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Modeling Latent Information in Voting Data with Dirichlet Process Priors

  • Richard Traunmüller (a1), Andreas Murr (a2) and Jeff Gill (a3)


We apply a specialized Bayesian method that helps us deal with the methodological challenge of unobserved heterogeneity among immigrant voters. Our approach is based on generalized linear mixed Dirichlet models (GLMDMs) where random effects are specified semiparametrically using a Dirichlet process mixture prior that has been shown to account for unobserved grouping in the data. Such models are drawn from Bayesian nonparametrics to help overcome objections handling latent effects with strongly informed prior distributions. Using 2009 German voting data of immigrants, we show that for difficult problems of missing key covariates and unexplained heterogeneity this approach provides (1) overall improved model fit, (2) smaller standard errors on average, and (3) less bias from omitted variables. As a result, the GLMDM changed our substantive understanding of the factors affecting immigrants' turnout and vote choice. Once we account for unobserved heterogeneity among immigrant voters, whether a voter belongs to the first immigrant generation or not is much less important than the extant literature suggests. When looking at vote choice, we also found that an immigrant's degree of structural integration does not affect the vote in favor of the CDU/CSU, a party that is traditionally associated with restrictive immigration policy.


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Authors' note: The authors would like to thank the participants at this event, two anonymous referees, and the editors for helpful comments and remarks. Full replication materials for this study are available on the Political Analysis Web site at

A previous version of this article was presented at the 3rd Annual General Conference of the European Political Science Association 2013 in Barcelona.



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Antoniak, Charles E. 1974. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Annals of Statistics 2:1152–74.
Bartels, L. 1997. Specification uncertainty and model averaging. American Journal of Political Science 41:641–74.
Berk, R. A., Bruce, W., and Weiss, Robert E. 1995. Statistical inference for apparent populations. Sociological Methodology 25:421–58.
Bird, K., Saalfeld, T. L., and Wüst, A. eds, 2011. The political representation of immigrants and minorities. London: Routledge.
Birnbaum, A. 1962. On the foundations of statistical inference. Journal of the American Statistical Association 57:269306.
Blackwell, D., and MacQueen, J. B. 1973. Discreteness of Ferguson selections. Annals of Statistics 1:365–58.
Burr, D., and Doss, H. 2005. A Bayesian semi-parametric model for random effects meta-analysis. Journal of the American Statistical Association 100:242–51.
Dancygier, R., and Saunders, E. N. 2006. A new electorate? Comparing preferences and partisanship between immigrants and natives. American Journal of Political Science 50:962–81.
Dey, D. K., Ghosh, S. K., and Mallick, B. K. 2000. Generalized linear models: A Bayesian perspective. New York: Marcel Dekker.
Dorazio, R. M., Mukherjee, B., Zhang, L., Ghosh, M., Jelks, H. L., and Jordan, F. 2007. Modelling unobserved sources of heterogeneity in animal abundance using a Dirichlet process prior. Biometrics 64:635–44.
Dorfman, D. D., and Alf, E. Jr 1969. Maximum-likelihood estimation of parameters of signal-detection theory and determination of confidence intervals rating-method data. Journal of Mathematical Psychology 6:487–96.
Doss, Hani. 1994. Bayesian nonparametric estimation for incomplete data via successive substitution sampling. Annals of Statistics 22:1763–86.
Efron, Bradley. 1983. Estimating the error rate of a prediction rule: Improvement on cross-validation. Journal of the American Statistical Association 78:316–31.
Escobar, M. D., and West, M. 1995. Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association 90:577–88.
Fahrmeir, L., and Tutz, G. 2001. Multivariate statistical modelling based on generalized linear models. 2nd ed. New York: Springer.
Ferguson, T. S. 1973. A Bayesian analysis of some nonparametric problems. Annals of Statistics 1:209–30.
Fisher, R. A. 1922. On the mathematical foundations of theoretical statistics. Philosophical Transmissions of the Royal Statistical Society A 222:309–68.
Geisser, Seymour. 1975. The predictive sample reuse method with applications. Journal of the American Statistical Association 70:320–28.
Gelman, A., and Hill, J. 2007. Data analysis using regression and multilevel/hierarchical models. Cambridge, UK: Cambridge University Press.
Gill, Jeff. 2007. Bayesian methods for the social and behavioral sciences. 2nd ed. New York: Chapman & Hall.
Gill, Jeff. 2008. Is partial-dimension convergence a problem for inferences from MCMC algorithms? Political Analysis 16:153–78.
Gill, Jeff, and Casella, George. 2009. Nonparametric priors for ordinal Bayesian social science models: Specification and estimation. Journal of the American Statistical Association 104:453–64.
Heath, A. F., Fisher, S. D., Rosenblatt, G., Sanders, D., and Sobolewska, M. 2013. The political integration of ethnic minorities in Britain. Oxford: Oxford University Press.
Hill, Jennifer L., and Kriesi, Hanspeter. 2001. Classification by opinion-changing behavior: A mixture model approach. Political Analysis 9:301–24.
Hobert, J. P., and Marchev, D. 2008. A theoretical comparison of the data augmentation, marginal augmentation and PX-DA algorithms. Annals of Statistics 36:532–54.
Jiang, Jiming. 2007. Linear and generalized linear mixed models and their applications. New York: Springer-Verlag.
Korwar, R. M., and Hollander, M. 1973. Contributions to the theory of Dirichlet processes. Annals of Probability 1:705–11.
Kyung, M., Gill, J., and Casella, G. 2009. Characterizing the variance improvement in linear Dirichlet random effects models. Statistics and Probability Letters 79:2343–50.
Kyung, M., Gill, J., and Casella, G. 2010. Estimation in Dirichlet random effects models. Annals of Statistics 38:9791009.
Kyung, M., Gill, J., and Casella, G. 2011. New findings from terrorism data: Dirichlet process random effects models for latent groups. Journal of the Royal Statistical Society, Series C 60:701–21.
Kyung, M., Gill, J., and Casella, G. 2012. Sampling schemes for generalized linear Dirichlet process random effects models. Statistical Methods and Applications 20:259–90.
Leamer, E. E. 1978. Specification searches: Ad hoc inference with nonexperimental data. New York: John Wiley & Sons.
Liu, J. S. 1996. Nonparametric hierarchical Bayes via sequential imputations. Annals of Statistics 24:911–30.
Lo, A. Y. 1984. On a class of Bayesian nonparametric estimates: I. Density estimates. Annals of Statistics 12:351–57.
MacEachern, S. N., and Müller, P. 1998. Estimating mixture of Dirichlet process model. Journal of Computational and Graphical Statistics 7:223–38.
Martin, Andrew, and Quinn, Kevin. 2002. Dynamic ideal point estimation via Markov chain Monte Carlo for the U.S. Supreme Court, 1953–1999. Political Analysis 10:134–53.
McCullagh, P., and Neider, J. A. 1989. Generalized linear models. 2nd ed. New York: Chapman & Hall.
McCulloch, C. E., and Searle, S. R. 2001. Generalized, linear, and mixed models. New York: John Wiley & Sons.
Neal, R. M. 2000. Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics 9:249–65.
Neyman, Jerzy. 1937. Outline of a theory of statistical estimation based on the classical theory of probability. In A selection of early statistical papers, ed. Neyman, J., 250–90. Berkeley: University of California Press.
Pearson, Karl. 1920a. The fundamental problem of practical statistics. Biometrika 13(1): 116.
Pearson, Karl. 1920b. Note on the fundamental problem of practical statistics. Biometrika 13:300301.
Poirer, D. J. 1988. Frequentist and subjectivist perspectives on the problems of model building in economics. Journal of Economic Perspectives 2:121–44.
Quinn, Kevin M., Martin, Andrew, and Whitford, Andrew B. 1999. Voter choice in multi-party democracies: A test of competing theories and models. American Journal of Political Science 43:1231–47.
Rubin, Donald B., and Schenker, Nathaniel. 1987. Logit-based interval estimation for binomial data using the Jeffreys prior. Sociological Methodology 17:131–44.
Schweinberger, Michael, and Snijders, Tom A. B. 2003. Settings in social networks: A measurement model. Sociological Methodology 33:307–41.
Sethuraman, J. 1994. A constructive definition of Dirichlet priors. Statistica Sinica 4:639–50.
Smith, Alastair. 1999. Testing theories of strategic choice: The example of crisis escalation. American Journal of Political Science 43:1254–83.
Spirling, Arthur, and Quinn, Kevin. 2010. Identifying intraparty voting blocs in the U.K. House of Commons. Journal of the American Statistical Association 105:447–57.
Stegmueller, Daniel. 2013. Modeling dynamic preferences: A Bayesian robust dynamic latent ordered probit model. Political Analysis 21:314–33.
Teh, Y. W., Jordan, M. I., Beal, M. J., and Blei, D. M. 2006. Hierarchical Dirichlet processes. Journal of the American Statistical Association 101:1566–81.
Ward, Michael D., Greenhill, Brian D., and Bakke, Kristin M. 2010. The perils of policy by p-value: Predicting civil conflicts. Journal of Peace Research 47:113.
Western, Bruce. 1998. Causal heterogeneity in comparative research: A Bayesian hierarchical modelling approach. American Journal of Political Science 42:1233–59.
Western, Bruce. 1996. Vague theory and model uncertainty in macrosociology. Sociological Methodology 26:165–92.
Western, Bruce, and Jackman, Simon. 1994. Bayesian inference for comparative research. American Political Science Review 88:412–23.
Womack, Andrew, Gill, Jeff, and Casella, George. 2014. Product partitioned Dirichlet process prior models for identifying substantive clusters and fitted subclusters in social science data. Washington University Technical Paper.
Wüst, Andreas M. 2011. Dauerhaft oder temporär? Zur Bedeutung des Migrationshintergrunds für Wahlbeteiligung und Parteiwahl bei der Bundestagswahl 2009. Politische Vierteljahresschrift 45:157–78.
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Political Analysis
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