FUNÇÕES SPLINES APLICADAS EM DADOS DE CRESCIMENTO
In animal breeding, new methodologies can be applied in statistical analysis to improve the genetic evaluation and, for this reason, they have been the subject in several studies. In the last years, several research works have intended the model development with more adjustable functions to the distinct variables. A set of functions known as Spline functions has called the attention of researches. Then, the purpose of this review is to discuss the use of Spline functions that are applied to growth data in animal breeding. Splines are segmented regression functions that are united by points known as joint points and have the ability to improve the curvature of models and, therefore, the function adjustment. These functions have interesting properties such as the interpolatory nature, less multicolinearity problems, parameter linearity and the ability of increasing the approximation domain, all of which provide estimates in a wide range of possible values. There are three types of Spline functions: natural spline functions, smoothing spline 223 Colloquium Agrariae, vol. 13, n. Especial 2, Jan–Jun, 2017, p. 222-234. ISSN: 1809-8215. DOI: 10.5747/ca.2017.v13.nesp2.000229 functions or nonparametric regression and B-splines functions. These latter functions are more applied to animal breeding, mainly as alternatives to random regression models (RRM) that use the Legendre polynomials. The matrices formed by RRMs with the use of B-spline functions or Legendre polynomials are more scarce and easier to be inverted. Then, the use of Spline functions has been more intensified in the last years because studies have had the purpose of improving the adjustment with less model parameters in functions. New studies will allow improving the methodology and finding out new applications to the Spline functions.