This group includes Robert Erikson and Robert Shapiro, who helped to pioneer the use of quantitative methods to study political behavior; Andrew Gelman, who received the prestigious Council of Presidents of Statistical Societies award for outstanding contributions by a person under the age of 40; and Donald P. Green, one of the most influential political scientists with respect to field experiments and causal inference.

The faculty offer a rich and diverse set of courses in quantitative and qualitative methodology that draws on their research contributions and offers comprehensive training for students at both the undergraduate and graduate levels.

In formal modeling and statistical methods, there are two tracks, one that assumes no specific mathematical background and one that assumes students have a basic level of mathematical training in calculus, linear algebra and methods of proof. Students who wish to take the mathematical courses but lack the training can take Political Science 4700 in their first semester. The core courses are listed below. Those with an * are courses that assume students have a strong math background (i.e., have taken GU4700 or its equivalent).

Core Methods Courses in the Department of Political Science

POLS GU4700  Mathematical Methods for Political Science

Provides students in political science with a basic set of tools needed to read, evaluate, and contribute in research areas that increasingly utilize sophisticated mathematical techniques.

POLS GU4764  Design & Analysis of Sample Surveys

[Prerequisites: Basic statistics and regression analysis, such as POLS GU4712, STAT 2024 or 4315, SOCI 4075]

Survey sampling is central to modern social science. We discuss how to design, conduct, and analyze surveys, with a particular focus on public opinion surveys in the United States.

POLS GU4768  Experimental Research: Design, Analysis & Interpretation

[Prerequisites: basic statistics and regression analysis, such as POLS GU4712, STAT 2024 or 4315, SOCI 4075]

In this course, we will discuss the logic of experimentation, its strengths and weaknesses compared to other methodologies, and the ways in which experimentation has been –and could be –used to investigate social phenomena. Students will learn how to interpret, design, and execute experiments.

POLS GU4710 Quantitative Political Research

Introduction to the use of quantitative techniques in political science and public policy. Topics include descriptive statistics and principles of statistical inference and probability through analysis of variance and ordinary least-squares regression. Computer applications are emphasized.

POLS GU4712 Analysis of Political Data

[Prerequisite: POLS GU4710 or the equivalent]

Multivariate and time-series analysis of political data. Topics include time-series regression, structural equation models, factor analysis, and other special topics. Computer applications are emphasized.

*POLS GU4714 Multivariate Political Analysis

[Prerequisite: basic data analysis and knowledge of basic calculus and matrix algebra OR concurrent enrollment in POLS GU4700]

Examines problems encountered in multivariate analysis of cross-sectional and time-series data. Covers fundamentals of probability and statistics and examines problems encountered in multivariate analysis of cross-sectional and time-series data. More mathematical treatment of topics covered in POLS GU4710 and GU4712.

*POLS GU4790 Advanced Topics in Quantitative Research

This course covers methods for empirical models that have dependent variables that are not continuous, including dichotomous and polychotomous response models, models for censored and truncated data, sample selection models and duration models.

POLS GU4792 Advanced Topics in Quantitative Research: Models for Panel and Time Series-Series Cross-Section Data

This course covers methods for making inferences with repeated observations data, focusing mostly on the theory and estimation of models for panel and time-series cross-section data.  Topics covered include fixed effects, random effects, differences-in-differences models, dynamic panel models, random coefficient models, models for qualitative dependent variables, and panel attrition.

STAT UN4330 Applied Regression and Multilevel Models

A second course in regression. First third of the course covers applied linear regression, logistic regression, and generalized linear models, focusing on practical data analysis and computation. Rest of the course covers multilevel regression. Examples from social sciences and public health. Computation in R and Bugs. The course will be jointly offered with Bayesian data analysis (see below), since we are teaching regression from a Bayesian perspective. Students registered for this course will be expected to have a more applied focus.

POLS GU4730 Game Theory and Political Theory

[Prerequisites: POLS GU4700 or equivalent level of calculus]

Introduction to the application of noncooperative game theory to strategic situations in politics. Topics include solution concepts, asymmetric information, repeated games, and folk theorems.

*POLS GU4732  Research Topics in Game Theory

[Prerequisite: POLS GU4730 or the instructor’s permission]

Covers repeated games, games of incomplete information and principal-agent models with applications to voting, bargaining, lobbying and conflict. Results from social choice theory, mechanism design and auction theory will also be treated. The course will concentrate on mathematical techniques for constructing and solving games. Students will be required to develop a research paper.

STAT GR6102/6104  Statistical Modelling for Data Analysis

[Prerequisite: STAT GR6101 or the instructor’s permission]

We will cover Bayesian data analysis--modeling, inference, computing, and model checking. Computation in R. The course will be jointly offered with applied regression and multilevel models, since we will focus on regression models. Registered students will be expected to have a more mathematical focus.

See here for sample course sequences in methodology
 

Methodology Resources

Methods Workshop

Graduate Student Organizers: Kolby Hanson (krh2137), Erik York (eay2109)

The Columbia Political Science Methods Workshop is a graduate student led series introducing various applied statistical methods and topics in statistical computing. Our primary constituency is comprised of PhD students and faculty in the political science department at Columbia. The workshop meets approximately twice a month and covers topics as varied as experimental methods, causal inference, regression discontinuity, Bayesian statistics, process tracing, networks, machine learning, and best practices in statistical computing. To learn more about the workshop, including information about current and past sessions, please visit the workshop website at http://cupsmethods.wordpress.com/ or contact one of the Graduate Student Organizers.

The Columbia Applied Statistics Center is involved with many political science projects. Its research is supported by the National Science Foundation, Institute of Education Sciences, National Security Agency, National Institutes of Health, and Department of Energy. The center runs a "playroom" in the department that normally meets two afternoons per week and serves as a forum for presenting and discussing work in progress.

Columbia University Libraries provides a gateway to its extensive data holdings on its GIS & Statistical Data Resources page.  

American National Election Studies

Roper Center

Pew Research Center