Metodologia para análise de adaptabilidade e estabilidade por meio de regressão quantílica

Abstract

Resumo -O objetivo deste trabalho foi desenvolver e validar uma metodologia de análise da adaptabilidade e da estabilidade fenotípica baseada em regressão quantílica (RQ). Para tanto, foram simulados valores fenotípicos com distribuição simétrica e com distribuição assimétrica à direita e à esquerda, com ou sem a presença de "outliers". A metodologia proposta foi aplicada a um conjunto de dados provenientes de um experimento com 92 genótipos de alfafa (Medicago sativa), avaliados em 20 ambientes, e comparada às metodologias de Eberhart & Russell e de regressão não paramétrica. A metodologia da RQ proporcionou resultados iguais ou superiores aos obtidos com as metodologias alternativas avaliadas. No entanto, a ocorrência de resultados discordantes entre as metodologias evidencia a importância de se avaliar a simetria na distribuição dos valores fenotípicos. Para distribuições simétricas, na presença de "outliers", deve-se utilizar a RQ com valor de quantil estimado (t) em 0,50; na ausência de "outliers", pode-se utilizar tanto a metodologia de Eberhart & Russell quanto a RQ (t = 0,50). Para distribuições assimétricas, indica-se o uso da RQ com t = 0,25, para assimetria à direita, e com t = 0,75, para assimetria à esquerda, independentemente da presença de "outliers".Termos para indexação: Medicago sativa, distribuição assimétrica, interação genótipo x ambiente, melhoramento vegetal, outliers, regressão não paramétrica. Methodology for analysis of adaptability and stability using quantile regressionAbstract -The objective of this work was to develop and validate a methodology for analyzing phenotypic adaptability and stability based on quantile regression (QR). For this, phenotypic values were simulated with symmetrical distribution and with asymmetrical distribution to the right and to the left, with or without outliers. The proposed methodology was applied to a data set from an experiment with 92 alfalfa (Medicago sativa) genotypes, evaluated in 20 environments, and compared with the methodologies of Eberhart & Russell and nonparametric regression. The QR methodology provided equal or superior results, compared to the evaluated alternative methodologies. However, the occurrence of disagreeing results between methodologies evidences the importance of evaluating symmetry in the distribution of phenotypic values. For symmetric distributions with outliers, QR should be used with estimated quantile value (t) of 0.50; in the absence of outliers, both the methodology of Eberhart & Russel and QR (t = 0.50) may be used. For asymmetric distributions, the use of RQ with t = 0.25 is suggested for asymmetry to the right, and with t = 0.75 for asymmetry to the left, regardless of the presence of outliers.

<b>Fuzzy control systems for decision-making in cultivars recommendation

“…There are methods based on analysis of variance (Plaisted & Peterson, 1959;Wricke, 1965), regression (Cruz, Torres, & Vencovsky, 1989;Eberhart & Russell, 1966;Finlay & Wilkinson, 1963;Tai, 1971;Barroso et al, 2015), nonparametric methods (Lin & Binns, 1988;Rocha, Muro-Abad, Araújo, & Cruz, 2005;Nascimento et al, 2015), linear mixed models Reml/Blup (Resende, 2004), bayesian methods (Couto et al, 2015), and artificial neural networks (Barroso et al, 2013;.…”

Analysis of the adaptability of black bean cultivars by means of quantile regression

“…It should be emphasized that the concept of adaptability used in QR models is similar to the one described by EBERHART & RUSSELL (1966); i.e., adaptability refers to the ability of cultivars to benefit from the environment. BARROSO et al, (2015) suggested that the following model of quantile regression is used in studies of adaptability and phenotypic stability:…”

“…Although interesting, such studies evaluate the adaptability in average terms, i.e., the correlation between environmental variation (X) and phenotypic response (Y) is explained by conditional expectation E(Y|X). In order to obtain information on different levels of the productivity variable, BARROSO et al (2015) proposed the use of quantile regression (KOENKER & BASSET, 1978) for adaptability and stability studies considering 92 genotypes of alfalfa (Medicago sativa L.) assessed in 20 different environmental conditions. In order to explain the functional relationship between the environmental variation (X) and the phenotypic response (Y), this method, unlike the methods based on linear regression (EBERHART & RUSSELL, 1966) provides a generalized explanation for any quantile of phenotypic values.…”

Research Article Methods of adaptability and stability applied to the improvement of flooded rice

“…They differ in their biometric estimation concepts and procedures (Buitrago et al, 2011;Silva, 2012). Among these, we can mention methods that are already consolidated in the literature as those based on analysis of variance (Plaisted and Peterson, 1959;Wricke, 1965;Annicchiarico, 1992), linear regression (Finlay and Wilkinson, 1963;Eberhart and Russell, 1966;Tai, 1971;Cruz et al, 1989), methods non-parametric (Lin and Binns, 1988;Carneiro, 1998;Rocha et al, 2005), Multiple methods centroids (Nascimento et al, 2009;Nascimento et al, 2015), mixed linear models REML/Blup (Resende, 2004), Bayesian methods (Nascimento et al, 2011, Couto et al, 2015, quantile regression (Barroso et al, 2015), Artificial Neural Networks (Barroso et al, 2013), AMMI model (Gauch, 1992) and GGE biplot (Yan et al, 2011).…”