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Semiparametric Bayesian classification with longitudinal markers

Author

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  • Rolando De la Cruz‐Mesía
  • Fernando A. Quintana
  • Peter Müller

Abstract

Summary. We analyse data from a study involving 173 pregnant women. The data are observed values of the β human chorionic gonadotropin hormone measured during the first 80 days of gestational age, including from one up to six longitudinal responses for each woman. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from data that are available at the early stages of pregnancy. We achieve the desired classification with a semiparametric hierarchical model. Specifically, we consider a Dirichlet process mixture prior for the distribution of the random effects in each group. The unknown random‐effects distributions are allowed to vary across groups but are made dependent by using a design vector to select different features of a single underlying random probability measure. The resulting model is an extension of the dependent Dirichlet process model, with an additional probability model for group classification. The model is shown to perform better than an alternative model which is based on independent Dirichlet processes for the groups. Relevant posterior distributions are summarized by using Markov chain Monte Carlo methods.

Suggested Citation

  • Rolando De la Cruz‐Mesía & Fernando A. Quintana & Peter Müller, 2007. "Semiparametric Bayesian classification with longitudinal markers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(2), pages 119-137, March.
  • Handle: RePEc:bla:jorssc:v:56:y:2007:i:2:p:119-137
    DOI: 10.1111/j.1467-9876.2007.00569.x
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    File URL: https://doi.org/10.1111/j.1467-9876.2007.00569.x
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    Citations

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    Cited by:

    1. Navarrete, Carlos A. & Quintana, Fernando A., 2011. "Similarity analysis in Bayesian random partition models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 97-109, January.
    2. De la Cruz, Rolando & Meza, Cristian & Arribas-Gil, Ana & Carroll, Raymond J., 2016. "Bayesian regression analysis of data with random effects covariates from nonlinear longitudinal measurements," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 94-106.
    3. Silvia Montagna & Surya T. Tokdar & Brian Neelon & David B. Dunson, 2012. "Bayesian Latent Factor Regression for Functional and Longitudinal Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1064-1073, December.
    4. De la Cruz, Rolando, 2008. "Bayesian non-linear regression models with skew-elliptical errors: Applications to the classification of longitudinal profiles," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 436-449, December.
    5. Wang, Xianlong & Qu, Annie, 2014. "Efficient classification for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 119-134.
    6. Luts, Jan & Molenberghs, Geert & Verbeke, Geert & Van Huffel, Sabine & Suykens, Johan A.K., 2012. "A mixed effects least squares support vector machine model for classification of longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 611-628.
    7. Gutiérrez, Luis & Gutiérrez-Peña, Eduardo & Mena, Ramsés H., 2014. "Bayesian nonparametric classification for spectroscopy data," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 56-68.
    8. Gutiérrez, Luis & Mena, Ramsés H. & Ruggiero, Matteo, 2016. "A time dependent Bayesian nonparametric model for air quality analysis," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 161-175.
    9. Bhattacharya, Abhishek & Dunson, David, 2012. "Nonparametric Bayes classification and hypothesis testing on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 1-19.

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