土壤学报2018，Vol.55Issue(2)：467-478,12.DOI:10.11766/trxb201709140242
提高三元肥效模型建模成功率的主成分回归技术研究
Principal Component Regression Technology of Ternary Fertilizer Response Model for Improving Success Rate of Modeling
摘要
Abstract
[Objective]There is a large number of non-typical 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(XTX)of the matrix X designed for the"3414"field experimentsand variance inflation factors (VIF) of the model parametersshows 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 ofearly 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. Theproportions ofthe non-typical typed models, such as no maximum-yield point, unreasonablesigns of monomial coefficientor 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 non-typical models with unreasonable coefficient symbolsby a large marginfrom 14.6%to zero, and the proportion of non-typical models with no maximum-yield point from 36.8% to 21.1%, which fully manifested the positive effect of eliminating the hazardof multicollinearity on success rate of modeling. Seven-principal-component 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 non-typical 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 ofternary typical fertilizing effect modelsto predict early rice response to N, P and K fertilization.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)Key words
Early rice/N/P and K/Fertilizing effect model/Multicollinearity/Principal component regression/Ordinary least squares (OLS)分类
农业科技引用本文复制引用
李娟,章明清,许文江,孔庆波,姚宝全..提高三元肥效模型建模成功率的主成分回归技术研究[J].土壤学报,2018,55(2):467-478,12.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(2016PI-31)和农业部测土配方施肥项目(2011-2015)资助 Supported by the National Natural Science Foundation of China(No.31572203)and PI Project of Fujian Academy of Agricultural Sciences(No.2016PI-31)and Soil-Test-Based Formulated Fertilizer Project of the Ministry of Agriculture of the People's Republic of China(No.2011-2015) （31572203）
