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Semiparametric regression for count data

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  • Cinzia Carota

Abstract

We introduce a class of Bayesian semiparametric models for regression problems in which the response variable is a count. Our goal is to provide a flexible, easy-to-implement and robust extension of generalised linear models, for datasets of moderate or large size. Our approach is based on modelling the distribution of the response variable using a Dirichlet process, whose mean distribution function is itself random and is given a parametric form, such as a generalised linear model. The effects of the explanatory variables on the response are modelled via both the parameters of the mean distribution function of the Dirichlet process and the total mass parameter. We discuss modelling options and relationships with other approaches. We derive in closed form the marginal posterior distribution of the regression coefficients and discuss its use in inference and computing. We illustrate the benefits of our approach with a prognostic model for early breast cancer patients. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Cinzia Carota, 2002. "Semiparametric regression for count data," Biometrika, Biometrika Trust, vol. 89(2), pages 265-281, June.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:265-281
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    Cited by:

    1. Griffin, J. E. & Steel, M. F. J., 2004. "Semiparametric Bayesian inference for stochastic frontier models," Journal of Econometrics, Elsevier, vol. 123(1), pages 121-152, November.
    2. Bisaglia, Luisa & Canale, Antonio, 2016. "Bayesian nonparametric forecasting for INAR models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 70-78.
    3. Z. Yuan & R. Chappell & H. Bailey, 2007. "The Continual Reassessment Method for Multiple Toxicity Grades: A Bayesian Quasi-Likelihood Approach," Biometrics, The International Biometric Society, vol. 63(1), pages 173-179, March.
    4. Nan Zheng & Brajendra C. Sutradhar, 2018. "Inferences in semi-parametric dynamic mixed models for longitudinal count data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 215-247, February.
    5. José Santos & M. Neves, 2008. "A local maximum likelihood estimator for Poisson regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 257-270, November.
    6. Rodríguez, Abel, 2013. "On the Jeffreys prior for the multivariate Ewens distribution," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1539-1546.
    7. Michael L. Pennell & David B. Dunson, 2008. "Nonparametric Bayes Testing of Changes in a Response Distribution with an Ordinal Predictor," Biometrics, The International Biometric Society, vol. 64(2), pages 413-423, June.
    8. Krnjajic, Milovan & Kottas, Athanasios & Draper, David, 2008. "Parametric and nonparametric Bayesian model specification: A case study involving models for count data," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2110-2128, January.

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