Alfadaly, Fadlallah G. and Garthwaite, Paul H.
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Suitable elicitation methods play a key role in Bayesian analysis of generalized linear models (GLMs) by obtaining and including expert knowledge as a prior distribution for the model parameters. Some elicitation methods for GLMs available in the literature focus mainly on logistic regression. A more general elicitation method of quantifying opinion about any GLM was developed in Garthwaite and Al-Awadhi (2006). The relationship between each continuous predictor and the dependant variable was modeled as a piecewise-linear function and each of its dividing points is accompanied with a regression coefficient. However, a simplifying assumption was made regarding independence between these coefficients, in the sense that regression coefficients were a priori independent if associated with different predictors. In this current research we relax the independence assumption between coefficients of different variables. In this case the variance-covariance matrix of the prior distribution is no longer block-diagonal. A method of elicitation for this more complex case is given and it is shown that the resulting covariance matrix is positive-definite. The method was designed to be used with the aid of interactive graphical software. It has been used in practical case studies to quantify the opinions of ecologists and medical doctors (Al-Awadhi and Garthwaite (2006); Garthwaite, Chilcott, Jenkinson, and Tappenden (2008)). The software is being revised and extended further in this research to handle the case of GLM with correlated pairs of covariates.
|Item Type:||Conference Item|
|Copyright Holders:||2010 by The Islamic Countries Society of Statistical Sciences (ISOSS)|
|Extra Information:||Published in 'Proceedings of the ICCS-X Tenth Islamic Countries Conference on Statistical Sciences: Statistics for Development and Good Governance Volume I', ISBN: 978-977-416-365-8|
|Keywords:||elicitation methods; expert opinion; assessment task; prior distribution; generalized linear model; interactive graphical software|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Sarah Frain|
|Date Deposited:||10 Mar 2011 15:01|
|Last Modified:||13 Feb 2013 12:07|
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