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Modeling Dynamic Preferences: A Bayesian Robust Dynamic Latent Ordered Probit Model

Published online by Cambridge University Press:  04 January 2017

Daniel Stegmueller
Daniel Stegmueller*
Affiliation:
Department of Government, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK e-mail: [email protected]
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Abstract

Much politico-economic research on individuals' preferences is cross-sectional and does not model dynamic aspects of preference or attitude formation. I present a Bayesian dynamic panel model, which facilitates the analysis of repeated preferences using individual-level panel data. My model deals with three problems. First, I explicitly include feedback from previous preferences taking into account that available survey measures of preferences are categorical. Second, I model individuals' initial conditions when entering the panel as resulting from observed and unobserved individual attributes. Third, I capture unobserved individual preference heterogeneity both via standard parametric random effects and a robust alternative based on Bayesian nonparametric density estimation. I use this model to analyze the impact of income and wealth on preferences for government intervention using the British Household Panel Study from 1991 to 2007.

Type
Research Article
Information
Political Analysis , Volume 21 , Issue 3 , Summer 2013 , pp. 314 - 333
Copyright
Copyright © The Author 2013. Published by Oxford University Press on behalf of the Society for Political Methodology 

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References

Aitkin, Murray. 1999. A general maximum likelihood analysis of variance components in generalized linear models. Biometrics 55: 117–28.Google Scholar
Akay, Alpaslan. 2012. Finite-sample comparison of alternative methods for estimating dynamic panel data models. Journal of Applied Econometrics 27: 1189–204.Google Scholar
Albert, James H., and Chib, Siddhartha. 1993. Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88: 669–79.Google Scholar
Albert, Jim, and Chib, Siddhartha. 1995. Bayesian residual analysis for binary response regression models. Biometrika 82: 747–59.Google Scholar
Alesina, Alberto, and Ferrara, Eliana La. 2005. Preferences for redistribution in the land of opportunities. Journal of Public Economics 89: 897–931.CrossRefGoogle Scholar
Alesina, Alberto, and Angeletos, George-Marios. 2005. Fairness and redistribution. American Economic Review 95: 960–80.Google Scholar
Alesina, Alberto, and Giuliano, Paola. 2011. Preferences for redistribution. In Handbook of social economics, eds. Benhabib, Jess, Bisin, Alberto, and Jackson, Matthew O., 93–131. San Diego, CA: North-Holland.Google Scholar
Anderson, T. W., and Hsiao, C. 1981. Estimation of dynamic models with error components. Journal of the American Statistical Association 76: 598–606.Google Scholar
Antoniak, Charles E. 1974. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Annals of Statistics 2: 1152–74.CrossRefGoogle Scholar
Arellano, Manuel, and Bond, Stephen. 1991. Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58: 277.Google Scholar
Arellano, Manuel, and Carrasco, Raquel. 2003. Binary choice panel data models with predetermined variables. Journal of Econometrics 115: 125–57.Google Scholar
Arulampalam, Wiji. 2000. Unemployment persistence. Oxford Economic Papers 52: 24–50.Google Scholar
Arulampalam, Wiji, and Stewart, Mark B. 2009. Simplified implementation of the Heckman estimator of the dynamic probit model and a comparison with alternative estimators. Oxford Bulletin of Economics and Statistics 71: 659–81.Google Scholar
Bartels, Brandon L., Box-Steffensmeier, Janet M., Smidt, Corwin D., and Smith, Rene M. 2011. The dynamic properties of individual-level party identification in the United States. Electoral Studies 30: 210–22.Google Scholar
Beck, Nathaniel, and Katz, Jonathan N. 1996. Nuisance vs. substance: Specifying and estimating time-series-cross-section models. Political Analysis 6: 1–36.Google Scholar
Blundell, Richard, and Bond, Stephen. 1998. Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87: 115–43.Google Scholar
Brooks, Stephen P., and Roberts, Gareth O. 1998. Convergence assessment techniques for Markov chain Monte Carlo. Statistics and Computing 8: 319–35.Google Scholar
Cusack, Thomas, Iversen, Torbern, and Rehm, Phillip. 2005. Risks at work: The demand and supply sides of government redistribution. Oxford Review of Economic Policy 22: 365–89.Google Scholar
Cusack, Thomas, Iversen, Torbern, and Rehm, Phillip. 2008. Economic shocks, inequality, and popular support for redistribution. In Democracy, inequality, and representation: A comparative perspective, eds. Beramendi, Pablo and Anderson, Christopher J., 203–31. New York: Russell Sage Foundation.Google Scholar
Czado, Claudia, Heyn, Anette, and Müller, Gernot. 2011. Modeling individual migraine severity with autoregressive ordered probit models. Statistical Methods and Application 20: 101–21.Google Scholar
Dunson, David B., Pillai, Natesh, and Park, Ju-Hyun. 2007. Bayesian density regression. Journal of the Royal Statistical Society B 69: 163–83.Google Scholar
Eckstein, Zvi, and Wolpin, Kenneth. 1999. Why youths drop out of high school: The impact of preferences, opportunities, and abilities. Econometrica 67: 1295–339.Google Scholar
Escobar, Michael D. 1995. Nonparametric Bayesian methods in hierarchical models. Journal of Statistical Planning and Inference 43: 97–106.Google Scholar
Escobar, Michael D., and West, Mike. 1998. Computing Bayesian nonparametric hierarchical models. In Practical nonparametric and semiparametric Bayesian statistics, eds. Dey, Dipak K., Müller, Peter, and Sinha, Debajyoti, 1–22. Springer.Google Scholar
Ferguson, Thomas S. 1973. A Bayesian analysis of some nonparametric problems. Annals of Statistics 1: 209–30.Google Scholar
Ferguson, Thomas S. 1974. Prior distributions on spaces of probability measures. Annals of Statistics 2: 615–29.Google Scholar
Follmann, Dean A., and Lambert, Diane. 1989. Generalizing logistic regression by nonparametric mixing. Journal of the American Statistical Association 84: 295–300.Google Scholar
Fotouhi, Ali Reza. 2005. The initial conditions problem in longitudinal binary process: A simulation study. Simulation Modelling Practice and Theory 13: 566–83.Google Scholar
Franses, Philip Hans, and Cramer, J. S. 2010. On the number of categories in an ordered regression model. Statistica Neerlandica 64: 125–8.Google Scholar
Friedman, M. 1957. A Theory of the Consumption Function. Princeton, NJ: Princeton University Press.Google Scholar
Gelman, Andrew. 2006. Prior distributions for variance parameters in hierarchical models. Bayesian Analysis 1: 515–34.Google Scholar
Gelman, Andrew. 2008. Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine 27: 2865–73.Google Scholar
Gelman, Andrew, Carlin, John B., Stern, Hal S., and Rubin, Donald B. 2004. Bayesian Data Analysis. Boca Raton, FL: Chapman & Hall.Google Scholar
Gelman, Andrew, and Rubin, Donald. 1992. Inference from iterative simulation using multiple sequences. Statistical Science 7: 457–511.Google Scholar
Ghosh, J. K., and Ramamoorthi, R. V. 2003. Bayesian nonparametrics. New York: Springer.Google Scholar
Gill, Jeff. 2008a. Bayesian methods: A social and behavioral sciences approach. Boca Raton, FL: Chapman & Hall.Google Scholar
Gill, Jeff. 2008b. 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: 1–12.Google Scholar
Greene, William, and Hensher, David. 2010. Modeling ordered choices: A primer. Cambridge, UK: Cambridge University Press.Google Scholar
Grimmer, Justin. 2010. An introduction to Bayesian inference via variational approximations. Political Analysis 19: 32–47.Google Scholar
Hagenaars, A., de Vos, K., and Zaidi, M. A. 1994. Poverty statistics in the late 1980s: Research based on micro-data. Luxembourg: Office for Official Publications of the European Communities.Google Scholar
Hanson, Timothy E., Branscum, Adam J., and Johnson, Wesley O. 2005. Bayesian nonparametric modeling and data analysis: An introduction. In Handbook of statistics, Vol. 25, 245–78. Amsterdam: Elsevier.Google Scholar
Harris, Mark N., Matyas, Laszlo, and Sevestre, Patrick. 2008. Dynamic models for short panels. In The econometrics of panel data: Fundamentals and recent developments in theory and practice, eds. Matyas, Laszlo and Sevestre, Patrick, 249–78. Berlin, Germany: Springer.Google Scholar
Hasegawa, Hikaru. 2009. Bayesian dynamic panel-ordered probit model and its application to subjective well-being. Communications in Statistics: Simulation and Computation 38: 1321–47.Google Scholar
Heckman, James J. 1978. Dummy endogeneous variables in a simultaneous equation system. Econometrica 46: 931–59.Google Scholar
Heckman, James J. 1981a. Heterogeneity and state dependence. In Studies in labor markets, ed. Rosen, Sherwin, 91–140. Chicago: University of Chicago Press.Google Scholar
Heckman, James J. 1981b. The incidental parameters problem and the problem of initial conditions in estimating a discrete time-discrete data stochastic process. In Structural analysis of discrete data with econometric applications, eds. Manski, C. F. and McFadden, Daniel, 179–95. Cambridge, MA: MIT Press.Google Scholar
Heckman, James J., and Singer, B. 1984. A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52: 271–320.Google Scholar
Imai, Kosuke, Lu, Ying, and Strauss, Aaron. 2008. Bayesian and likelihood inference for 2 x 2 ecological tables: An incomplete-data approach. Political Analysis 16: 41–69.Google Scholar
Iversen, Torben, and Soskice, David. 2001. An asset theory of social policy preferences. American Political Science Review 95: 875–93.Google Scholar
Jackman, Simon. 2000. Estimation and inference are missing data problems: Unifying social science statistics via Bayesian simulation. Political Analysis 8: 307–32.Google Scholar
Jackman, Simon. 2009. Bayesian analysis for the social sciences. New York: Wiley.Google Scholar
Jackman, Simon, and Western, Bruce. 1994. Bayesian inference for comparative research. American Political Science Review 88: 412–23.Google Scholar
Jara, Alejandro, Jose Garcia-Zattera, Maria, and Lesaffre, Emmanuel. 2007. A Dirichlet process mixture model for the analysis of correlated binary responses. Computational Statistics and Data Analysis 51: 5402–15.Google Scholar
Johnson, Valen E., and Albert, Jim H. 1999. Ordinal data modeling. New York: Springer.Google Scholar
Keane, M. P. 1997. Modeling heterogeneity and state dependence in consumer choice behavior. Journal of Business & Economic Statistics 15: 310–27.Google Scholar
Kleinman, Ken P., and Ibrahim, Joseph G. 1998. A semiparametric Bayesian approach to the random effects model. Biometrics 54: 921–38.Google Scholar
Kottas, Athanasios, Müller, Peter, and Quintana, Fernando. 2005. Nonparametric Bayesian modeling for multivariate ordinal data. Journal of Computational and Graphical Statistics 14: 610–25.Google Scholar
Kyung, Minyung, Gill, Jeff, and Casella, George. 2010. Estimation in Dirichlet random effects models. Annals of Statistics 38: 979–1009.Google Scholar
Laird, N. 1978. Nonparametric maximum likelihood estimation of a mixture distribution. Journal of the American Statistical Association 73: 805–11.Google Scholar
Lange, Kenneth L., Little, Roderick J. A., and Taylor, Jeremy M. G. 1989. Robust statistical modeling using the t-distribution. Journal of the American Statistical Association 84: 881–96.Google Scholar
Lindsay, Bruce. 1995. Mixture models: Theory, geometry and applications. Hayward, CA: Institute of Mathematical Statistics.Google Scholar
Lunn, David J., Wakefield, Jon, and Racine-Poon, Amy. 2001. Cumulative logit models for ordinal data: A case study involving allergic rhinitis severity scores. Statistics in Medicine 20: 2261–85.Google Scholar
Margalit, Yotam. 2013. Explaining social policy preferences: Evidence from the great recession. American Political Science Review 107: 80–103.Google Scholar
McKelvey, Richard D., and Zavoina, William. 1975. A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology 4: 103–20.Google Scholar
Moene, Kark Ove, and Wallerstein, Michael. 2001. Inequality, social insurance, and redistribution. American Political Science Review 95: 859–74.Google Scholar
Müller, Gernot, and Czado, Claudia. 2005. An autoregressive ordered probit model with application to high-frequency financial data. Journal of Computational and Graphical Statistics 14: 320–38.Google Scholar
Müller, Peter, and Quintana, Fernando. 2004. Nonparametric Bayesian data analysis. Statistical Science 19: 95–110.Google Scholar
Müller, Peter, Quintana, Fernando, and Rosner, Gary L. 2007. Semiparametric Bayesian inference for multilevel repeated measurement data. Biometrics 63: 280–89.Google Scholar
Mundlak, Yair. 1978. On the pooling of time-series and cross-section data. Econometrica 46: 69–85.Google Scholar
Navarro, Daniel J., Griffiths, Thomas L., Steyvers, Mark, and Lee, Michael D. 2006. Modeling individual differences using Dirichlet processes. Journal of Mathematical Psychology 50: 101–22.Google Scholar
Nerlove, Marc, Sevestre, Patrick, and Balestra, Pietro. 2008. Introduction. In The econometrics of panel data: Fundamentals and recent developments in theory and practice, eds. Matyas, Laszlo and Sevestre, Patrick, 3–22. Berlin: Springer.Google Scholar
Neustadt, Ilja. 2010. Do religious beliefs explain preferences for income redistribution? Experimental evidence. University of Zurich, Socioeconomic Institute working paper 1009.Google Scholar
Nickell, Stephen. 1981. Biases in dynamic models with fixed effects. Econometrica 49: 1417–26.Google Scholar
Pang, Xun. 2010. Modeling heterogeneity and serial correlation in binary time-series cross-sectional data: A Bayesian multilevel model with AR(p) errors. Political Analysis 18: 470–98.Google Scholar
Pudney, Stephen. 2006. The dynamics of perception: Modelling subjective well-being in a short panel. ISER working paper 2006–27.Google Scholar
Pudney, Stephen. 2008. The dynamics of perception: Modelling subjective well-being in a short panel. Journal of the Royal Statistical Society A 171: 21–40.Google Scholar
Rabe-Hesketh, Sophia, and Skrondal, A. 2008. Generalized linear mixed effects models. In Longitudinal data analysis: A handbook of modern statistical methods, eds. Fitzmaurice, Garret, Davidian, Marie, Verbeke, Geert, and Molenberghs, Geert, 79–106. Boca Raton, FL: Chapman & Hall.Google Scholar
Rehm, Philipp. 2011. Risk inequality and the polarized American electorate. British Journal of Political Science 41: 363–87.Google Scholar
Rehm, Philipp, Hacker, Jacob S., and Schlesinger, Mark. 2012. Insecure alliances: Risk, inequality, and support for the welfare state. American Political Science Review 106: 386–406.Google Scholar
Robert, Christan P. 2007. The Bayesian choice: From decision-theoretic foundations to computational implementation. New York: Springer.Google Scholar
Rossi, Peter E., Allenby, Greg M., and Mcculloch, Robert. 2005. Bayesian statistics and marketing. Chichester, UK: Wiley.Google Scholar
Scheve, Kenneth, and Stasavage, David. 2006. Religion and preferences for social insurance. Quarterly Journal of Political Science 1: 255–86.Google Scholar
Shayo, Moses. 2009. A model of social identity with an application to political economy: Nation, class, and redistribution. American Political Science Review 103: 147–74.Google Scholar
Skrondal, Anders, and Rabe-Hesketh, Sophia. 2004. Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models. Boca Raton, FL: Chapman & Hall.Google Scholar
Spiegelhalter, D. J., Thomas, A., Best, N., and Gilks, W. R. 1997. BUGS: Bayesian inference using Gibbs sampling manual. Cambridge, UK: Medical Research Council Biostatistics Unit.Google Scholar
Spirling, Arthur, and Quinn, Kevin M. 2010. Identifying intraparty voting blocs in the U.K. House of Commons. Journal of the American Statistical Association 105: 447–57.Google Scholar
Stegmueller, Daniel. 2011. Apples and oranges? The problem of equivalence in comparative research. Political Analysis 19: 471–87.Google Scholar
Varin, Cristiano, and Czado, Claudia. 2010. A mixed autoregressive probit model for ordinal longitudinal data. Biostatistics 11: 127–38.Google Scholar
Vella, F., and Verbeek, Marno. 1998. Whose wages do unions raise? A dynamic model of unionism and wage rate determination for young men. Journal of Applied Econometrics 13: 163–83.Google Scholar
Vermunt, Jeroen. 2004. An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models. Statistica Neerlandica 58: 220–33.Google Scholar
Vermunt, Jeroen, Tran, Bac, and Magidson, Jay. 2008. Latent class models in longitudinal research. In Handbook of longitudinal research, design, measurement, and analysis, ed. Menard, Scott, 373–85. Waltham, MA: Academic Press.Google Scholar
Wawro, G. 2002. Estimating dynamic panel data models in political science. Political Analysis 10: 25–48.Google Scholar
Winkelmann, Rainer. 2005. Subjective well-being and the family: Results from an ordered probit model with multiple random effects. Empirical Economics 30: 749–61.Google Scholar
Wlezien, Christopher. 1995. The public as thermostat: Dynamics of preferences for spending. American Journal of Political Science 39: 981–1000.Google Scholar
Wooldridge, Jeffrey M. 2002. Econometric analysis of cross section and panel data. Cambridge, MA: MIT Press.———. 2005. Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity. Journal of Applied Econometrics 20: 39–54.Google Scholar
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