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Markov Chain Monte Carlo Analysis of Correlated Count Data

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  • Chib, Siddhartha
  • Winkelmann, Rainer

Abstract

This article is concerned with the analysis of correlated count data. A class of models is proposed in which the correlation among the counts is represented by correlated latent effects. Special cases of the model are discussed and a tuned and efficient Markov chain Monte Carlo algorithm is developed to estimate the model under both multivariate normal and multivariate-t assumptions on the latent effects. The methods are illustrated with two real data examples of six and sixteen variate correlated counts.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 19 (2001)
Issue (Month): 4 (October)
Pages: 428-35

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Handle: RePEc:bes:jnlbes:v:19:y:2001:i:4:p:428-35

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Cited by:
  1. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
  2. Hilger, James & Englin, Jeffrey, 2009. "Utility theoretic semi-logarithmic incomplete demand systems in a natural experiment: Forest fire impacts on recreational values and use," Resource and Energy Economics, Elsevier, vol. 31(4), pages 287-298, November.
  3. Markus Jochmann & Roberto León-González, 2004. "Estimating the demand for health care with panel data: a semiparametric Bayesian approach," Health Economics, John Wiley & Sons, Ltd., vol. 13(10), pages 1003-1014.
  4. Peter Congdon, 2013. "Modelling small-area inequality in premature mortality using years of life lost rates," Journal of Geographical Systems, Springer, vol. 15(2), pages 149-167, April.
  5. Hellström, Jörgen & Nordström, Jonas, 2005. "Demand and Welfare Effects in Recreational Travel Models: A Bivariate Count Data Approach," UmeÃ¥ Economic Studies 648, Umeå University, Department of Economics.
  6. Minjung Kyung & Jeff Gill & George Casella, 2011. "Sampling schemes for generalized linear Dirichlet process random effects models," Statistical Methods and Applications, Springer, vol. 20(3), pages 259-290, August.
  7. Wedel, Michel & Böckenholt, Ulf & Kamakura, Wagner A., 2003. "Factor models for multivariate count data," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 356-369, November.
  8. Ferdous, Nazneen & Eluru, Naveen & Bhat, Chandra R. & Meloni, Italo, 2010. "A multivariate ordered-response model system for adults' weekday activity episode generation by activity purpose and social context," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 922-943, September.
  9. Herriges, Joseph A. & Phaneuf, Daniel J. & Tobias, Justin L., 2008. "Estimating demand systems when outcomes are correlated counts," Journal of Econometrics, Elsevier, vol. 147(2), pages 282-298, December.
  10. Dimitris Karlis & Ioannis Ntzoufras, . "Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R," Journal of Statistical Software, American Statistical Association, vol. 14(i10).
  11. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
  12. Atella, Vincenzo & Deb, Partha, 2008. "Are primary care physicians, public and private sector specialists substitutes or complements? Evidence from a simultaneous equations model for count data," Journal of Health Economics, Elsevier, vol. 27(3), pages 770-785, May.
  13. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
  14. B.P.M. McCabe & G.M. Martin, 2003. "Coherent Predictions of Low Count Time Series," Monash Econometrics and Business Statistics Working Papers 8/03, Monash University, Department of Econometrics and Business Statistics.
  15. Hellström, Jörgen & Nordström, Jonas, 2012. "Demand and welfare effects in recreational travel models: Accounting for substitution between number of trips and days to stay," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(3), pages 446-456.
  16. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
  17. Jung, Robert & Kukuk, Martin & Liesenfeld, Roman, 2005. "Time Series of Count Data : Modelling and Estimation," Economics Working Papers 2005,08, Christian-Albrechts-University of Kiel, Department of Economics.
  18. De Oliveira, Victor, 2013. "Hierarchical Poisson models for spatial count data," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 393-408.
  19. Congdon, P., 2007. "Bayesian modelling strategies for spatially varying regression coefficients: A multivariate perspective for multiple outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2586-2601, February.
  20. Alfò, Marco & Rocchetti, Irene, 2013. "A flexible approach to finite mixture regression models for multivariate mixed responses," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1754-1758.
  21. Congdon, Peter, 2008. "A bivariate frailty model for events with a permanent survivor fraction and non-monotonic hazards; with an application to age at first maternity," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4346-4356, May.

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