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Eliciting prior distributions for extra parameters in some generalized linear models

Elfadaly, Fadlalla G. and Garthwaite, Paul H. (2015). Eliciting prior distributions for extra parameters in some generalized linear models. Statistical Modelling, 15(4) pp. 345–365.

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To elicit an informative prior distribution for a normal linear model or a gamma generalized linear model (GLM), expert opinion must be quantified about both the regression coefficients and the extra parameters of these models. The latter task has attracted comparatively little attention. In this article, we introduce two elicitation methods that aim to complete the prior structure of the normal and gamma GLMs. First, we develop a method of assessing a conjugate prior distribution for the error variance in normal linear models. The method quantifies an expert's opinions through assessments of a median and conditional medians. Second, we propose a novel method for eliciting a lognormal prior distribution for the scale parameter of gamma GLMs. Given the mean value of a gamma distributed response variable, the method is based on conditional quartile assessments. It can also be used to quantify an expert's opinion about the prior distribution for the shape parameter of any gamma random variable, if the mean of the distribution has been elicited or is assumed to be known. In the context of GLMs, the mean value is determined by the regression coefficients. Interactive graphics is the medium through which assessments for the two proposed methods are elicited. Examples illustrating use of the methods are given. Computer programs that implement both methods are available.

Item Type: Journal Item
Copyright Holders: 2015 SAGE Publications
ISSN: 1477-0342
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetThe Open University (OU)
Keywords: Elicitation; subjective prior distribution; normal linear model; gamma distribution; generalized linear model; interactive graphical software
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 49482
Depositing User: Fadlalla Elfadaly
Date Deposited: 26 May 2017 08:56
Last Modified: 07 Dec 2018 10:51
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