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Elfadaly, Fadlalla and Garthwaite, Paul H.
(2010).
URL: http://www.iccs-x.org.eg/pages/Volume%201.pdf#page...
Abstract
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.
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