Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-23T21:43:48.683Z Has data issue: false hasContentIssue false
  • English
  • Français

Modeling Latent Information in Voting Data with Dirichlet Process Priors

Published online by Cambridge University Press:  04 January 2017

Richard Traunmüller ,
Andreas Murr  and
Jeff Gill
Richard Traunmüller
Affiliation:
Department of Social Sciences, Goethe University Frankfurt, Frankfurt am Main, D-60323, Germany, e-mail: [email protected]
Andreas Murr
Affiliation:
Department of Politics and International Relations, University of Oxford, Oxford, OX1 3UQ, United Kingdom, e-mail: [email protected]
Jeff Gill*
Affiliation:
Departments of Political Science, Biostatistics, and Surgery, Washington University, St. Louis, MO 63130-4899, United States
*
e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
Political Analysis , Volume 23 , Issue 1 , Winter 2015 , pp. 1 - 20
Copyright
Copyright © The Author 2014. Published by Oxford University Press on behalf of the Society for Political Methodology 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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 http://dx.doi.org/10.7910/DVN/27564.

†

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

References

Antoniak, Charles E. 1974. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Annals of Statistics 2:1152–74.CrossRefGoogle Scholar
Bartels, L. 1997. Specification uncertainty and model averaging. American Journal of Political Science 41:641–74.CrossRefGoogle Scholar
Berk, R. A., Bruce, W., and Weiss, Robert E. 1995. Statistical inference for apparent populations. Sociological Methodology 25:421–58.CrossRefGoogle Scholar
Bird, K., Saalfeld, T. L., and Wüst, A. eds, 2011. The political representation of immigrants and minorities. London: Routledge.Google Scholar
Birnbaum, A. 1962. On the foundations of statistical inference. Journal of the American Statistical Association 57:269–306.CrossRefGoogle Scholar
Blackwell, D., and MacQueen, J. B. 1973. Discreteness of Ferguson selections. Annals of Statistics 1:365–58.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Dey, D. K., Ghosh, S. K., and Mallick, B. K. 2000. Generalized linear models: A Bayesian perspective. New York: Marcel Dekker.CrossRefGoogle Scholar
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.Google ScholarPubMed
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.CrossRefGoogle Scholar
Doss, Hani. 1994. Bayesian nonparametric estimation for incomplete data via successive substitution sampling. Annals of Statistics 22:1763–86.CrossRefGoogle Scholar
Efron, Bradley. 1983. Estimating the error rate of a prediction rule: Improvement on cross-validation. Journal of the American Statistical Association 78:316–31.CrossRefGoogle Scholar
Escobar, M. D., and West, M. 1995. Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association 90:577–88.CrossRefGoogle Scholar
Fahrmeir, L., and Tutz, G. 2001. Multivariate statistical modelling based on generalized linear models. 2nd ed. New York: Springer.CrossRefGoogle Scholar
Ferguson, T. S. 1973. A Bayesian analysis of some nonparametric problems. Annals of Statistics 1:209–30.CrossRefGoogle Scholar
Fisher, R. A. 1922. On the mathematical foundations of theoretical statistics. Philosophical Transmissions of the Royal Statistical Society A 222:309–68.Google Scholar
Geisser, Seymour. 1975. The predictive sample reuse method with applications. Journal of the American Statistical Association 70:320–28.CrossRefGoogle Scholar
Gelman, A., and Hill, J. 2007. Data analysis using regression and multilevel/hierarchical models. Cambridge, UK: Cambridge University Press.Google Scholar
Gill, Jeff. 2007. Bayesian methods for the social and behavioral sciences. 2nd ed. New York: Chapman & Hall.CrossRefGoogle Scholar
Gill, Jeff. 2008. Is partial-dimension convergence a problem for inferences from MCMC algorithms? Political Analysis 16:153–78.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Hill, Jennifer L., and Kriesi, Hanspeter. 2001. Classification by opinion-changing behavior: A mixture model approach. Political Analysis 9:301–24.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Jiang, Jiming. 2007. Linear and generalized linear mixed models and their applications. New York: Springer-Verlag.Google Scholar
Korwar, R. M., and Hollander, M. 1973. Contributions to the theory of Dirichlet processes. Annals of Probability 1:705–11.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Kyung, M., Gill, J., and Casella, G. 2010. Estimation in Dirichlet random effects models. Annals of Statistics 38:979–1009.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
Leamer, E. E. 1978. Specification searches: Ad hoc inference with nonexperimental data. New York: John Wiley & Sons.Google Scholar
Liu, J. S. 1996. Nonparametric hierarchical Bayes via sequential imputations. Annals of Statistics 24:911–30.CrossRefGoogle Scholar
Lo, A. Y. 1984. On a class of Bayesian nonparametric estimates: I. Density estimates. Annals of Statistics 12:351–57.CrossRefGoogle Scholar
MacEachern, S. N., and Müller, P. 1998. Estimating mixture of Dirichlet process model. Journal of Computational and Graphical Statistics 7:223–38.Google Scholar
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.CrossRefGoogle Scholar
McCullagh, P., and Neider, J. A. 1989. Generalized linear models. 2nd ed. New York: Chapman & Hall.CrossRefGoogle Scholar
McCulloch, C. E., and Searle, S. R. 2001. Generalized, linear, and mixed models. New York: John Wiley & Sons.Google Scholar
Neal, R. M. 2000. Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics 9:249–65.Google Scholar
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.Google Scholar
Pearson, Karl. 1920a. The fundamental problem of practical statistics. Biometrika 13(1): 1–16.CrossRefGoogle Scholar
Pearson, Karl. 1920b. Note on the fundamental problem of practical statistics. Biometrika 13:300–301.CrossRefGoogle Scholar
Poirer, D. J. 1988. Frequentist and subjectivist perspectives on the problems of model building in economics. Journal of Economic Perspectives 2:121–44.Google Scholar
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.CrossRefGoogle Scholar
Rubin, Donald B., and Schenker, Nathaniel. 1987. Logit-based interval estimation for binomial data using the Jeffreys prior. Sociological Methodology 17:131–44.CrossRefGoogle Scholar
Schweinberger, Michael, and Snijders, Tom A. B. 2003. Settings in social networks: A measurement model. Sociological Methodology 33:307–41.CrossRefGoogle Scholar
Sethuraman, J. 1994. A constructive definition of Dirichlet priors. Statistica Sinica 4:639–50.Google Scholar
Smith, Alastair. 1999. Testing theories of strategic choice: The example of crisis escalation. American Journal of Political Science 43:1254–83.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Stegmueller, Daniel. 2013. Modeling dynamic preferences: A Bayesian robust dynamic latent ordered probit model. Political Analysis 21:314–33.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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 47:1–13.CrossRefGoogle Scholar
Western, Bruce. 1998. Causal heterogeneity in comparative research: A Bayesian hierarchical modelling approach. American Journal of Political Science 42:1233–59.CrossRefGoogle Scholar
Western, Bruce. 1996. Vague theory and model uncertainty in macrosociology. Sociological Methodology 26:165–92.CrossRefGoogle Scholar
Western, Bruce, and Jackman, Simon. 1994. Bayesian inference for comparative research. American Political Science Review 88:412–23.CrossRefGoogle Scholar
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.Google Scholar
Wüst, Andreas M. 2011. Dauerhaft oder temporär? Zur Bedeutung des Migrationshintergrunds für Wahlbeteiligung und Parteiwahl bei der Bundestagswahl 2009. Politische Vierteljahresschrift 45:157–78.Google Scholar