Graduate Methods Curriculum

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 should take POLS GU4700, Mathematical Methods for Political Science, in their first semester. 

Methods courses and resources

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 rely on mathematical techniques.

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]

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 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 focuses on mathematical techniques for constructing and solving games. Students will be required to develop a research paper.

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. Instruction in 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]

Instruction in 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 learn how to interpret, design, and execute experiments.

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

STAT GR6102/6104  Statistical Modeling for Data Analysis

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

Covers Bayesian data analysis--modeling, inference, computing, and model checking. Computation in R. The course is jointly offered with applied regression and multilevel models (STAT UN4330), since it focuses on regression models. Registered students will be expected to have a more mathematical focus.

The research tool requirement for the M.A. degree in both the one-year M.A. program and the Ph.D. program may be fulfilled by completing with an average grade of at least B one of the approved two-course sequences listed below.

The second research tool requirement for the M.Phil. may be fulfilled by completing a second two-course sequence with an average grade of at least B.

Courses taken to fulfill the research tool requirement can count toward the eight courses required for the degree.

For Ph.D. students, methods courses completed in fulfillment of the research tool requirement simultaneously fulfill the one-course requirement for the M.Phil., but they may not count toward the four-course requirement for those completing quantitative methods as a minor subfield.

Two-course sequences for the research tool requirement
Quantitative analysis
  • POLS GU4710 and GU4712 (Quantitative Political Research and Analysis of Political Data)
  • POLS GU4710 and GU4714 (Quantitative Political Research and Multivariate Political Analysis)
  • POLS GU4710 and GU4730 (Quantitative Political Research and Game Theory & Political Theory)
  • POLS GU4714 and GU4790 (Multivariate Political Research and Advanced Topics in Quantitative Research)
  • POLS GU4764 (Design & Analysis of Sample Surveys) and any above 4000-level quantitative courses 
  • POLS GU4768 (Experimental Research) and any above 4000-level quantitative courses
Formal modeling
  • POLS GU4730 and GU4732 (Game Theory & Political Theory and Research Topics in Game Theory)
  • POLS GU4700 and GU4730 (Mathematical Methods for Political Science and Game Theory & Political Theory)
Qualitative Methodology

A qualitative methodology course may be combined with any quantitative or formal modeling course numbered 4710 or higher with an average grade of B or better.

  • POLS GU4702 (Methods of Inquiry and Research Design)
  • POLS GR4780 (Qualitative & Interpretative Methods in Political Science)
  • SOC GR6091 (Historical Method & Documentary Analysis)
  • Or an alternative approved by the Director of Graduate Studies

The minor in quantitative methods is intended for political science doctoral students whose research plans call for a strong background in statistics or mathematical modeling. The minor will usually include four or more courses in statistical or formal methods taught at the graduate level. Students may take graduate level courses in the Departments of Economics, Sociology, and Statistics or in the Business School.

Students pursuing the minor should submit for approval by the Methods Coordinator or Director of Graduate Studies an application containing the following

  • A proposal for a particular course of study
  • A statement of research plans
  • The names of at least two faculty members, which may include one outside the Department of Political Science, who have agreed to serve as advisers and examiners

After the completion of all coursework, the student will submit and defend a research paper before a committee of three faculty members. The paper must demonstrate ability to deploy advanced quantitative methods and/or mathematical modeling in service of substantive research in political science.

Successful defense of the methods paper and the maintenance of a 3.0 average in the quantitative courses taken for the minor will determine whether the student has successfully completed the minor in quantitative methods.

The exam paper may not be used for seminar credit in any other course, nor may it be used to fulfill the Mini-APSA requirement.

No course taken in fulfillment of the research tool requirement may count toward any part of the minor in quantitative methods, and no course taken in fulfillment of the minor in quantitative methods may count toward the research tool requirement

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

The Columbia Political Science Methods Workshop is a series led by graduate students that introduces applied statistical methods and topics in statistical computing. The workshop's primary constituency is Ph.D. students and faculty in the political science department at Columbia. The workshop meets approximately twice each month and addresses topics such 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 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