Prior distribution elicitation for generalized linear and piecewise-linear models

Garthwaite, Paul H.; Al-Awadhi, Shafeeqah A.; Elfadaly, Fadlalla G. and Jenkinson, David J. (2013). Prior distribution elicitation for generalized linear and piecewise-linear models. Journal of Applied Statistics, 40(1) pp. 59–75.

DOI: https://doi.org/10.1080/02664763.2012.734794

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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