IDEAS home Printed from https://ideas.repec.org/a/bla/jorssa/v183y2020i3p959-981.html
   My bibliography  Save this article

On quantifying expert opinion about multinomial models that contain covariates

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssa.12546
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssa.12546?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    5. 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.
    6. Robert Tsutakawa & Hsin Lin, 1986. "Bayesian estimation of item response curves," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 251-267, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Claire Copeland & Britta Turner & Gareth Powells & Kevin Wilson, 2022. "In Search of Complementarity: Insights from an Exercise in Quantifying Qualitative Energy Futures," Energies, MDPI, vol. 15(15), pages 1-21, July.
    3. Jiayuan Dong & Jiankan Liao & Xun Huan & Daniel Cooper, 2023. "Expert elicitation and data noise learning for material flow analysis using Bayesian inference," Journal of Industrial Ecology, Yale University, vol. 27(4), pages 1105-1122, August.
    4. Danila Azzolina & Paola Berchialla & Silvia Bressan & Liviana Da Dalt & Dario Gregori & Ileana Baldi, 2022. "A Bayesian Sample Size Estimation Procedure Based on a B-Splines Semiparametric Elicitation Method," IJERPH, MDPI, vol. 19(21), pages 1-15, October.
    5. Saurabh Bansal & Genaro J. Gutierrez & Mahesh Nagarajan, 2021. "Theory-Driven Practical Approach to Integrate R&D and Production Planning for Portfolio Management in Agribusiness," Interfaces, INFORMS, vol. 51(5), pages 332-346, September.
    6. Danila Azzolina & Paola Berchialla & Dario Gregori & Ileana Baldi, 2021. "Prior Elicitation for Use in Clinical Trial Design and Analysis: A Literature Review," IJERPH, MDPI, vol. 18(4), pages 1-21, February.
    7. 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.
    8. 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.
    9. Maarten Ijzerman & Lotte Steuten, 2011. "Early assessment of medical technologies to inform product development and market access," Applied Health Economics and Health Policy, Springer, vol. 9(5), pages 331-347, September.
    10. Julia R. Falconer & Eibe Frank & Devon L. L. Polaschek & Chaitanya Joshi, 2022. "Methods for Eliciting Informative Prior Distributions: A Critical Review," Decision Analysis, INFORMS, vol. 19(3), pages 189-204, September.
    11. Sheng Wu & Weng Kee Wong & Catherine M. Crespi, 2017. "Maximin optimal designs for cluster randomized trials," Biometrics, The International Biometric Society, vol. 73(3), pages 916-926, September.
    12. Jacobs, Michael & Kiefer, Nicholas M., 2010. "The Bayesian Approach to Default Risk: A Guide," Working Papers 10-01, Cornell University, Center for Analytic Economics.
    13. Mohammed Abdellaoui & Han Bleichrodt & Emmanuel Kemel & Olivier l’Haridon, 2021. "Measuring Beliefs Under Ambiguity," Operations Research, INFORMS, vol. 69(2), pages 599-612, March.
    14. Yeojin Chung & Sophia Rabe-Hesketh & Vincent Dorie & Andrew Gelman & Jingchen Liu, 2013. "A Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 685-709, October.
    15. Nicholas Tibor Longford, 2016. "Decision Theory Applied to Selecting the Winners, Ranking, and Classification," Journal of Educational and Behavioral Statistics, , vol. 41(4), pages 420-442, August.
    16. Robert Stewart & Marie Urban & Samantha Duchscherer & Jason Kaufman & April Morton & Gautam Thakur & Jesse Piburn & Jessica Moehl, 2016. "A Bayesian machine learning model for estimating building occupancy from open source data," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(3), pages 1929-1956, April.
    17. Jesus Palomo & David Rios Insua & Fabrizio Ruggeri, 2007. "Modeling External Risks in Project Management," Risk Analysis, John Wiley & Sons, vol. 27(4), pages 961-978, August.
    18. Abhinav B. Agrawal & Kash Barker & Yacov Y. Haimes, 2011. "Adaptive multiplayer approach for risk‐based decision‐making: 2006 Virginia Gubernatorial Inauguration," Systems Engineering, John Wiley & Sons, vol. 14(4), pages 455-470, December.
    19. Mitchell J. Small, 2008. "Methods for Assessing Uncertainty in Fundamental Assumptions and Associated Models for Cancer Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 28(5), pages 1289-1308, October.
    20. Nicholas M. Kiefer, 2011. "Default estimation, correlated defaults, and expert information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 173-192, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssa:v:183:y:2020:i:3:p:959-981. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.