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提高三元肥效模型建模成功率的主成分回归技术研究 
李 娟,章明清,许文江,孔庆波,姚宝全

1.福建省农业科学院土壤肥料研究所;2.福建省亚热带植物研究所;3.福建省农田建设与土壤肥料技术推广总站


摘要: 
三元二次多项式肥效模型在施肥实践中存在大量非典型式，严重制约了肥效模型计量精确性和应用价值。为提高田间肥效试验建模成功率，本研究探讨肥效模型建模新方法。根据福建省早稻171个“3414”设计的氮磷钾田间肥效试验结果，研究三元二次多项式肥效模型多重共线性的危害和诊断方法以及主成分回归建模技术。结果表明，试验设计矩阵X的方阵（X^{T}X）条件数和方差膨胀因子的诊断指标均显示，三元二次多项式肥效模型存在严重的多重共线性，且这种共线性主要是因模型设定本身造成的。多重共线性严重制约了普通最小二乘法（OLS）的有效性，OLS回归建模的三元典型肥效模型比例仅占试验总数的27.5%。主成分回归对设计矩阵提取互不相关的9个主成分，消除了多重共线性危害。采用前7个主成分回归建模，三元典型肥效模型比例提高至43.3%，为OLS法的1.6倍。尤其是主成分回归大幅度降低了模型系数符号不合理的非典型式，从OLS建模的14.6%下降至零；模型无最高产量点的非典型式比例从OLS建模的36.8%下降至21.1%。7个主成分回归建模利用了试验设计矩阵X 99.9%以上的方差信息，其所得典型式与OLS法所得典型式在推荐施肥量和预测产量上几乎无差别。针对主成分回归是一种有偏估计，采用OLS法结合前7个主成分回归建模，三元典型肥效模型所占比例进一步提高至55.6%，为OLS法的2.0倍，结果明显优于单独使用OLS回归或者主成分回归。因此，主成分回归可消除三元二次多项式肥效模型的多重共线性危害，OLS法结合前7个主成分回归建模是显著提高水稻氮磷钾三元典型肥效模型比例的最优建模策略。 
关键词: 早稻 氮磷钾 肥效模型 多重共线性 主成分回归 普通最小二乘法（OLS） 
DOI：10.11766/trxb201709140242 
分类号: 
基金项目:国家自然科学基金项目（31572203）、福建省农业科学院PI项目（2016PI31）和农业部测土配方施肥项目（20112015）资助 

Principal Component Regression Technology of Ternary Fertilizer Response Model for Improving Success Rate of Modeling 
LI Juan^{1}, ZHANG Mingqing^{1}, XU Wenjiang^{2}, KONG Qingbo^{3}, YAO Baoquan^{4}

1.Soil and Fertilizer Institute, Fujian Academy of Agricultural Science;2.Fujian Institute of Subtropical Plants;3.Soil and Fertilizer Institute, Fujian Academy of Agricultural Sciences;4.Fujian Cropland Construction and Soil and Fertilizer Station

Abstract: 
【Objective】There is a large number of nontypical ones of ternary quadratic polynomial models for fertilizing effect (TQPM) used in fertilization practice, severely affecting accuracy and practicality of the fertilizing effect models. In order to improve success rate of modeling for field fertilization experiments, this study was oriented to explore new modeling methods. 【Method】Based on 171 field fertilization experiments of“3414”in design on response of early rice to N, P and K fertilization in Fujian Province, efforts were made to explore methods to diagnose multicollinearity of TQPMs and technology for modeling with principal component regression and effects of their usage. 【Result】Diagnoses of number of conditions of the square matrix（X^{T}X）of the matrix X designed for the “3414”field experiments and variance inflation factors (VIF) of the model parameters shows that TQPMs do have serious multicollinearity, which is mainly caused by the specification of the models per se, and severely restrains application value of the ordinary least squares (OLS). Among the 171 field experiments of early rice response to N, P and K fertilization in Fujian province, ternary typical fertilizing effect models using the OLS regression modeling method accounted for only 27.5% of the total. The proportions of the nontypical typed models, such as no maximumyield point, unreasonable signs of monomial coefficient or quadratic coefficient, and extrapolation of recommended fertilization rate, reached 36.8%, 14.6% and 5.3%, respectively, of the total using the OLS modeling method. Principal component regression（PCR）extracted 9 unrelated principal components from the designed matrix, thus eliminating the negative effect of multicollinearity. When the first 7 principal components were used in regression modeling, the proportion of ternary typical fertilizing effect models increased up to 43.3% or 1.6 times as high as that using the OLS method. What is more, compared with the OLS modeling method, PCR decreased the proportions of nontypical models with unreasonable coefficient symbols by a large margin from 14.6% to zero, and the proportion of nontypical models with no maximumyield point from 36.8% to 21.1%, which fully manifested the positive effect of eliminating the hazard of multicollinearity on success rate of modeling. Sevenprincipalcomponent regression modeling made use of more than 99.9% of the variance information of the designed experimental matrix X, and all the typical models established by PCR modeling did not differ much from those by OLS modeling in recommending fertilization rate and predicting yields. As principal component regression is a kind of biased estimate, only the experimental designed matrix was taken into account in extracting principal components, but not relationship between each principal component and yield of each corresponding treatment. As affected by regression bias, typical models by OLS regression may occasionally turn into nontypical ones. Therefore, from the aspect of practical application, the use of OLS modeling in combination with modeling based on regression of the first seven principal component, increased the proportion of ternary typical fertilizing effect models up to 55.6%, or 2.0 times as high as that using OLS modeling alone, and was much better than using the PCR alone. 【Conclusion】Principal components regression can eliminate the defect of multicollinearity of the ternary quadratic polynomial fertilizing effect model The use of the ordinary least squares method in combination with the PCR modeling based on the first seven principal components is the optimal modeling strategy that can significantly increase the proportion of of ternary typical fertilizing effect models to predict early rice response to N, P and K fertilization. 
Key words: Early rice N, P and K, Fertilizing effect model Multicollinearity Principal component regression Ordinary least squares (OLS) 





