Functional Regression
AbstractThis chapter deals with the main theoretical fundamentals and practical issues of using functional regression in the context of genomic prediction. We explain how to represent data in functions by means of basis functions and considered two basis functions: Fourier for periodic or near-periodic data and B-splines for nonperiodic data. We derived the functional regression with a smoothed coefficient function under a fixed model framework and some examples are also provided under this model. A Bayesian version of functional regression is outlined and explained and all details for its implementation in glmnet and BGLR are given. The examples take into account in the predictor the main effects of environments and genotypes and the genotype × environment interaction term. The examples are done with small data sets so that the user can run them on his/her own computer and can understand the implementation process.