The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Hurdle Model for Longitudinal Zero-Inflated Count Data Analysis

영과잉 경시적 가산자료 분석을 위한 허들모형

  • Jin, Iktae (Department of Statistics, Sungkyunkwan University) ;
  • Lee, Keunbaik (Department of Statistics, Sungkyunkwan University)
  • Received : 2014.10.13
  • Accepted : 2014.11.05
  • Published : 2014.12.31
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Abstract

The Hurdle model can to analyze zero-inflated count data. This model is a mixed model of the logit model for a binary component and a truncated Poisson model of a truncated count component. We propose a new hurdle model with a general heterogeneous random effects covariance matrix to analyze longitudinal zero-inflated count data using modified Cholesky decomposition. This decomposition factors the random effects covariance matrix into generalized autoregressive parameters and innovation variance. The parameters are modeled using (generalized) linear models and estimated with a Bayesian method. We use these methods to carefully analyze a real dataset.

허들모형은 영이 과잉 가산자료를 분석하기 위해서 사용되어 왔다. 이 모형은 이산부분을 위한 로짓모형과 절삭된 가산부분을 위한 절삭된 포아송모형의 혼합모형이다. 이 논문에서 우리는 경시적 영과잉 가산자료를 분석하기 위해서 수정된 콜레스키 분해을 이용하여 일반적인 이분산성을 가지는 변량효과 공분산행렬을 제안한다. 수정된 콜레스키 분해는 변량효과 공분산행렬을 일반화자기상관 모수와 혁신분산모수로 분리되면, 이러한 모수들은 베이지안 일반화 선형모형을 통해 추정된다. 그리고 실제 자료분석을 통하여 설명한다.

Keywords

References

  1. Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 125-134.
  2. Celeux, G., Forbes, F., Robert, C. P. and Titterington, D. M. (2006). Deviance Information Criteria for Missing Data Models, Bayesian Analysis, 1, 651-674. https://doi.org/10.1214/06-BA122
  3. Daniels, J. M. and Pourahmadi, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data, Biometrika, 89, 553-566. https://doi.org/10.1093/biomet/89.3.553
  4. Daniels, J. M. and Zhao, Y. D. (2003). Modelling the random effects covariance matrix in longitudinal data, Statistics in Medicine, 22, 1631-1647. https://doi.org/10.1002/sim.1470
  5. Daniels, M. J. and Hogan, J. W.(2008). Missing data in longitudinal studies: Strategies for Bayesian modeling and sensitivity analysis, Chapman & Hall/CRC.
  6. Gelfand, A. E. and Ghosh, S. K. (1998). Model choice: A minimum posterior predictive loss approach, Biometrika, 85, 1-13. https://doi.org/10.1093/biomet/85.1.1
  7. Heagerty, P. J. and Kurland, B. F. (2001). Misspecified maximum likelihood estimates and generalised linear mixed models, Biometrika, 88, 973-985. https://doi.org/10.1093/biomet/88.4.973
  8. Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing, Technometrics, 34, 1-14. https://doi.org/10.2307/1269547
  9. Lee, K., Joo, Y., Song, J. J. and Harper, D. W. (2011). Analysis of zero-inflated clustered count data: A marginalized model approach, Computational Statistics & Data Analysis, 55, 824-837. https://doi.org/10.1016/j.csda.2010.07.005
  10. Lee, K. (2013). Bayesian modeling of random effects covariance matrix for generalized linear mixed models, Communications for Statistical Applications and Methods, 20, 235-240. https://doi.org/10.5351/CSAM.2013.20.3.235
  11. Mullahy, J. (1986). Specification and testing of some modified count data models, Journal of Econometics, 33, 341-365. https://doi.org/10.1016/0304-4076(86)90002-3
  12. Min, Y. and Agresti, A. (2005). Random effect models for repeated measures of zero-inflated count data, Statistical Modelling, 5, 1-19. https://doi.org/10.1191/1471082X05st084oa
  13. Neelon, B. H., O'Malley, A. J. and Normand, S. T. (2010). A Bayesian model for repeated measures zeroinflated count data with application to outpatient psychiatric service use, Statistical Modelling, 10, 421-439. https://doi.org/10.1177/1471082X0901000404
  14. Pan, J. X. and Mackenzie, G. (2003). Model selection for joint mean-covariance structures in longitudinal studies, Biometrika, 90, 239-244. https://doi.org/10.1093/biomet/90.1.239
  15. Pan, J. X. and MacKenzie, G. (2006). Regression models for covariance structures in longitudinal studies, Statistical Modelling, 6, 43-57. https://doi.org/10.1191/1471082X06st105oa
  16. Pourahmadi, M. (1999). Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation, Biometrika, 86, 677-690. https://doi.org/10.1093/biomet/86.3.677
  17. Pourahmadi, M. (2000). Maximum likelihood estimation of generalized linear models for multivariate normal covariance matrix, Biometrika, 87, 425-435. https://doi.org/10.1093/biomet/87.2.425
  18. Pourahmadi, M. and Daniels, M. J. (2002). Dynamic conditionally linear mixed models for longitudinal data, Biometrika, 58, 225-231.