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A bayesian approach to model-based clustering for panel probit models

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  • Aßmann, Christian
  • Boysen-Hogrefe, Jens

Abstract

Consideration of latent heterogeneity is of special importance in non linear models for gauging correctly the effect of explaining variables on the dependent variable. This paper adopts the stratified model-based clustering approach for modeling latent heterogeneity for panel probit models. Within a Bayesian framework an estimation algorithm dealing with the inherent label switching problem is provided. Determination of the number of clusters is based on the marginal likelihood and out-of-sample criteria. The ability to decide on the correct number of clusters is assessed within a simulation study indicating high accuracy for both approaches. Different concepts of marginal effects incorporating latent heterogeneity at different degrees arise within the considered model setup and are directly at hand within Bayesian estimation via MCMC methodology. An empirical illustration of the developed methodology indicates that consideration of latent heterogeneity via latent clusters provides the preferred model specification compared to a pooled and a random coefficient specification. --

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Bibliographic Info

Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2009,03.

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Date of creation: 2009
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Handle: RePEc:zbw:cauewp:200903

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Web page: http://www.wiso.uni-kiel.de/econ/
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Keywords: Bayesian Estimation; MCMC Methods; Panel Probit Model; Mixture Modelling;

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  1. Heard, Nicholas A. & Holmes, Christopher C. & Stephens, David A., 2006. "A Quantitative Study of Gene Regulation Involved in the Immune Response of Anopheline Mosquitoes: An Application of Bayesian Hierarchical Clustering of Curves," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 18-29, March.
  2. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model-based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354.
  3. Ishwaran H. & James L.F. & Sun J., 2001. "Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1316-1332, December.
  4. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  5. Dunson, David B. & Herring, Amy H. & Siega-Riz, Anna Maria, 2008. "Bayesian Inference on Changes in Response Densities Over Predictor Clusters," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1508-1517.
  6. Fruhwirth-Schnatter, Sylvia & Kaufmann, Sylvia, 2008. "Model-Based Clustering of Multiple Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 78-89, January.
  7. Bertschek, Irene & Lechner, Michael, 1995. "Convenient Estimators for the Panel Probit Model," Discussion Papers 528, Institut fuer Volkswirtschaftslehre und Statistik, Abteilung fuer Volkswirtschaftslehre.
  8. Aßmann, Christian, 2007. "Determinants and Costs of Current Account Reversals under Heterogeneity and Serial Correlation," Economics Working Papers 2007,17, Christian-Albrechts-University of Kiel, Department of Economics.
  9. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
  10. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
  11. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
  12. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
  13. Chen, Jiahua & Khalili, Abbas, 2008. "Order Selection in Finite Mixture Models With a Nonsmooth Penalty," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1674-1683.
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