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Bayesian semiparametric zero-inflated Poisson model for longitudinal count data. (English) Zbl 05720271
Summary: This paper presents new methods, using a Bayesian approach, for analyzing longitudinal count data with excess zeros and nonlinear effects of continuously valued covariates. In longitudinal count data there are many problems that can make the use of a zero-inflated Poisson (ZIP) model ineffective. These problems are unobserved heterogeneity and nonlinear effects of continuously valued covariates. Our proposed semiparametric model can simultaneously handle these problems in a unified framework. The framework accounts for heterogeneity by incorporating random effects and has two components. The parametric component of the model which deals with the linear effects of time invariant covariates and the non-parametric component which gives an arbitrary smooth function to model the effect of time or time-varying covariates on the logarithm of mean count. The proposed methods are illustrated by analyzing longitudinal count data on the assessment of an efficacy of pesticides in controlling the reproduction of whitefly.

62-XX Statistics
SemiPar; BayesDA; WinBUGS
Full Text: DOI
[1] Lee, A.H.; Wang, K.; Yau, K.K.W.; Carrivick, P.J.W.; Stevenson, M.R., Modeling bivariate count series with excess zeros, Math. biosci., 196, 226, (2005) · Zbl 1071.62079
[2] Welsh, A.H.; Cunningham, R.B.; Donnelly, C.F.; Lindenmayer, D.B., Modeling the abundance of rare species: statistical models for counts with extra zeros, Ecol. model., 88, 297, (1996)
[3] Dagne, G.A., Hierarchical Bayesian analysis of correlated zero-inflated count data, Biometr. J., 46, 653, (2004)
[4] Cheung, Y.B., Zero-inflated models for regression analysis of count data: a study of growth and development, Stat. med., 21, 1461, (2002)
[5] Shankar, V.; Milton, J.; Mannering, F., Modeling accident frequencies as zero-altered probability processes: an empirical inquiry, Accident anal. prev., 29, 829, (1997)
[6] Bőhning, D.; Dietz, E.; Schlattmann, P.; Mendonca, L.; Kirchner, U., Zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology, J. R. stat. soc. ser. A, 162, 195, (1999)
[7] Lambert, D., Zero-inflated Poisson regression, with an application to defects in manufacturing, Technometrics, 34, 1, (1992) · Zbl 0850.62756
[8] Yau, K.K.W.; Lee, A.H.; Carrivick, P.J.W., Modeling zero-inflated count series with application to occupational health, Comput. meth. prog. biomed., 74, 1, 47, (2004)
[9] Crainiceanu, C.M.; Ruppert, D.; Wand, M.P., Bayesian analysis for penalized spline regression using winbugs, J. stat. softw., 14, 1, (2005)
[10] Wood, S.N., Thin plate regression splines, J. R. stat. soc. ser. B, 65, 95, (2003) · Zbl 1063.62059
[11] Gilks, W.R.; Richardson, S.; Spiegelhalter, D.J., Markov chain Monte Carlo in practice, (1996), Chapman and Hall London · Zbl 0832.00018
[12] Spiegelhalter, D.; Thomas, A.; Best, N., Winbugs version 1.4 user manual, (2003), Medical Research Council Biostatistics Unit Cambridge
[13] Eilers, P.H.C.; Marx, B.D., Flexible smoothing with B-splines and penalties (with comments and rejoinder), Stat. sci., 11, 2, 89, (1996) · Zbl 0955.62562
[14] Ruppert, R.; Wand, M.P.; Carroll, R.J., Semiparametric regression, (2002), Cambridge University Cambridge · Zbl 1038.62042
[15] Lang, S.; Bretzger, A., Bayesian P-splines, J. comput. graph. stat., 13, 183, (2004)
[16] Ruppert, R., Selecting the number of knots for penalized splines, J. comput. graph. stat., 11, 735, (2002)
[17] Lunn, D.J.; Thomas, A.; Best, N.; Spiegelhalter, D., Winbugs – a Bayesian modelling framework: concepts, structure, an extensibility, Stat. comput., 10, 325, (2000)
[18] Spiegelhalter, D.J.; Best, N.G.; Carlin, B.P.; Van der Linde, A., Bayesian measures of model complexity and fit (with discussion), J. R. stat. soc. ser. B, 64, 583, (2002) · Zbl 1067.62010
[19] Carlin, B.; Louis, T.A., Bayes and empirical Bayes methods for data analysis, (2000), Chapman and Hall/CRC London, Boca Raton, FL · Zbl 1017.62005
[20] Gelman, A.; Carlin, J.B.; Stern, H.S.; Rubin, D.B., Bayesian data analysis, (2003), CRC London
[21] Guo, X.; Carlin, B.P., Separate and joint modeling of longitudinal and event time data using standard computer packages, Am. stat., 58, 16, (2004)
[22] van Iersel, M.; Oetting, R.D.; Hall, D.B., Imidacloprid applications by subirrigation for control of silverleaf whitefly (homoptera: aleyrodidae) on poinsettia, J. econ. entomol., 93, 813, (2000)
[23] Dagne, G.A., Multiclass models for correlated zero-inflated count data, Far east J. theoret. stat., 21, 203, (2007) · Zbl 1137.62407
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