Fractional Polynomial Models as Special Cases of Bayesian Generalized Nonlinear Models

Abstract

We propose a framework for fitting multivariable fractional polynomial models as special cases of Bayesian generalized nonlinear models, applying an adapted version of the genetically modified mode jumping Markov chain Monte Carlo algorithm. The universality of the Bayesian generalized nonlinear models allows us to employ a Bayesian version of fractional polynomials in any supervised learning task, including regression, classification, and time-to-event data analysis. We show through a simulation study that our novel approach performs similarly to the classical frequentist multivariable fractional polynomials approach in terms of variable selection, identification of the true functional forms, and prediction ability, while naturally providing, in contrast to its frequentist version, a coherent inference framework. Real-data examples provide further evidence in favor of our approach and show its flexibility.

Keywords

• Bayesian model selection
• MCMC
• nonlinear effects