三元肥效模型异方差诊断及其可行广义最小二乘回归建模研究

doi:10.3864/j.issn.0578-1752.2018.04.012

中国农业科学 ›› 2018, Vol. 51 ›› Issue (4): 728-737.doi: 10.3864/j.issn.0578-1752.2018.04.012

• 土壤肥料·节水灌溉·农业生态环境 • 上一篇下一篇

三元肥效模型异方差诊断及其可行广义最小二乘回归建模研究

孔庆波¹，章明清¹，李娟¹，许文江²，章赞德³，姚建族⁴

¹福建省农业科学院土壤肥料研究所，福州350013；²福建省亚热带植物研究所，福建厦门361006；³大田县土壤肥料技术推广站，福建大田366100；⁴永春县农业技术推广站，福建永春362200

收稿日期:2017-05-03 出版日期:2018-02-16 发布日期:2018-02-16
通讯作者: 章明清，E-mail：zhangmq2001@163.com
作者简介:孔庆波，E-mail： qbkong@qq.com
基金资助:
国家自然科学基金项目（31572203）、福建省农业科学院PI项目（2016PI-31）、农业部测土配方施肥（2011-2015）

Heteroskedasticity Diagnosis and Feasible Generalized Least Squares Regression Modeling of Ternary Fertilizer Efficiency Model

KONG QingBo¹, ZHANG MingQing¹, LI Juan¹, XU WenJiang², ZHANG ZanDe³, YAO JianZu⁴

¹Institute of Soil and Fertilizer, Fujian Academy of Agricultural Science, Fuzhuo 350013; ²Fujian Institute of Subtropical Botany, Xiamen 361006, Fujian; ³Datian Soil and Fertilizer Technology Popularization Station, Datian 366100, Fujian; ⁴Yongchun Agro-Technical Extension Station, Yongchun 362200, Fujian

Received:2017-05-03 Online:2018-02-16 Published:2018-02-16

摘要/Abstract

摘要： 【目的】探讨肥效模型建模新方法，旨在进一步提高肥效模型建模科学性和田间试验成功率。【方法】根据171个早稻“3414”设计的氮磷钾田间肥效试验结果，应用现代回归分析理论，研究三元肥效模型异方差的产生原因和统计检验方法，应用可行广义最小二乘法（FGLS）建模策略消除肥效模型异方差的危害。【结果】根据肥效模型的专业特点，田间试验设计及其管理水平、土壤肥力水平及其空间异质性、模型设定优劣等因素是肥效模型产生异方差的主要原因。怀特（White）检验、帕克（Park）检验和冠因克-巴塞特（KB）检验表明，三元肥效模型异方差达到统计显著水平的比例为25.15%。针对严重异方差的田间试验资料，FGLS回归建模能将部分试验点的试验结果，由普通最小二乘法（OLS）回归建模未达统计显著水平转化为达到统计显著水平，或者将非典型式转化为典型肥效模型；典型式出现几率由OLS回归建模的27.68%提高到34.99%。对典型三元肥效模型，FGLS回归模型的推荐施肥量与OLS回归模型的推荐施肥量大致相当。研究表明，与OLS回归建模相比，FGLS回归建模大幅度降低回归模型的误差均方，同时也明显减小模型各个参数的方差，从而改善了肥效模型的拟合精度和模型预测能力。【结论】FGLS是消除或缓解三元二次多项式肥效模型异方差的有效方法，可明显提高田间试验资料的建模成功率。

关键词: 早稻, 氮、磷、钾肥, 肥效模型, 异方差, 广义最小二乘法

Abstract: 【Objective】 This paper presented the new strategy to develop fertilizer efficiency models, so as to improve the scientificity of fertilizer effect models and the success rate of the field experiment. 【Method】 According to the results from the 171 “3414” NPK field experiments with early rice, using the modern regression analysis theory, the reason of the ternary model heteroscedasticity and the statistical test methods were studied in the paper. Feasible generalized least squares (FGLS) was used to eliminate the heteroscedasticity effect. 【Result】 According to the professional characteristics of fertilizer efficiency models, the field experiment design and its management practices, soil fertility and its spatial heterogeneity were the key reasons for the models’ heteroscedasticity. Based on the White test, Park test and KB test, the heteroscedasticity of the 25.15% ternary fertilizer efficiency model showed the statistical significantly level. In view of the serious heteroscedastic of the field experimental data, FGLS regression model could convert part of field experimental results into significant level, whereas the Ordinary Least Square (OLS) could not; or the FGLS could convert the no-typical model into typical model; the probability of typical models increased from 27.68% to 34.99%. For the typical ternary model, the recommended fertilization rate of FGLS regression model roughly was equate to the rate of OLS model. Compared to the OLS modeling, the FGLS regression modeling could decrease the Mean Square Error (MSE) greatly, at the same time, which also could decease the variance from the parameters. Thus the FGLS regression model could improve the fitting precision and the predication ability. 【Conclusion】 FGLS is an effect way to eliminate or ease the heteroscedasticity from the ternary quadratic polynomial model, and can obviously improve the success rate of the field experimental data modeling.

Key words: early rice, N, P, K fertilizer, fertilizer efficiency model, heteroscedasticity, feasible generalized least squares

孔庆波，章明清，李娟，许文江，章赞德，姚建族. 三元肥效模型异方差诊断及其可行广义最小二乘回归建模研究[J]. 中国农业科学, 2018, 51(4): 728-737.

KONG QingBo, ZHANG MingQing, LI Juan, XU WenJiang, ZHANG ZanDe, YAO JianZu. Heteroskedasticity Diagnosis and Feasible Generalized Least Squares Regression Modeling of Ternary Fertilizer Efficiency Model[J]. Scientia Agricultura Sinica, 2018, 51(4): 728-737.

0
/ / 推荐

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: https://www.chinaagrisci.com/CN/10.3864/j.issn.0578-1752.2018.04.012

https://www.chinaagrisci.com/CN/Y2018/V51/I4/728

参考文献

[1] VALKAMA E, UUSITALO R, TURTOLA E. Yield response models to phosphorus application: a research synthesis of Finnish field trials to optimize fertilizer P use of cereals. Nutrient Cycling in Agroecosystems, 2011, 91(1): 1-15.

[2] GRWGORT M C, ZORITA M D, DARDANELLI J, Bongiovanni R G. Regional model for nitrogen fertilization of site-specific rainfed corn in haplustolls of the central Pampas, Argentina. Precision Agriculture, 2011, 12(6): 831-849.

[3] 毛达如, 张承东. 推荐施肥技术中施肥模型与试验设计的研究. 土壤通报, 1991, 22(5): 216-218.

MAO D R , ZHANG C D. Fertilization model and the experiment design of fertilization recommendation technology. Chinese Journa1 of Soil Science, 1991, 22(5): 216-218. (in Chinese)

[4] 王兴仁. 二元二次肥料效应曲面等产线图在科学施肥中的位置（一）. 土壤通报, 1985, 16(1): 30-34.

WANG X R. The positions of contour map of yield of binary quadratic fertilizer response curve in scientific fertilization (part 1). Chinese Journa1 of Soil Science, 1985, 16(1): 30-34. (in Chinese)

[5] 王兴仁. 二元二次肥料效应曲面等产线图在科学施肥中的位置（二）. 土壤通报, 1985, 16(2): 86-88.

WANG X R. The positions of contour map of yield of binary quadratic fertilizer response curve in scientific fertilization (part 2). Chinese Journa1 of Soil Science, 1985, 16(2): 86-88. (in Chinese)

[6] 章明清, 林仁埙, 林代炎, 姜永. 极值判别分析在三元肥效模型推荐施肥中的作用. 福建农业学报, 1995, 10(2): 54-59.

ZHANG M Q, LIN R X, LIN D Y, JIANG Y. Function of distinguish analysis on extreme value in recommendatory fertilization for three-fertilizer efficiency model. Fujian Journal of Agricultural Sciences, 1995, 10(2): 54-59. (in Chinese)

[7] CERRATO M E, BLACKMER A M. Comparison of models for describing corn yield response to nitrogen fertilizer. Agronomy Journal, 1990, 82(1): 138-143.

[8] 杨靖一, WADSWORTH G A, GREENWOOD D J. 三种蔬菜N肥效应曲线的比较研究. 植物营养与肥料学报, 1995, 1(1): 71-78.

YANG J Y, WADSWORTH G A, Greenwood D J. Comparative study on three kinds of vegetables response to N fertilizer curve. Plant Nutrition and Fertilizer Science, 1995, 1(1): 71-78. (in Chinese)

[9] 陈新平, 周金池, 王兴仁, 张福锁, 宝德俊. 小麦-玉米轮作制中氮肥效应模型的选择——经济和环境效益分析. 土壤学报, 2000, 37(3): 346-354.

CHEN X P, ZHOU J C, WANG X R, ZHANG F S, BAO D J. Economic and environmental evaluation on models for describing crop yield response to nitrogen fertilizers at winter-wheat and summer-corn rotation system. Acta Pedologica Sinica, 2000, 37(3): 346-354. (in Chinese)

[10] 吴平, 陶勤南. 氮磷钾肥效模型的研究及其应用. 浙江农业大学学报, 1989, 15(4): 383-388.

WU P, TAO Q N. Study on N, P and K fertilizer response model and its application. Journal of Zhejiang Agricultural University, 1989, 15(4): 383-388. (in Chinese)

[11] 章明清. 米氏肥效方程的灰色建模法. 土壤通报, 1997, 28(1): 18-19.

ZHANG M Q. Gray modeling method of Mitsherlich fertilizer response equations. Chinese Journa1 of Soil Science, 1997, 28(1): 18-19. (in Chinese)

[12] 章明清, 徐志平, 姚宝全, 林琼, 颜明娟. Monte Carlo 法在多元肥效模型参数估计和推荐施肥中的应用. 植物营养与肥料学报, 2009, 15(2): 366-373.

ZHANG M Q, XU Z P, YAO B Q, LIN Q, YAN M J. Using Monte Carlo method for parameter estimation and fertilization recommendation of multivariate fertilizer response model. Plant Nutrition and Fertilizing Science, 2009, 15(2): 366-373. (in Chinese)

[13] COLWELL J D. The erivation of fertilizer recommendations for crops in non-uniform environment. Crop Quality and Economy, 1974: 936-961.

[14] 王兴仁, 陈伦寿, 毛达如, 张才东. 分类回归综合法及其在区域施肥决策中的应用. 土壤通报, 1989, 20(1): 17-21.

WANG X R, CHEN L S, MAO D R, ZHANG C D. Classification of regression synthesis and its application for regional fertilization decision-making. Chinese Journa1 of Soil Science, 1989, 20(1): 17-21. (in Chinese)

[15] 毛达如, 张承东. 多点肥料效应函数的动态聚类方法. 北京农业大学学报, 1991, 17(2): 49-54.

MAO D R, ZHANG C D. Cluster analysis of quadratic response function on the fertilizer dispersed experiment. Acta Agriculturae Universitatis Pekinensis, 1991, 17(2): 49-54. (in Chinese)

[16] MONTGOMERY D C, PECK E A, VINING G G. 线性回归分析导论. 第5版. 王辰勇, 译. 北京: 机械工业出版社, 2016: 91-268.

MONTGOMERY D C, PECK E A, VINING G G. Introduction to Linear Regression Analysis. 5th ed. WANG C Y, trans. Beijing: China Machine Press, 2016: 91-268. (in Chinese)

[17] 李娟, 章明清, 孔庆波, 姚宝全, 颜明娟. 福建早稻测土配方施肥指标体系研究. 植物营养与肥料学报, 2010, 16(4): 938-946.

LI J, ZHANG M Q, KONG Q B, YAO B Q, YAN M J. Soil testing and formula fertilization index for early rice in Fujian Province. Plant Nutrition and Fertilizer Science, 2010, 16(4): 938- 946. (in Chinese)

[18] 鲁如坤. 土壤农业化学分析方法. 北京: 中国农业科技出版社, 2000: 146-196.

LU R K. Soil Agricultural Chemical Analysis Method. Beijing: China's Agricultural Science and Technology Press, 2000: 146-196. (in Chinese)

[19] GUJARATI D N, PORTER D C. 计量经济学基础 (上册). 第5版. 费剑平, 译. 北京: 中国人民大学出版社, 2011: 313-399.

GUJARATI D N, PORTER D C. Econometrics Foundation. 5th ed. FEI J P, trans. Beijing: China Renmin University Press, 2011: 313-399. (in Chinese)

[20] 尹光霞. 多元线性回归模型中的异方差性问题. 湖北大学学报(自然科学版), 2003, 25(2): 121-125.

YIN G X. Problems on heteroscedasticity in multilinear regression models. Journal of Hubei University (Natural Science Edition), 2003, 25(2): 121-125. (in Chinese)

[21] 何晓群，刘文卿. 应用回归分析. 3版. 北京: 中国人民大学出版社, 2013: 158-170.

HE X Q, LIU W Q. Applied Regression Analysis. 3rd ed. Beijing: China Renmin University Press, 2013: 158-170. (in Chinese)

[22] 陈强. 高级计量经济学及Stata应用. 2版. 北京: 高等教育出版社, 2015: 87-99.

CHEN Q. Advanced Econometric and Stata Applications.2nd ed. Beijing: Higher Education Press, 2015: 87-99. (in Chinese)

[23] 章明清, 李娟, 孔庆波, 严芳. 作物肥料效应函数模型研究进展与展望. 土壤学报, 2016, 53(6): 1143-1156.

ZHANG M Q, LI J, KONG Q B, YAN F. Progress and prospect of the study on crop-response-to -fertilization function model. Acta Pedologica Sinica, 2016, 53(6): 1143-1156. (in Chinese)

三元肥效模型异方差诊断及其可行广义最小二乘回归建模研究

Heteroskedasticity Diagnosis and Feasible Generalized Least Squares Regression Modeling of Ternary Fertilizer Efficiency Model

RichHTML

PDF

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

Metrics

本文评价

推荐阅读 0

[1]	朱铁忠,柯健,姚波,陈婷婷,何海兵,尤翠翠,朱德泉,武立权. 沿江双季稻北缘区机插早稻的超高产群体特征[J]. 中国农业科学, 2021, 54(7): 1553-1564.
[2]	陈惠哲,徐一成,张玉屏,向镜,张义凯,朱德峰. 超级早稻钵形毯状秧苗机插效果及产量形成[J]. 中国农业科学, 2019, 52(23): 4240-4250.
[3]	刘维，李祎君，吕厚荃. 早稻抽穗开花至成熟期气候适宜度对气候变暖与提前移栽的响应[J]. 中国农业科学, 2018, 51(1): 49-59.
[4]	王春乙，姚蓬娟，张继权，任义方. 长江中下游地区双季早稻冷害、热害综合风险评价[J]. 中国农业科学, 2016, 49(13): 2469-2483.
[5]	李文西,鲁剑巍,陈防,李小坤 . 苏丹草-黑麦草轮作制中氮、磷、钾肥施用效果研究[J]. 中国农业科学, 2010, 43(7): 1414-1422 .
[6]	李木英,石庆华,胡志红,潘晓华,谭雪明. 高温胁迫对不同早稻品种胚乳淀粉合成酶类活性的影响[J]. 中国农业科学, 2007, 40(8): 1622-1630 .
[7]	@姜东$南京农业大学/农业部作物生长调控. 氮磷钾肥长期配合施用对冬小麦籽粒品质的影响[J]. 中国农业科学, 2004, 37(04): 566-566 .