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Multivariate generalized Poisson geometric process model with scale mixtures of normal distributions

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  • Chan, Jennifer So Kuen
  • Wan, Wai Yin

Abstract

This paper proposes a new model named as the multivariate generalized Poisson log-t geometric process (MGPLTGP) model to study multivariate time-series of counts with overdispersion or underdispersion, non-monotone trends within each time-series and positive or negative correlation between pairs of time-series. This model assumes that the multivariate counts follow independent generalized Poisson distributions with an additional parameter to adjust for different degrees of dispersion including overdispersion and underdispersion. Their means after discounting the trend effect geometrically by ratio functions form latent stochastic processes and follow a multivariate log-t distribution with a flexible correlation structure to capture both positive correlation and negative correlation. By expressing the multivariate Student’s t-distribution in scale mixtures of normals, the model can be implemented through Markov chain Monte Carlo algorithms via the user-friendly WinBUGS software. The applicability of the MGPLTGP model is illustrated through an analysis of the possession and/or use of two illicit drugs, amphetamines and narcotics in New South Wales, Australia.

Suggested Citation

  • Chan, Jennifer So Kuen & Wan, Wai Yin, 2014. "Multivariate generalized Poisson geometric process model with scale mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 72-87.
    • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:72-87
    DOI: 10.1016/j.jmva.2014.02.002
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    References listed on IDEAS

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    1. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    2. Wan, Wai-Yin & Chan, Jennifer So-Kuen, 2011. "Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 687-702, January.
    3. Karlis, Dimitris, 2005. "EM Algorithm for Mixed Poisson and Other Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 3-24, May.
    4. Lam Yeh & So Kuen Chan, 1998. "Statistical inference for geometric processes with lognormal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 27(1), pages 99-112, March.
    5. Chan, Jennifer S. K. & Lam, Yeh & Leung, Doris Y. P., 2004. "Statistical inference for geometric processes with gamma distributions," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 565-581, October.
    6. S. Choy & A. Smith, 1997. "Hierarchical models with scale mixtures of normal distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 205-221, June.
    7. Chan, J.S.K. & Lam, C.P.Y. & Yu, P.L.H. & Choy, S.T.B. & Chen, C.W.S., 2012. "A Bayesian conditional autoregressive geometric process model for range data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3006-3019.
    8. S. Kocherlakota, 1988. "On the compounded bivariate Poisson distribution: A unified treatment," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(1), pages 61-76, March.
    9. Jennifer Chan & Doris Leung, 2010. "Binary geometric process model for the modeling of longitudinal binary data with trend," Computational Statistics, Springer, vol. 25(3), pages 505-536, September.
    10. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    Cited by:

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    2. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

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