Hurdle Model for Longitudinal Zero-Inflated Count Data Analysis Jin, Iktae; Lee, Keunbaik;
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.
Random effects covariance matrix;generalized linear model;modified Cholesky decomposition;truncated Poisson model;
Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 125-134.
Celeux, G., Forbes, F., Robert, C. P. and Titterington, D. M. (2006). Deviance Information Criteria for Missing Data Models, Bayesian Analysis, 1, 651-674.
Daniels, J. M. and Pourahmadi, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data, Biometrika, 89, 553-566.
Daniels, J. M. and Zhao, Y. D. (2003). Modelling the random effects covariance matrix in longitudinal data, Statistics in Medicine, 22, 1631-1647.
Daniels, M. J. and Hogan, J. W.(2008). Missing data in longitudinal studies: Strategies for Bayesian modeling and sensitivity analysis, Chapman & Hall/CRC.
Gelfand, A. E. and Ghosh, S. K. (1998). Model choice: A minimum posterior predictive loss approach, Biometrika, 85, 1-13.
Heagerty, P. J. and Kurland, B. F. (2001). Misspecified maximum likelihood estimates and generalised linear mixed models, Biometrika, 88, 973-985.
Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing, Technometrics, 34, 1-14.
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.
Lee, K. (2013). Bayesian modeling of random effects covariance matrix for generalized linear mixed models, Communications for Statistical Applications and Methods, 20, 235-240.
Mullahy, J. (1986). Specification and testing of some modified count data models, Journal of Econometics, 33, 341-365.
Min, Y. and Agresti, A. (2005). Random effect models for repeated measures of zero-inflated count data, Statistical Modelling, 5, 1-19.
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.
Pan, J. X. and Mackenzie, G. (2003). Model selection for joint mean-covariance structures in longitudinal studies, Biometrika, 90, 239-244.
Pan, J. X. and MacKenzie, G. (2006). Regression models for covariance structures in longitudinal studies, Statistical Modelling, 6, 43-57.
Pourahmadi, M. (1999). Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation, Biometrika, 86, 677-690.
Pourahmadi, M. (2000). Maximum likelihood estimation of generalized linear models for multivariate normal covariance matrix, Biometrika, 87, 425-435.
Pourahmadi, M. and Daniels, M. J. (2002). Dynamic conditionally linear mixed models for longitudinal data, Biometrika, 58, 225-231.