Genetic Algorithms Applied to Fractional Polynomials for Power Selection: Application to Diabetes Data

Abstract

Fractional polynomials are powerful statistic tools used in multivariable building model to select relevant variables and their functional form. This selection of variables, together with their corresponding power is performed through a multivariable fractional polynomials (MFP) algorithm that uses a closed test procedure, called function selection procedure (FSP), based on the statistical significance level α. In this paper, Genetic algorithms, which are stochastic search and optimization methods based on string representation of candidate solutions and various operators such as selection, crossover and mutation; reproducing genetic processes in nature, are used as alternative to MFP algorithm to select powers in an extended set of real numbers (to be specified) by minimizing the Bayesian Information Criteria (BIC). A simulation study and an application to a real dataset are performed to compare the two algorithms in many scenarios. Both algorithms perform quite well in terms of mean square error with Genetic algorithms that yied a more parsimonious model comparing to MFP Algorithm .