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Adaptive functional mixed NHPP models for the analysis of recurrent event panel data

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  • Nielsen, J.D.
  • Dean, C.B.

Abstract

An adaptive semi-parametric model for analyzing longitudinal panel count data is presented. Panel data refers here to data collected as the number of events occurring between specific followup times over a period or disjoint periods of observation of a subject. The counts are assumed to arise from a mixed nonhomogeneous Poisson process where frailties account for heterogeneity common to this type of data. The generating intensity of the counting process is assumed to be a smooth function modeled with penalized splines. A main feature is that the penalization used to control the amount of smoothing, usually assumed to be time homogeneous, is allowed to be time dependent so that the spline can more easily adapt to sharp changes in curvature regimes. Splines are also used to model time dependent covariate effects. Penalized quasi-likelihood (PQL;Â [Breslow, N.E., Clayton, D.G., 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9-25]) is used to derive estimating equations for this adaptive spline model so that only low moment assumptions are required for inference. Both jackknife and bootstrap variance estimators are developed. The finite sample properties of the proposed estimating functions are investigated empirically by simulation. Comparisons with a model assuming a time homogeneous penalty are made. The methods are used in an analysis of data from an experiment to test the effectiveness of pheromones in disrupting the mating pattern of the cherry bark tortrix moth. Recommendations are provided on when the simpler model with a time homogeneous penalty may provide a fair approximation to data and where such an approach will be lacking, calling for the more complicated adaptive methods.

Suggested Citation

  • Nielsen, J.D. & Dean, C.B., 2008. "Adaptive functional mixed NHPP models for the analysis of recurrent event panel data," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3670-3685, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3670-3685
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    References listed on IDEAS

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    1. M. P. Wand, 2000. "A Comparison of Regression Spline Smoothing Procedures," Computational Statistics, Springer, vol. 15(4), pages 443-462, December.
    2. Wenxin Mao & Linda H. Zhao, 2003. "Free‐knot polynomial splines with confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 901-919, November.
    3. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    4. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
    6. Alexandre Pintore & Paul Speckman & Chris C. Holmes, 2006. "Spatially adaptive smoothing splines," Biometrika, Biometrika Trust, vol. 93(1), pages 113-125, March.
    7. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
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    1. Fei Qin & Zhangsheng Yu, 2021. "Penalized spline estimation for panel count data model with time-varying coefficients," Computational Statistics, Springer, vol. 36(4), pages 2413-2434, December.

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