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The quantile probability model

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  • Heyard, Rachel
  • Held, Leonhard

Abstract

There is now a large literature on optimal predictive model selection. Bayesian methodology based on the g-prior has been developed for the linear model where the median probability model (MPM) has certain optimality features. However, it is unclear if these properties also hold in the generalised linear model (GLM) framework, frequently used in clinical prediction models. In an application to the GUSTO-I trial based on logistic regression where the goal was the development of a clinical prediction model for 30-day mortality, sensitivity of the MPM with respect to commonly used prior choices on the model space and the regression coefficients was encountered. This makes a decision on a final model difficult. Therefore an extension of the MPM has been developed, the quantile probability model (QPM), that uses posterior inclusion probabilities to define a drastically reduced set of candidate models. Predictive model selection criteria are then applied to identify the model with best predictive performance. In the application the QPM turns out to be independent of the prior choices considered and gives better predictive performance than the MPM. In addition, a novel batching method is presented to efficiently estimate the Monte Carlo standard error of the predictive model selection criterion.

Suggested Citation

  • Heyard, Rachel & Held, Leonhard, 2019. "The quantile probability model," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 84-99.
    • Handle: RePEc:eee:csdana:v:132:y:2019:i:c:p:84-99
    DOI: 10.1016/j.csda.2018.08.022
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    References listed on IDEAS

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    1. Joyee Ghosh & Andrew E. Ghattas, 2015. "Bayesian Variable Selection Under Collinearity," The American Statistician, Taylor & Francis Journals, vol. 69(3), pages 165-173, August.
    2. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, October.
    3. Valen E. Johnson, 2008. "Properties of Bayes Factors Based on Test Statistics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 354-368, June.
    4. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Jianhua Hu & Valen E. Johnson, 2009. "Bayesian model selection using test statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 143-158, January.
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