三元肥料效应模型的整合与优化建模策略

针对当前作物肥效模型建模成功率普遍偏低的问题，探讨了提高建模成功率的优化建模策略。在分析整合三元非结构肥效模型非线性最小二乘（NLS）和三元二次多项式肥效模型普通最小二乘（OLS）、主成分回归（PCR）和可行广义最小二乘回归（FGLS）四种建模法的适用性基础上，根据水稻和露地蔬菜的1 122个氮磷钾田间肥效试验结果，探讨三元肥效模型的综合应用方法。结果表明，三元肥效模型不同函数式及其建模法的适用性有明显差别。三元二次多项式肥效模型OLS建模法的典型式比例平均仅有19.8%，克服多重共线性危害的PCR建模法和克服异方差危害的FGLS建模法均有利于提高典型式比例，而同时克服了模型设定偏误和多重共线性危害的非结构肥效模型及其NLS建模法的典型式比例则提高至41.4%。根据不同模型及其建模法的适用性，提出三元肥效模型四步建模法，结果使典型式的比例进一步提高至57.5%，且在双季稻、单季稻和露地蔬菜中的相关比例差异很小。因此，四步建模法是大幅度提高三元肥效模型建模成功率的有效技术方法。

Integration and Optimization Modeling Strategy for Ternary Fertilizer Response Model

Objective] To tackle the present problem of fertilizer response modeling being generally low in success rate, this paper was devoted to discussions about strategies to optimize modeling and to improve its success rate.Method] Based on collation and analysis of the following four modeling methods, i.e. nonlinear least-squares (NLS) modeling method for ternary non-structured fertilizer response model (TNFM), and ordinary least squares (OLS) method, principal component regression (PCR) method and feasible generalized least squares regression (FGLS) method for ternary quadratic polynomial fertilizer response mode l(TPFM), for adoptability and 1122 NPK fertilizer field experiments conducted in paddy fields and open vegetable gardens, an optimal modeling technology was designed and brought forth for comprehensive application of ternary fertilizer response models.Result] Results show that ternary fertilizer response modeling using different functional equations and different modeling methods varied significantly in adoptability. The OLS modeling method for TPFM reached only 19.8% on average in proportion of typical models, while the PCR and FGLS modeling methods that had overcome the impacts of multicollinearity and heteroscedasticity, did up to 34.0% and 27.1%, respectively, and the NLS modeling method for TNFM after overcoming the obstacles of model specification bias and multicollinearity simultaneously rose further up to 41.4%, which improved the success rate of modeling. Using the classical OLS modeling method for TPFMs, the modeling had 28.7% failing the Duncan test, 30.1% having unreasonable model coefficient symbols, 15.2% missing maximum yield points and 6.1% extrapolating fertilization recommendation. However, the PCR modeling method reduced significantly the proportion having unreasonable coefficient symbols and increased that extrapolating fertilization recommendation, and the FGLS modeling method brought down to zero the proportion failing the Duncan test, but increased by a large margin in the proportion having unreasonable coefficient symbols. The ternary non-structural fertilizer response model significantly reduced the proportion having unreasonable coefficient symbols or missing maximum yield points, while increasing the proportion of non-typical models extrapolating fertilizer recommendation. Since agricultural production goes on in conditions of extreme complexity and diversity, it is certain that the curve or curved surface that reflects crops response to fertilization diversifies. Therefore, in the light of the applicability of the models and their modeling methods, a four-step modeling method is brought forth herewith for comprehensive application of the ternary fertilizer response model, which may raise the proportion of typical models up to 57.5%, and minimize the differences between double-cropping rice, single-cropping rice and vegetable crops in relevant proportion.Conclusion] The four-step modeling method is an effective technical method to improve success rate of the modeling for ternary fertilizer response models.