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Classification by Opinion-Changing Behavior: A Mixture Model Approach

Published online by Cambridge University Press:  04 January 2017

Jennifer L. Hill  and
Hanspeter Kriesi
Jennifer L. Hill
Affiliation:
Department of Statistics, Harvard University, 1 Oxford St., Cambridge, MA 02138. e-mail: [email protected]
Hanspeter Kriesi
Affiliation:
Department of Political Science, University of Geneva, UNI-MAIL, 102 bd Carl-Vogt, CH-1211 Geneva 4, Switzerland. e-mail: [email protected]
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Abstract

We illustrate the use of a class of statistical models, finite mixture models, that can be used to allow for differences in model parameterizations across groups, even in the absence of group labels. We also introduce a methodology for fitting these models, data augmentation. Neither finite mixture models nor data augmentation is routine in the world of political science methodology, but both are quite standard in the statistical literature. The techniques are applied to an investigation of the empirical support for a theory (developed fully by Hill and Kriesi 2001) that extends Converse's (1964) “black-and-white” model of response stability. Our model formulation enables us (1) to provide reliable estimates of the size of the two groups of individuals originally distinguished in this model, opinion holders and unstable opinion changers; (2) to examine the evidence for Converse's basic claim that these unstable changers truly exhibit nonattitudes; and (3) to estimate the size of a newly defined group, durable changers, whose members exhibit more stable opinion change. Our application uses survey data collected at four time points over nearly 2 years which track Swiss citizens' readiness to support pollution-reduction policies. The results, combined with flexible model checks, provide support for portions of Converse and Zaller's (1992) theories on response instability and appear to weaken the measurement-error arguments of Achen (1975) and others. This paper concentrates on modeling issues and serves as a companion paper to Hill and Kriesi (2001), which uses the same data set and model but focuses more on the details of the opinion-changing behavior debate.

Type
Research Article
Information
Political Analysis , Volume 9 , Issue 4 , 2001 , pp. 301 - 324
Copyright
Copyright © 2001 by the Society for Political Methodology 

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References

Achen, C. H. 1975. “Mass Political Attitudes and the Survey Response.” American Political Science Review 69: 1218–1231.Google Scholar
Belin, T., and Rubin, D. 1995. “The Analysis of Repeated-Measures Data on Schizophrenic Reaction Times Using Mixture Models.” Statistics in Medicine 90: 694–707.Google Scholar
Brooks, S. P., and Gelman, A., 1998. “General Methods for Monitoring Convergence of Iterative Simulations.” Journal of Computational and Graphical Statistics 7: 434–455.Google Scholar
Converse, P. E. 1964. “The Nature of Belief Systems in Mass Publics.” In Ideology and Discontent, ed. Apter, D. New York: Free Press, pp. 206–261.Google Scholar
Everitt, B. S., and Hand, D. J. 1981. Finite Mixture Distributions. London: Chapman & Hall.Google Scholar
Gelman, A., and King, G. 1990. “Estimating the Electoral Consequences of Legislative Redistricting.” Journal of the American Statistical Association 85.Google Scholar
Gelman, A., Meng, X.-L., and Stern, H. 1996. “Posterior Predictive Assessment of Model Fitness via Realized Discrepancies.” Statistica Sinica 6: 733–760 (discussion: pp. 760–807).Google Scholar
Gelman, A., and Rubin, D. B. 1992. “Inference from Iterative Simulation Using Multiple Sequences.” Statistical Science 7: 457–472 (discussion: pp. 483–501, 503–511).Google Scholar
Hill, J. L. 2001. “Accommodating Missing Data in Mixture Models for Classification by Opinion-Changing Behavior.” Journal of Educational and Behavioral Statistics (in press).Google Scholar
Hill, J. L., and Kriesi, H. 2001. “An Extension and Test of Converse's “Black-and-White” Model of Response Stability.” American Political Science Review 95: 397–413.Google Scholar
Jackman, S. 2000. “Estimation and Inference Are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation.” Political Analysis 8(4): 307–332.Google Scholar
Jagodzinski, W., Khnel, S. M., and Schmidt, P. 1987. “Is There a ‘Socratic Effect’ in Nonexperimental Panel Studies? Consistency of an Attitude Toward Guestworkers.” Sociological Methods and Research 15(3): 259–302.Google Scholar
Krosnick, J. A., and Fabrigar, L. R. 1995. “No Opinion Filters and Attitude Strength,” Tech. Rep. Columbus: Department of Psychology, Ohio State University.Google Scholar
Lindsay, B. G. 1995. Mixture Models: Theory, Geometry and Applications. Hayward, CA: Institute of Mathematical Statistics.Google Scholar
Little, R. J. A., and Rubin, D. B. 1987. Statistical Analysis with Missing Data. New York: John Wiley & Sons.Google Scholar
McCutcheon, A. L. 1987. Latent Class Analysis. Beverly Hills, CA: Sage.Google Scholar
McGuire, W. J. 1960. “A Syllogistic Analysis of Cognitive Relationships.” In Attitude Organization and Change, eds. Rosenberg, M. J., Hovland, C., McGuire, W., Abelson, R., and Brehm, J. Westport, CT: Greenwood Press, pp. 65–111.Google Scholar
Rubin, D. B. 1984. “Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician.” Annals of Statistics 12: 1151–1172.Google Scholar
Saris, W. E., and van den Putte, B. 1987. “True Score or Factor Models. A Secondary Analysis of the ALLBUS-Test-Retest Data.” Sociological Methods and Research 17(2): 123–157.Google Scholar
Tanner, M. A., and Wong, W. H. 1987. “The Calculation of Posterior Distributions by Data Augmentation.” Journal of the American Statistical Association 82: 528–540 (C/R: pp. 541–550).Google Scholar
Titterington, D., Smith, A., and Makov, U. 1985. Statistical Analysis of Finite Mixture Distributions. New York: John Wiley.Google Scholar
Turner, D., and West, M. 1993. “Bayesian Analysis of Mixtures Applied to Postsynaptic Potential Fluctuations.” Journal of Neuroscience Methods 47: 1–23.Google Scholar
van Dyk, D. A., and Protassov, R. 1999. “Statistics: Handle with Care,” Tech. Rep. Cambridge, MA: Harvard University.Google Scholar
Zaller, J. R. 1992. The Nature and Origins of Mass Opinion. New York: Cambridge University Press.Google Scholar