Nitrogen rate trials are often performed to determine the economically optimum N application rate. For this purpose, the yield is modeled as a function of the N application. The regression analysis provides an estimate of the modeled function and thus also an estimate of the economic optimum, N opt . Obtaining the accuracy of such estimates by confidence intervals for N opt is subject to the model assumptions. The dependence of these assumptions is a further source of inaccuracy. The N opt estimate also strongly depends on the N level design, i.e. , the area on which the model is fitted. A small area around the supposed N opt diminishes the dependence of the model assumptions, but prolongs the confidence interval. The investigations of the impact of the mentioned sources on the inaccuracy of the N opt estimate rely on N rate trials on the experimental field Sieblerfeld (Bavaria). The models applied are the quadratic and the linear-plus-plateau yield regression model.
KeywordsConfidence IntervalEconomic OptimumN Rate TrialsQuadratic ModelLinear-plus-Plateau Model
Lambert, D., Lowenberg-DeBoer, J. and Bongiovanni, R. (2002) Spatial Regression, an alternative statistical analysis for landscape scale on-farm trials: Case study of variable rate nitrogen application in Argentina. Proceedings of the 6th International Conference on Precision Agriculture, ASA/CSSA/SSSA, Madison.
Hernandez, J.A. and Mulla, D.J. (2008) Estimating Uncertainty of economically optimum fertilizer rates. Agronomy Journal, 100, 1221-1229. doi:10.2134/agronj2007.0273
Wagner, P. (1999) Produktionsfunktionen und Precision Farming (Response functions in the context of Precision Farming). Zukunftsorientierte Betriebswirtschaft und Informationstechnologien in der Agrarwirtschaft. Gie?ener Schriften zur Agrarund Ern?hrungswirtschaft, 29, 39-66.
Lark, R.M. and Wheeler, H.C. (2003) A method to investigate within-field variation of the response of combinable crops to an input. Agronomy Journal, 95, 1093-1104. doi:10.2134/agronj2003.1093
National Academy of Sciences, National Research Council (1961) Statistical methods of research in economic and agronomic aspects of fertilizer response and use. Committee on economics of fertilizer use of the agricultural board, NAS-NRC Pub. 918, NAS-NRC, Washington DC.
Cerrato, M.E. and Blackmer, A.M. (1990) Comparison of models for describing corn yield response to nitrogen fertilizer. Agronomy Journal, 82, 138-143. doi:10.2134/agronj1990.00021962008200010030x
Bullock, D.G. and Bullock, D.S. (1986) Quadratic and quadratic-plus-plateau models for predicting optimal nitrogen rate of corn: A comparison. Agronomy Journal, 86, 191-195. doi:10.2134/agronj1994.00021962008600010033x
Le Bail, M., Jeuffroy, M.-H., Bouchard, C. and Barbottin, A. (2005) Is it possible to forecast the grain quality and yield of different varieties of winter wheat from Minolta SPAD meter measurements? European Journal of Agronomy, 23, 379-391. doi:10.1016/j.eja.2005.02.003
Lehmann, E.L. (1986) Testing statistical hypothesis. John Wiley & Sons, Inc., New York.
Weisberg, S. (2005) Applied linear regression. John Wiley & Sons, Inc., New York. doi:10.1002/0471704091
Bachmaier, M. (2009) A confidence set for that x-Coordinate where the quadratic regression model has a given gradient. Statistical Papers, 50, 649-660. doi:10.1007/s00362-007-0104-1
Bachmaier, M. (2011) Fortran programs: 1. Confidence set for the economically optimum nitrogen fertilization in the quadratic model: VINO.EXE. 2. Confidence set for that x-coordinate where the quadratic regression model has a given gradient (incl. special case: confidence set for the x-coordinate of the parabola’s vertex): CIGIGRAD. EXE and CIVERTEX.EXE. http://www.tec.wzw.tum.de/index.php?id=46&L=1
Fieller, E.C. (1954) Some problems in interval estimation. Journal of the Royal Statistical Society, B16, 175-185.
Koziol, D. and Zielinski, W. (2003) Comparison of confidence intervals for maximum of a quadratic regression function. Biometrical Letters, 40, 57-64.
Mittelhammer, R.C., Judge, G.G. and Miller, D.J. (2000) Econometric foundations. Cambridge University Press, Cambridge, 183-185.
Casella, G. and Berger, R.L. (2002) Statistical inference. Duxbury Press, Belmont.
Cook, R.D. and Weisberg, S. (1990) Confidence curves in nonlinear regression. Journal of the American Statistical Association, 85, 544-551. doi:10.2307/2289796
Boyd, D.A., Yuen, L.T.K. and Needham, P. (1976) Nitrogen requirement of cereals. Journal of Agricultural Science, 87, 149-162. doi:10.1017/S0021859600026708
Waugh, D.L., Cate, R.B. and Nelson, L.A. (1973) Discontinuous models for rapid correlations, interpretation und utilization of soil analysis and fertilizer response data. International Soil Fertility Evaluation and Improvement Program, North Carolina Sate University, Raleigh.
Motulsky, H.J. and Christopoulos, A. (2003) PRISM, Version 4.0. Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting, GraphPad Software Inc., San Diego.
Liebler, J. (2003) Feldspektroskopische messungen zur ermittlung des stickstoffstatus von winterweizen und mais auf heterogenen schl?gen. Herbert Utz Verlag, Munich.
Hurley, T.M., Malzer, G.L. and Kilian, B. (2004) Estimating site-specific nitrogen crop response functions: A conceptual framework and geostatistical model. Agronomy Journal, 96, 1331-1343. doi:10.2134/agronj2004.1331
Hurley, T.M., Oishi, K. and Malzer, G.L. (2005) Estimating the potential value of variable rate nitrogen applications: A comparison of spatial econometric and geostatistical models. Journal of Agricultural and Resource Economics, 30, 231-249.
Anselin, L., Bongiovanni, R. and Lowen-berg-DeBoer, J. (2004) A spatial economic approach to the economics of site-specific nitrogen management in corn production. American Journal of Agricultural Economics, 86, 675- 687. doi:10.1111/j.0002-9092.2004.00610.x
Bullock, D.S., Lowenberg-DeBoer, J. and Swinton, S.M. (2002) Adding value to spatially managed inputs by understanding site-specific yield response. Agricultural Economics, 27, 233-245. doi:10.1111/j.1574-0862.2002.tb00119.x
Bachmaier, M. and Gandorfer, M. (2009) A conceptual framework for judging the precision agriculture hypothesis with regard to site-specific nitrogen fertilization. Precision Agriculture, 10, 95-110. doi:10.1007/s11119-008-9069-x
Abraham, T.P. and Rao, V.Y. (1965) An investigation on functional models for fertilizer response studies. Journal of the Indian Society of Agricultural Statistics, 18, 45-61.
Anderson, R.L. and Nelson, L.A. (1975) A family of models involving intersecting straight lines and concomitant experimental designs useful in evaluating response to fertilizer nutrients. Biometrics, 31, 303-318. doi:10.2307/2529422
Barreto, H.J. and Westermann, R.L. (1987) YIELDFIT: A computer program for determining economic fertilization rates. Journal of Agronomical Education, 16, 11-14.
Nelson, L.A., Voss, R.D. and Pesek, J.T. (1985) Agronomic and statistical evaluation of fertilizer response. In: Engelstad, O.P., Ed., Fertilizer Technology and Use, ASA, Madison, 53-90.