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：多变量分析有助于厘清因变量间的内在关联，该方法在诸多知识领域均具备广阔应用前景。本研究旨在拟合并对比单变量、多变量形式的戈姆佩茨（Gompertz）与逻辑斯蒂（Logistic）非线性模型，以阐释太阳麻（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，对376株太阳麻植株的生产性状进行分析（每日取样4株），测定指标包括叶片鲜重（FML）、茎秆鲜重（FMS）以及地上部鲜重（FMAP）。针对每项生产性状，分别拟合戈姆佩茨与逻辑斯蒂单变量模型。对于多变量模型的拟合，则通过计算误差协方差矩阵实现。针对各性状求取矩阵的乔莱斯基分解因子，进而构建多变量戈姆佩茨（GG）、逻辑斯蒂（LL）非线性模型，以及二者的组合模型（GL与LG）。为确定最优模型，本研究计算了残差标准差（RSD）、决定系数（R²）、赤池信息准则（AIC）、平均绝对偏差（MAD），以及内在非线性性（INL）与参数非线性性（PNL）等评估指标。研究结果表明，多变量逻辑斯蒂（LL）非线性模型适配性良好，可有效表征太阳麻的生产性状。