Using genetic algorithms for order selection in fractional polynomials

In fitting regression models, data analysts are often faced with many predictor variables which may influence the outcome. Several strategies for selection of variables to identify a subset of 'important' predictors are available for many years. A further issue to model building is how to deal with non-linearity in the relationship between outcome and continuous predictors. Royston and Altman (1994) proposed the use of fractional polynomial models for modelling such non-linear covariate effects. Fractional Polynomials models are selected through a function selection procedure(FSP) that selects powers in a restricted set S = {−2,−1,−0.5,0,0.5,1,2,3} proposed by Royston and Altman (1994) for practical use. This thesis aims to implement a stochastic optimization technique, termed Genetic Algorithms (GAs), to select powers in an extended set (to be specified) by minimizing the Bayesian Information Criteria (BIC). Models using powers selected by genetic algorithms are compared with fractional polynomials models through real datasets application. The former seems to provide slightly improved fits than the latter.