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On quantifying expert opinion about multinomial models that contain covariates

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  • Fadlalla G. Elfadaly
  • Paul H. Garthwaite

Abstract

The paper addresses the task of forming a prior distribution to represent expert opinion about a multinomial model that contains covariates. The task has not previously been addressed. We suppose that the sampling model is a multinomial logistic regression and represent expert opinion about the regression coefficients by a multivariate normal distribution. This logistic–normal model gives a flexible prior distribution that can capture a broad variety of expert opinion. The challenge is to find meaningful assessment tasks that an expert can perform and which should yield appropriate information to determine the values of parameters in the prior distribution, and to develop theory for determining the parameter values from the assessments. A method is proposed that meets this challenge. The method is implemented in interactive easy‐to‐use software that is freely available. It provides a graphical interface that the expert uses to assess quartiles of sets of proportions and the method determines a mean vector and a positive definite covariance matrix to represent the expert's opinions. The assessment tasks chosen yield parameter values that satisfy the usual laws of probability without the expert being aware of the constraints that this imposes. Special attention is given to feedback that encourages the expert to consider his or her opinions from a different perspective. The method is illustrated in an example that shows its viability and usefulness.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:183:y:2020:i:3:p:959-981
    DOI: 10.1111/rssa.12546
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    References listed on IDEAS

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    1. John Paul Gosling, 2018. "SHELF: The Sheffield Elicitation Framework," International Series in Operations Research & Management Science, in: Luis C. Dias & Alec Morton & John Quigley (ed.), Elicitation, chapter 0, pages 61-93, Springer.
    2. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    3. Fadlalla Elfadaly & Paul Garthwaite, 2013. "Eliciting Dirichlet and Connor–Mosimann prior distributions for multinomial models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 628-646, November.
    4. Rita Esther Zapata-V�zquez & Anthony O'Hagan & Leonardo Soares Bastos, 2014. "Eliciting expert judgements about a set of proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1919-1933, September.
    5. 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.
    6. Robert Tsutakawa & Hsin Lin, 1986. "Bayesian estimation of item response curves," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 251-267, June.
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    Cited by:

    1. Yunting Song & Nuo Wang, 2021. "On probability distributions of the time deviation law of container liner ships under interference uncertainty," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 354-367, January.

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