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Mixing Methods: A Bayesian Approach


We develop an approach to multimethod research that generates joint learning from quantitative and qualitative evidence. The framework—Bayesian integration of quantitative and qualitative data (BIQQ)—allows researchers to draw causal inferences from combinations of correlational (cross-case) and process-level (within-case) observations, given prior beliefs about causal effects, assignment propensities, and the informativeness of different kinds of causal-process evidence. In addition to posterior estimates of causal effects, the framework yields updating on the analytical assumptions underlying correlational analysis and process tracing. We illustrate the BIQQ approach with two applications to substantive issues that have received significant quantitative and qualitative treatment in political science: the origins of electoral systems and the causes of civil war. Finally, we demonstrate how the framework can yield guidance on multimethod research design, presenting results on the optimal combinations of qualitative and quantitative data collection under different research conditions.

Corresponding author
Macartan Humphreys is Professor, Department of Political Science, Columbia University, New York (
Alan M. Jacobs is Associate Professor, Department of Political Science, University of British Columbia, Vancouver, Canada (
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Barton Allen H., and Lazarsfeld Paul F.. 1955. Some Functions of Qualitative Analysis in Social Research. Vol. 181. Bobbs Merrill Indianapolis, Indiana.
Beach Derek, and Pedersen Rasmus Brun. 2013. Process-Tracing Methods: Foundations and Guidelines. Ann Arbor: University of Michigan Press.
Beck Nathaniel. 2010. “Causal Process ‘Observation’: Oxymoron or (Fine) Old Wine.” Political Analysis 18 (4): 499505.
Bennett Andrew. 2008. “Process Tracing. A Bayesian Perspective.” In The Oxford Handbook of Political Methodology, eds. Box-Steffensmeier Janet M., Brady Henry E., and Collier David. Oxford, UK: Oxford University Press.
Bennett Andrew. 2010. “Process Tracing and Causal Inference.” In Rethinking Social Inquiry: Diverse Tools, Shared Standards, eds. Collier David and Brady Henry E.. Lanham, MD: Rowman & Littlefield, 207–20.
Bennett Andrew. 2015. “Appendix.” In Process Tracing: From Metaphor to Analytic Tool, eds. Bennett Andrew and Checkel Jeffrey. New York: Cambridge University Press, 276–98.
Boix Carles. 1999. “Setting the Rules of the Game: The Choice of Electoral Systems in Advanced Democracies.” The American Political Science Review 93 (3): 609–24.
Brady H. E., and Collier D.. 2004. Rethinking Social Inquiriy: Diverse Tools, Shared Standards. Lanham, MD: Rowman & Littlefield.
Chickering David Maxwell, and Pearl Judea. 1996. “A Clinician’s Tool for Analyzing Non-Compliance.” In Proceedings of the National Conference on Artificial Intelligence. Palo Alto, California: Association for the Advancement of Artificial Intelligence (AAAI), pp. 1269–76.
Collier David. 2011. “Understanding Process Tracing.” PS: Political Science and Politics 44 (04): 823–30.
Collier David, Brady Henry E., and Seawright Jason. 2004. “Sources of Leverage in Causal Inference: Toward an Alternative View of Methodology.” In Rethinking Social Inquiry: Diverse Tools, Shared Standards, edited by Collier David and Brady Henry E. Lanham, MD: Rowman & Littlefield, 229–66.
Collier David, Brady Henry E., and Seawright Jason. 2010. “Sources of Leverage in Causal Inference: Toward an Alternative View of Methodology.” In Rethinking Social Inquiry: Diverse Tools, Shared Standards, eds. Collier David and Brady Henry E.. Lanham, MD: Rowman & Littlefield, 161200.
Collier P., and Sambanis N.. 2005. Understanding Civil War: Africa. Washington, D.C.: Stand Alone Series World Bank.
Collier Paul, and Hoeffler Anke. 2004. “Greed and Grievance in Civil War.” Oxford Economic Papers 56 (4): 563–95.
Creswell J. W., and Garrett Amanda L.. 2008. “The ‘Movement’ of Mixed Methods Research and the Role of Educators.” South African Journal of Education 28 (08/2008): 321–33.
Ericson William A. 1969. “Subjective Bayesian Models in Sampling Finite Populations.” Journal of the Royal Statistical Society. Series B (Methodological) 31: 195224.
Fairfield Tasha. 2013. “Going Where the Money Is: Strategies for Taxing Economic Elites in Unequal Democracies.” World Development 47 (221–236): 4257.
Freedman David A. 2010. “On Types of Scientific Inquiry: The Role of Qualitative Reasoning.” In Rethinking Social Inquiry: Diverse Tools, Shared Standards, eds. Collier David and Brady Henry E.. Lanham, MD: Rowman & Littlefield, 251–73.
Gelman Andrew, Carlin John B., Stern Hal S., Dunson David B., Vehtari Aki, and Rubin Donald B.. 2013. Bayesian Data Analysis. Boca Raton, FL: CRC Press.
Gerber Alan S., Green Donald P., and Kaplan Edward H.. 2004. “The Illusion of Learning from Observational Research.” In Problems and Methods in the Study of Politics, ed. Shapiro Ian, Smith Rogers M., and Masoud Tarek E.. Cambridge, UK: Cambridge University Press.
Gerring J. 2012. Social Science Methodology: A Unified Framework. Strategies for Social Inquiry. Cambridge, UK: Cambridge University Press.
Gill Jeff, and Walker Lee D.. 2005. “Elicited Priors for Bayesian Model Specifications in Political Science Research.” Journal of Politics 67 (3): 841–72.
Glynn Adam N., Wakefield Jon, Handcock Mark S., and Richardson Thomas S.. 2008. “Alleviating Linear Ecological Bias and Optimal Design with Subsample Data.” Journal of the Royal Statistical Society: Series A (Statistics in Society) 171 (1): 179202.
Glynn Adam N., and Quinn Kevin M.. 2011. “Why Process Matters for Causal Inference.” Political Analysis 19: 273–86.
Glynn Adam N., and Ichino Nahomi. 2014. “Using Qualitative Information to Improve Causal Inference.” American Journal of Political Science 59 (4): 1055–71.
Goertz G., and Mahoney J.. 2012. Tale of Two Cultures - Contrasting Qualitative and Quantitative. Princeton: University Press Group Limited.
Gordon Sanford C., and Smith Alastair. 2004. “Quantitative Leverage Through Qualitative Knowledge: Augmenting the Statistical Analysis of Complex Causes.” Political Analysis 12 (3): 233–55.
Hall Peter A. 2003. “Aligning Ontology and Methodology in Comparative Research.” In Comparative Historical Analysis in the Social Sciences, ed. Mahoney James and Rueschemeyer Dietrich. Cambridge, UK and New York: Cambridge University Press.
Herron Michael, and Quinn Kevin. 2009. “A Careful Look at Modern Case Selection Methods.” Paper Presented at the 67th Annual Meeting of the Midwest Political Science Association.
Imbens Guido W., and Rubin Donald B.. 1997. “Bayesian Inference for Causal Effects in Randomized Experiments with Noncompliance.” The Annals of Statistics 25 (1): 305–27.
King G., Keohane R. O., and Verba S.. 1994. Designing Social Inquiry: Scientific Inference in Qualitative Research. Princeton, NJ: Princeton University Press.
Kreuzer Marcus. 2010. “Historical Knowledge and Quantitative Analysis: The Case of the Origins of Proportional Representation.” American Political Science Review 104 (5): 369–92.
Lengfelder Christina. 2012. “Triangular Development Cooperation: How Emerging Powers Change the Landscape of Development Cooperation.” Ph.D. dissertation, Universidad Catolica de Chile.
Lieberman E. S. 2003. Race and Regionalism in the Politics of Taxation in Brazil and South Africa. Cambridge Studies in Comparative Politics. Cambridge, UK: Cambridge University Press.
Lieberman Evan S. 2005. “Nested Analysis as a Mixed-Method Strategy for Comparative Research.” American Political Science Review 99 (7): 435–52.
Mahoney James. 2012. “The Logic of Process Tracing Tests in the Social Sciences.” Sociological Methods and Research 41 (4): 570–97.
Paluck Elizabeth Levy. 2010. “The Promising Integration of Qualitative Methods and Field Experiments.” The ANNALS of the American Academy of Political and Social Science 628 (1): 5971.
Pearl Judea. 2000. Causality: Models, Reasoning and Inference. Vol. 29. Cambridge, UK: Cambridge University Press.
Rohlfing Ingo. 2012. Case Studies and Causal Inference: An Integrative Framework. Research Methods Series. New York: Palgrave Macmillan.
Ross Michael L. 2004. “How do Natural Resources Influence Civil War? Evidence from Thirteen Cases.” International Organization 58 (01): 3567.
Rubin Donald B. 1974. “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies.” Journal of Educational Psychology 66: 688701.
Schlag Karl H., Tremewan James, and Van der Weele Joel J.. 2013. “A Penny for Your Thoughts: A Survey of Methods for Eliciting Beliefs.” Experimental Economics: 1–34.
Seawright Jason. ND. Multi-method Social Science: Combining Qualitative and Quantitative Tools. Cambridge, UK: Cambridge, Cambridge University Press.
Seawright Jason, and Gerring John. 2008. “Case Selection Techniques in Case Study Research: A Menu of Qualitative and Quantitative Options.” Political Research Quarterly 61 (2): 294308.
Stan Development Team. 2014. “RStan: the R interface to Stan, Version 2.5.0.”
Stokes S.C. 2001. Mandates and Democracy: Neoliberalism by Surprise in Latin America. Cambridge Studies in Comparative Politics Cambridge University Press. Cambridge, UK: Cambridge University Press.
Swank D. 2002. Global Capital, Political Institutions, and Policy Change in Developed Welfare States. Cambridge Studies in Comparative Politics Cambridge University Press. Cambridge, UK: Cambridge University Press.
Van Evera Stephen. 1997. Guide to Methods for Students of Political Science. Ithaca, NY: Cornell University Press.
Western Bruce, and Jackman Simon. 1994. “Bayesian Inference for Comparative Research.” American Political Science Review 88 (6): 412–23.
White Howard, and Philips Daniel. 2012. “Addressing Attribution of Cause and Effect in Small N Impact Evaluations: Towards an Integrated Framework.” Technical Report 15 International Initiative for Impact Evaluation Working Papers.
Williamson Jon. 2004. “Bayesian Nets and Causality: Philosophical and Computational Foundations.” Oxford, UK: Oxford University Press.
Young Forrest W. 1981. “Quantitative Analysis of Qualitative Data.” Psychometrika 46 (4): 357–88.
Zaks Sherry. 2013. “Relationships Among Rivals: Contending Hypotheses and the Logic of Process Tracing.” Paper prepared for the Short Course 1 on Multi-Method Research, 2012 Annual Meeting of the American Political Science Association, New Orleans, LA.
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Supplementary materials

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