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Semiparametric analysis of longitudinal zero-inflated count data

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  • Feng, Jiarui
  • Zhu, Zhongyi
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    Abstract

    In this article, we consider a semiparametric zero-inflated Poisson mixed model that postulates a possible nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate in the longitudinal studies. A penalized log-likelihood function is proposed and Monte Carlo expectation-maximization algorithm is used to derive the estimates. Under some mild conditions, we establish the consistency and asymptotic normality of the resulting estimators. Simulation studies are carried out to investigate the finite sample performance of the proposed method. For illustration purposes, the method is applied to a data set from a pharmaceutical company where the variable of interest is the number of episodes of side effects after the patient has taken the treatments.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 102 (2011)
    Issue (Month): 1 (January)
    Pages: 61-72

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:1:p:61-72

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    Related research

    Keywords: ZIP regression Mixed model Penalized spline MCEM algorithm;

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    3. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    4. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
    5. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
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