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Bayesian Analysis of the Heterogeneity Model

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  • Fruhwirth-Schnatter, Sylvia
  • Tuchler, Regina
  • Otter, Thomas

Abstract

We consider Bayesian estimation of a finite mixture of models with random effects, which is also known as the heterogeneity model. First, we discuss the properties of various Markov chain Monte Carlo samplers that are obtained from full conditional Gibbs sampling by grouping and collapsing. Whereas full conditional Gibbs sampling turns out to be sensitive to the parameterization chosen for the mean structure of the model, the alternative sampler is robust in this respect. However, the logical extension of the approach to the sampling of the group variances does not further increase the efficiency of the sampler. Second, we deal with the identifiability problem due to the arbitrary labeling within the model. Finally, a case study involving metric conjoint analysis serves as a practical illustration.

Suggested Citation

  • Fruhwirth-Schnatter, Sylvia & Tuchler, Regina & Otter, Thomas, 2004. "Bayesian Analysis of the Heterogeneity Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 2-15, January.
    • Handle: RePEc:bes:jnlbes:v:22:y:2004:i:1:p:2-15
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    Citations

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    Cited by:

    1. Johannes Reichl & Sylvia Frühwirth-Schnatter, 2012. "A censored random coefficients model for the detection of zero willingness to pay," Quantitative Marketing and Economics (QME), Springer, vol. 10(2), pages 259-281, June.
    2. Pfarrhofer, Michael, 2023. "Measuring International Uncertainty Using Global Vector Autoregressions with Drifting Parameters," Macroeconomic Dynamics, Cambridge University Press, vol. 27(3), pages 770-793, April.
    3. Mohsen Maleki & Darren Wraith & Reinaldo B. Arellano-Valle, 2019. "A flexible class of parametric distributions for Bayesian linear mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 543-564, June.
    4. Niko Hauzenberger & Florian Huber & Gary Koop & James Mitchell, 2023. "Bayesian Modeling of Time-Varying Parameters Using Regression Trees," Working Papers 23-05, Federal Reserve Bank of Cleveland.
    5. Eller, Markus & Hauzenberger, Niko & Huber, Florian & Schuberth, Helene & Vashold, Lukas, 2021. "The impact of macroprudential policies on capital flows in CESEE," Journal of International Money and Finance, Elsevier, vol. 119(C).
    6. Angel Bujosa & Antoni Riera & Robert Hicks, 2010. "Combining Discrete and Continuous Representations of Preference Heterogeneity: A Latent Class Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 47(4), pages 477-493, December.
    7. Peter E. Rossi & Greg M. Allenby, 2003. "Bayesian Statistics and Marketing," Marketing Science, INFORMS, vol. 22(3), pages 304-328, July.
    8. Florian Huber & Tam'as Krisztin & Michael Pfarrhofer, 2018. "A Bayesian panel VAR model to analyze the impact of climate change on high-income economies," Papers 1804.01554, arXiv.org, revised Feb 2021.
    9. Buddhavarapu, Prasad & Scott, James G. & Prozzi, Jorge A., 2016. "Modeling unobserved heterogeneity using finite mixture random parameters for spatially correlated discrete count data," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 492-510.
    10. Niko Hauzenberger & Michael Pfarrhofer, 2021. "Bayesian State‐Space Modeling for Analyzing Heterogeneous Network Effects of US Monetary Policy," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(4), pages 1261-1291, October.
    11. Xiong, Yingge & Mannering, Fred L., 2013. "The heterogeneous effects of guardian supervision on adolescent driver-injury severities: A finite-mixture random-parameters approach," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 39-54.
    12. Weber, Anett & Steiner, Winfried J., 2021. "Modeling price response from retail sales: An empirical comparison of models with different representations of heterogeneity," European Journal of Operational Research, Elsevier, vol. 294(3), pages 843-859.
    13. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 14-085/III, Tinbergen Institute, revised 04 Sep 2014.
    14. Michael Pfarrhofer & Anna Stelzer, 2019. "The international effects of central bank information shocks," Papers 1912.03158, arXiv.org.
    15. Peter Lenk, 2014. "Bayesian estimation of random utility models," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 20, pages 457-497, Edward Elgar Publishing.
    16. Xiong, Yingge & Tobias, Justin L. & Mannering, Fred L., 2014. "The analysis of vehicle crash injury-severity data: A Markov switching approach with road-segment heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 109-128.
    17. Fruhwirth-Schnatter, Sylvia & Fruhwirth, Rudolf, 2007. "Auxiliary mixture sampling with applications to logistic models," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3509-3528, April.
    18. Aldo M. Garay & Heleno Bolfarine & Victor H. Lachos & Celso R.B. Cabral, 2015. "Bayesian analysis of censored linear regression models with scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2694-2714, December.
    19. Sylvia Frühwirth-Schnatter, 2011. "Panel data analysis: a survey on model-based clustering of time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 5(4), pages 251-280, December.
    20. Anett Weber & Winfried J. Steiner & Stefan Lang, 2017. "A comparison of semiparametric and heterogeneous store sales models for optimal category pricing," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 403-445, March.

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