Prior distribution elicitation for generalized linear and piecewise-linear models

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.

Keywords:

• assessment tasks
• elicitation
• generalized linear model
• piecewise-linear function
• prior distribution
• subjective probability

Acknowledgements

The work reported here was supported by the Queensland Department of Natural Resources, Kuwait University Grants SS03/02 and XE02/03 and the UK Department of Health. We are very grateful to Ahmed Al-Saber for help with the data analysis and to Abdul Rahman Khan and Salem Al-Hajraf, whose opinions were quantified in the example about pollution. We must also thank three referees whose helpful comments led to improvements in the paper.