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Prior distribution elicitation for generalized linear and piecewise-linear models

Author

Listed:
  • Paul H. Garthwaite
  • Shafeeqah A. Al-Awadhi
  • Fadlalla G. Elfadaly
  • David J. Jenkinson

Abstract

An elicitation method is proposed for quantifying subjective opinion about the regression coefficients of a generalized linear model. Opinion between a continuous predictor variable and the dependent variable is modelled by a piecewise-linear function, giving a flexible model that can represent a wide variety of opinion. To quantify his or her opinions, the expert uses an interactive computer program, performing assessment tasks that involve drawing graphs and bar-charts to specify medians and other quantiles. Opinion about the regression coefficients is represented by a multivariate normal distribution whose parameters are determined from the assessments. It is practical to use the procedure with models containing a large number of parameters. This is illustrated through practical examples and the benefit from using prior knowledge is examined through cross-validation.

Suggested Citation

  • Paul H. Garthwaite & Shafeeqah A. Al-Awadhi & Fadlalla G. Elfadaly & David J. Jenkinson, 2013. "Prior distribution elicitation for generalized linear and piecewise-linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(1), pages 59-75, January.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:1:p:59-75
    DOI: 10.1080/02664763.2012.734794
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    Citations

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    Cited by:

    1. Hosack, Geoffrey R. & Hayes, Keith R. & Barry, Simon C., 2017. "Prior elicitation for Bayesian generalised linear models with application to risk control option assessment," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 351-361.
    2. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    3. Fadlalla G. Elfadaly & Paul H. Garthwaite, 2020. "On quantifying expert opinion about multinomial models that contain covariates," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 959-981, June.
    4. Laura C. Dawkins & Daniel B. Williamson & Stewart W. Barr & Sally R. Lampkin, 2020. "‘What drives commuter behaviour?': a Bayesian clustering approach for understanding opposing behaviours in social surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 251-280, January.

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