Prior distribution elicitation for generalized linear and piecewise-linear models |
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Authors: | Paul H Garthwaite Shafeeqah A Al-Awadhi Fadlalla G Elfadaly David J Jenkinson |
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Institution: | 1. Department of Mathematics and Statistics , The Open University , Milton Keynes , MK7 6AA , UK;2. Statistics and Operations Research , Kuwait University , PO Box 5969, Safat , 13060 , Kuwait;3. Medical and Dental Sciences , University of Birmingham , B15 2TT , UK |
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Abstract: | An elicitation method is proposed for quantifying subjective opinion about the regression coefficients of a generalized linear model. Opinion between a continuous predictor variable and the dependent variable is modelled by a piecewise-linear function, giving a flexible model that can represent a wide variety of opinion. To quantify his or her opinions, the expert uses an interactive computer program, performing assessment tasks that involve drawing graphs and bar-charts to specify medians and other quantiles. Opinion about the regression coefficients is represented by a multivariate normal distribution whose parameters are determined from the assessments. It is practical to use the procedure with models containing a large number of parameters. This is illustrated through practical examples and the benefit from using prior knowledge is examined through cross-validation. |
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Keywords: | assessment tasks elicitation generalized linear model piecewise-linear function prior distribution subjective probability |
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