The Annals of Applied Statistics

A variational EM method for mixed membership models with multivariate rank data: An analysis of public policy preferences

Y. Samuel Wang, Ross L. Matsueda, and Elena A. Erosheva

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Abstract

In this article, we consider modeling ranked responses from a heterogeneous population. Specifically, we analyze data from the Eurobarometer 34.1 survey regarding public policy preferences toward drugs, alcohol, and AIDS. Such policy preferences are likely to exhibit substantial differences within as well as across European nations reflecting a wide variety of cultures, political affiliations, ideological perspectives, and common practices. We use a mixed membership model to account for multiple subgroups with differing preferences and to allow each individual to possess partial membership in more than one subgroup. Previous methods for fitting mixed membership models to rank data in a univariate setting have utilized an MCMC approach and do not estimate the relative frequency of each subgroup. We propose a variational EM approach for fitting mixed membership models with multivariate rank data. Our method allows for fast approximate inference and explicitly estimates the subgroup sizes. Analyzing the Eurobarometer 34.1 data, we find interpretable subgroups which generally agree with the “left versus right” classification of political ideologies.

Article information

Source
Ann. Appl. Stat. Volume 11, Number 3 (2017), 1452-1480.

Dates
Received: December 2015
Revised: February 2017
First available in Project Euclid: 5 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1507168836

Digital Object Identifier
doi:10.1214/17-AOAS1034

Keywords
Mixed membership rank data variational inference Eurobarometer public policy

Citation

Wang, Y. Samuel; Matsueda, Ross L.; Erosheva, Elena A. A variational EM method for mixed membership models with multivariate rank data: An analysis of public policy preferences. Ann. Appl. Stat. 11 (2017), no. 3, 1452--1480. doi:10.1214/17-AOAS1034. https://projecteuclid.org/euclid.aoas/1507168836


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References

  • Airoldi, E. M., Blei, D. M., Fienberg, S. E. and Xing, E. P. (2008). Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9 1981–2014.
  • Airoldi, E. M., Blei, D. M., Erosheva, E. A. and Fienberg, S. E. (2015). Introduction to mixed membership models and methods. In Handbook of Mixed Membership Models and Their Applications. Chapman & Hall/CRC Handb. Mod. Stat. Methods 3–13. CRC Press, Boca Raton, FL.
  • Beal, M. J. (2003). Variational algorithms for approximate Bayesian inference Ph.D. thesis, Univ. College, London.
  • Blei, D. M. and Lafferty, J. D. (2005). Correlated topic models. In Advances in Neural Information Processing Systems 18 [Neural Information Processing Systems, NIPS 2005, December 5–8, 2005, Vancouver, British Columbia, Canada] 147–154.
  • Blei, D. M., Ng, A. Y. and Jordan, M. I. (2003). Latent Dirichlet allocation. J. Mach. Learn. Res. 3 993–1022.
  • Bottou, L. (2010). Large-scale machine learning with stochastic gradient descent. In Proceedings of COMPSTAT’2010 177–186. Physica-Verlag/Springer, Heidelberg.
  • Brooks, C. and Manza, J. (2008). Why Welfare States Persist: The Importance of Public Opinion in Democracies. Univ. Chicago Press, Chicago, IL.
  • Burstein, P. (1998). Bringing the public back in: Should sociologists consider the impact of public opinion on public policy? Social Forces 77 27–62.
  • Busse, L. M., Orbanz, P. and Buhmann, J. M. (2007). Cluster analysis of heterogeneous rank data. In Machine Learning, Proceedings of the Twenty-Fourth International Conference (ICML 2007), Corvallis, Oregon, USA, June 2024, 2007 113–120.
  • Caron, F., Teh, Y. W. and Murphy, T. B. (2014). Bayesian nonparametric Plackett–Luce models for the analysis of preferences for college degree programmes. Ann. Appl. Stat. 8 1145–1181.
  • Cavadino, M. and Dignan, J. (2006). Penal policy and political economy. Criminology and Criminal Justice 6 435–456.
  • Cohen, A. and Mallows, C. (1983). Assessing goodness of fit of ranking models to data. The Statistician 32 361–374.
  • Erosheva, E. A., Fienberg, S. E. and Joutard, C. (2007). Describing disability through individual-level mixture models for multivariate binary data. Ann. Appl. Stat. 1 502–537.
  • Erosheva, E., Fienberg, S. and Lafferty, J. (2004). Mixed-membership models of scientific publications. Proc. Natl. Acad. Sci. USA 101 5220–5227.
  • Gill, J. (2008). Is partial-dimension convergence a problem for inferences from MCMC algorithms? Polit. Anal. 16 153–178.
  • Gormley, I. C. and Murphy, T. B. (2006). Analysis of Irish third-level college applications data. J. Roy. Statist. Soc. Ser. A 169 361–379.
  • Gormley, I. C. and Murphy, T. B. (2008). A mixture of experts model for rank data with applications in election studies. Ann. Appl. Stat. 2 1452–1477.
  • Gormley, I. C. and Murphy, T. B. (2009). A grade of membership model for rank data. Bayesian Anal. 4 265–295.
  • Grasmick, H. G., Davenport, E., Chamlin, M. B. and Bursik, R. J. (1992). Protestant fundamentalism and the retributive doctrine of punishment. Criminology 30 21–46.
  • Gross, J. H. and Manrique-Vallier, D. (2015). A mixed membership approach to the assessment of political ideology from survey responses. In Handbook of Mixed Membership Models and Their Applications. Chapman & Hall/CRC Handb. Mod. Stat. Methods 119–139. CRC Press, Boca Raton, FL.
  • Guiver, J. and Snelson, E. (2009). Bayesian inference for Plackett–Luce ranking models. In Proceedings of the 26th Annual International Conference on Machine Learning, ICML 2009, Montreal, Quebec, Canada, June 1418, 2009 377–384.
  • Hunter, D. R. (2004). MM algorithms for generalized Bradley–Terry models. Ann. Statist. 32 384–406.
  • Kitschelt, H. and Rehm, P. (2014). Occupations as a site of political preference formation. Comparative Political Studies 47 1670–1706.
  • Lange, T., Braun, M. L., Roth, V. and Buhmann, J. M. (2002). Stability-based model selection. In Advances in Neural Information Processing Systems 15 [Neural Information Processing Systems, NIPS 2002, December 9–14, 2002, Vancouver, British Columbia, Canada] 617–624.
  • Luce, R. D. (1977). The choice axiom after twenty years. J. Math. Psych. 15 215–233.
  • Marden, J. I. (1995). Analyzing and Modeling Rank Data. Monographs on Statistics and Applied Probability 64. Chapman & Hall, London.
  • Mayhew, P. and Van Kesteren, J. (2002). Cross-national attitudes to punishment. Changing Attitudes to Punishment 63–92.
  • Meila, M. and Chen, H. (2010). Dirichlet process mixtures of generalized mallows models. In UAI 2010, Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, Catalina Island, CA, USA, July 811, 2010 358–367.
  • Nocedal, J. and Wright, S. J. (1999). Numerical Optimization. Springer Series in Operations Research. Springer, New York.
  • Plackett, R. L. (1975). The analysis of permutations. J. R. Stat. Soc. Ser. C. Appl. Stat. 24 193–202.
  • R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna.
  • Reif, K. and Melich, A. (2001). Euro-barometer 34.1: Health Problems, Fall 1990.
  • Roberts, J. V. (2013). Public opinion and the nature of community penalties: Nternational findings. Changing Attitudes to Punishment 33.
  • Sen, A. K. (2014). Collective Choice and Social Welfare 11. Elsevier, Amsterdam.
  • Teh, Y. W., Jordan, M. I., Beal, M. J. and Blei, D. M. (2006). Hierarchical Dirichlet processes. J. Amer. Statist. Assoc. 101 1566–1581.
  • Tonry, M. (2007). Determinants of penal policies. Crime and Justice 36 1–48.
  • Wainwright, M. J. and Jordan, M. I. (2008). Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn. 1 1–305.
  • Wang, C. and Blei, D. M. (2015). A general method for robust Bayesian modeling. ArXiv preprint. Available at arXiv:1510.05078.
  • Wang, Y. S. and Erosheva, E. A. (2015). mixedMem: Tools for discrete multivariate mixed membership models. R package version 1.1.2. Available at https://cran.r-project.org/web/packages/mixedMem/index.html.
  • Wang, Y. S. and Erosheva, E. A. (2017). Supplement to “A variational EM method for mixed membership models with multivariate rank data: An analysis of public policy preferences.” DOI:10.1214/17-AOAS1034SUPP.
  • Zaller, J. (1992). The Nature and Origins of Mass Opinion. Cambridge Univ. Press, Cambridge, MA.

Supplemental materials

  • Supplement to “A variational EM method for mixed membership models with multivariate rank data: An analysis of public policy preferences”. By analyzing 1997 Irish presidential election data, we provide a direct computational and goodness-of-fit comparison to the MCMC method of Gormley and Murphy (2009).