Univariate and multivariate nonlinear models in productive traits of the sunn hemp

ABSTRACT Multivariate analysis helps to understand the relationships between dependent variables; this methodology has great potential in several areas of knowledge. The aim of this study was to adjust and compare the univariate and multivariate Gompertz and Logistic nonlinear models to describe the productive traits of sunn hemp (Crotalaria juncea L.). Two uniformity trials were performed, and the following productive traits were analyzed in 376 sunn hemp plants along 94 days of observations (four plants per day): the fresh mass of leaves (FML), the fresh mass of stem (FMS), and the fresh mass of the aerial parts (FMAP). The Gompertz and Logistic univariate models were adjusted for each productive trait. To adjust the multivariate models, the errors covariance matrix was calculated. The matrix (Cholesky factor) was obtained for each trait, and the multivariate Gompertz (GG) and Logistic (LL) nonlinear models were generated, together with the combination of both models (GL and LG). To define the best model, the residual standard deviation (RSD), the determination coefficient (R2), the Akaike information criterion (AIC), the mean absolute deviation (MAD), and the measures of intrinsic nonlinearity (INL) and parametric nonlinearity (PNL) were calculated. The nonlinear multivariate model LL was adequate and achieved satisfactory results to describe the productive traits of sunn hemp.

摘要 多变量分析有助于阐释因变量间的相互关联，该研究方法在众多学科领域均具备极高应用潜力。本研究旨在拟合并对比单变量与多变量形式的贡珀茨（Gompertz）非线性模型及逻辑斯蒂（Logistic）非线性模型，以刻画太阳麻（Crotalaria juncea L.）的生产性状。本研究开展了2组均匀性试验，在94天的观测周期内（每日取样4株），对376株太阳麻的3项生产性状进行测定分析：叶片鲜重（FML）、茎秆鲜重（FMS）及地上部鲜重（FMAP）。针对每项生产性状，分别拟合了单变量形式的贡珀茨模型与逻辑斯蒂模型。为拟合多变量模型，研究人员计算了误差协方差矩阵；针对各性状获取其乔莱斯基因子（Cholesky factor），进而构建了多变量贡珀茨（GG）、多变量逻辑斯蒂（LL）非线性模型，以及二者的组合模型（GL与LG）。为筛选最优模型，研究人员计算了残差标准差（residual standard deviation, RSD）、决定系数（determination coefficient, R²）、赤池信息准则（Akaike information criterion, AIC）、平均绝对偏差（mean absolute deviation, MAD），以及内在非线性性（intrinsic nonlinearity, INL）与参数非线性性（parametric nonlinearity, PNL）等多项评价指标。结果显示，多变量逻辑斯蒂（LL）非线性模型适配性良好，可有效刻画太阳麻的生产性状。