Teste para regressão spline linear: simulação e aplicação a dados de crescimento de ovinos

Abstract

The sheep flock has been increasing in Brazil but, is not yet sufficient to supply the domestic market, so that Brazil continues importing sheep meat from other countries so far. This shows to Brazil graziers the opportunity of developing mechanisms seeking to obtain high production, productivity, and high quality. A consistent and practical way of analysing the livestock productive efficiency is by studying growth curves, which describe a functional relationship between weight and age. Growth curves, however, are generally described using nonlinear models, which represent parameters for biological interpretation. The purpose of this study was to use linear and nonlinear regressions, with up to three segments, to describe growth curves on breed sheeps. We also assessed, by means of simulation studies, properties of parameters estimators of piecewise linear function, such as consistency and trend. Besides, we assessed the extra sum of squares as a statistical tool to estimate the number of significant segments of these segmented linear regressions. Weight data of the following genetic beef sheep groups were used: Dorper × Morada Nova, Dorper × Rabo Largo, and Dorper × Santa Inês. Parameters estimators of piecewise linear functions showed a slight bias, were found to be independent, and were consistent when errors had homoscedastic variance. Therefore, based on the extra sum of squares, the statistical test was found to be an excellent tool in estimating the number of significant segmented linear regressions.