영과잉 경시적 가산자료 분석을 위한 허들모형 = Hurdle Model for Longitudinal Zero-Inflated Count Data Analysis

국문 초록 (Abstract)

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.

다국어 초록 (Multilingual 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.

참고문헌 (Reference)

1 Lambert, D., "Zero-inflated Poisson regression, with an application to defects in manufacturing" 34 : 1-14, 1992

2 Mullahy, J., "Specification and testing of some modified count data models" 33 : 341-365, 1986

3 Pan, J. X., "Regression models for covariance structures in longitudinal studies" 6 : 43-57, 2006

4 Min, Y., "Random effect models for repeated measures of zero-inflated count data" 5 : 1-19, 2005

5 Daniels, J. M., "Modelling the random effects covariance matrix in longitudinal data" 22 : 1631-1647, 2003

6 Pan, J. X., "Model selection for joint mean-covariance structures in longitudinal studies" 90 : 239-244, 2003

7 Gelfand, A. E., "Model choice: A minimum posterior predictive loss approach" 85 : 1-13, 1998

8 Heagerty, P. J., "Misspecified maximum likelihood estimates and generalised linear mixed models" 88 : 973-985, 2001

9 Daniels, M. J., "Missing data in longitudinal studies: Strategies for Bayesian modeling and sensitivity analysis" Chapman & Hall/CRC 2008

10 Pourahmadi, M., "Maximum likelihood estimation of generalized linear models for multivariate normal covariance matrix" 87 : 425-435, 2000

11 Pourahmadi, M., "Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation" 86 : 677-690, 1999

12 Pourahmadi, M., "Dynamic conditionally linear mixed models for longitudinal data" 58 : 225-231, 2002

13 Celeux, G., "Deviance Information Criteria for Missing Data Models" 1 : 651-674, 2006

14 Daniels, J. M., "Bayesian analysis of covariance matrices and dynamic models for longitudinal data" 89 : 553-566, 2002

15 이근백, "Bayesian Modeling of Random Effects Covariance Matrix for Generalized Linear Mixed Models" 한국통계학회 20 (20): 235-240, 2013

16 Breslow, N. E., "Approximate inference in generalized linear mixed models" 88 : 125-134, 1993

17 Lee, K., "Analysis of zero-inflated clustered count data: A marginalized model approach" ELSEVIER SCIENCE BV 55 (55): 824-837, 2011

18 Neelon, B. H., "A Bayesian model for repeated measures zeroinflated count data with application to outpatient psychiatric service use" 10 : 421-439, 2010