Abstract
The objective of this paper is to modify the linear geographically weighted regression (GWR) estimator to accommodate the discontinuous join point, or “knot”, of the linear response with plateau (LRP). This is the first application to estimate a LRP site-specific crop response function (SSCRF) model with GWR. The data used in this heuristic application are from a variable rate nitrogen (VRN) trial for corn. Results from a partial budget comparison of uniform and VRN management are sensitive with respect to the choice of kernel used to weight yield observations. Challenges remain with respect to the availability and cost of equipment required to implement precision fertilizer recommendations based on spatially varying SSCRF. Ex post spatial cluster analysis of site-specific fertilizer prescriptions may be one approach for simplifying complex application maps into larger management units.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anselin, L. (1988). Model validation in spatial econometrics: A review and evaluation of alternative approaches. International Regional Science Review, 11(3), 279–316. https://doi.org/10.1177/016001768801100307
Anselin, L. (1996). The Moran scatterplot as an ESDA tool to assess local instability in spatial. Spatial Analytical, 4, 111. https://doi.org/10.1201/9780203739051-8
Anselin, L., Bongiovanni, R., & Lowenberg-DeBoer, J. (2004). A spatial econometric approach to the economics of site-specific nitrogen management in corn production. American Journal of Agricultural Economics, 86(3), 675–687. https://doi.org/10.1111/j.0002-9092.2004.00610.x
Bachmaier, M. (2009). A confidence set for that x-coordinate where a quadratic regression model has a given gradient. Statistical Papers, 50(3), 649–660. https://doi.org/10.1007/s00362-007-0104-1
Bongiovanni, R., & Lowenberg-DeBoer, J. (2000). Economics of variable rate lime in Indiana. Precision Agriculture, 2(1), 55–70. https://doi.org/10.1023/A:1009936600784
Bongiovanni, R., & Lowenberg-DeBoer, J. (2004). Precision agriculture and sustainability. Precision Agriculture, 5(4), 359–387. https://doi.org/10.1023/B:PRAG.0000040806.39604.aa
Boyer, C. N., Tyler, D. D., Roberts, R. K., English, B. C., & Larson, J. A. (2012). Switchgrass yield response functions and profit-maximizing nitrogen rates on four landscapes in Tennessee. Agronomy Journal, 104(6), 1579–1588. https://doi.org/10.2134/agronj2012.0179
Bullock, D. S., Lowenberg-DeBoer, J., & Swinton, S. M. (2002). Adding value to spatially managed inputs by understanding site-specific yield response. Agricultural Economics, 27(3), 233–245.
Cai, R., Yu, D., & Oppenheimer, M. (2014). Estimating the spatially varying responses of corn yields to weather variations using geographically weighted panel regression. Journal of Agricultural and Resource Economics. https://doi.org/10.22004/ag.econ.186586
Casetti, E. (1972). Generating models by the expansion method: Applications to geographical research. Geographical Analysis, 4(1), 81–91. https://doi.org/10.1111/j.1538-4632.1972.tb00458.x
Cho, W., Lambert, D. M., Fornah, A., & Raun, W. R. (2020). Bayesian estimation and economic analysis of under-replicated field trials with a linear response plateau function. Journal of Agricultural Science., 12(10), 1–15. https://doi.org/10.5539/jas.v12n10p1
Cleveland, W. S., & Devlin, S. J. (1988). Locally weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Association, 83(403), 596–610. https://doi.org/10.1080/01621459.1988.10478639
Cressie, N. (1993). Aggregation in geostatistical problems. Geostatistics Troia’92 (pp. 25–36). Dordrecht: Kluwer Academic Publishers.
Dhakal, C., Lange, K., Parajulee, M. N., & Segarra, E. (2019). Dynamic optimization of nitrogen in plateau cotton yield functions with nitrogen carryover considerations. Journal of Agricultural and Applied Economics, 51(3), 1–17. https://doi.org/10.1017/aae.2019.6
Dillon, J. L., & Anderson, J. R. (1990). The analysis of response in crop and livestock production (3rd ed.). Pergamon, UK: Oxford.
Farber, S., & Páez, A. (2007). A systematic investigation of cross-validation in GWR model estimation: Empirical analysis and Monte Carlo simulations. Journal of Geographical Systems, 9(4), 371–396. https://doi.org/10.1007/s10109-007-0051-3
Finley, A. O., & Banerjee, S. (2020). Bayesian spatially varying coefficient models in the spBayes R package. Environmental Modelling & Software, 125, 104608. https://doi.org/10.1016/j.envsoft.2019.104608
Foster, S. A., & Gorr, W. L. (1992). Federal health care policy and the geographic diffusion of physicians: A macro-scale analysis. Policy Sciences, 25(2), 117–134. https://doi.org/10.1007/BF00233744
Fotheringham, A. S., Charlton, M., & Brunsdon, C. (1996). The geography of parameter space: An investigation of spatial non-stationarity. International Journal of Geographical Information Systems, 10(5), 605–627. https://doi.org/10.1080/02693799608902100
Gelfand, A. E., Kim, H. J., Sirmans, C. F., & Banerjee, S. (2003). Spatial modeling with spatially varying coefficient processes. Journal of the American Statistical Association, 98(462), 387–396. https://doi.org/10.1198/016214503000170
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. Boca Raton, FL: CRC Press.
Getis, A., & Ord, J. K. (1993). The analysis of spatial association by use of distance statistics. Geographical Analysis, 25, 276–276. https://doi.org/10.1111/j.1538-4632.1992.tb00261.x
Griffin, T., & Lowenberg-DeBoer, J. (2020). Modeling local terrain attributes in landscape-scale site-specific data using spatially lagged independent variable via cross regression. Precision Agriculture, 21(5), 937–954. https://doi.org/10.1007/s11119-019-09702-5
Haankuku, C., Epplin, F. M., & Kakani, V. G. (2014). Forage sorghum response to nitrogen fertilization and estimation of production cost. Agronomy Journal, 106(5), 1659–1666. https://doi.org/10.2134/agronj14.0078
Haque, M., Epplin, F. M., & Taliaferro, C. M. (2009). Nitrogen and harvest frequency effect on yield and cost for four perennial grasses. Agronomy Journal, 101(6), 1463–1469. https://doi.org/10.2134/agronj2009.0193
Harmon, X., Boyer, C. N., Lambert, D. M., Larson, J. A., & Gwathmey, C. O. (2016). Comparing the value of soil test information using deterministic and stochastic yield response plateau functions. Journal of Agricultural and Resource Economics, 41, 307. https://doi.org/10.22004/ag.econ.235192
Holan, S., Wang, S., Arab, A., Sadler, E. J., & Stone, K. (2008). Semiparametric geographically weighted response curves with application to site-specific agriculture. Journal of Agricultural, Biological, and Environmental Statistics, 13(4), 424.
Holloway, G., & Paris, Q. (2002). Production efficiency in the von Liebig model. American Journal of Agricultural Economics, 84(5), 1271–1278. https://doi.org/10.1111/1467-8276.00389
Hurley, T. M., Oishi, K., & 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. https://doi.org/10.22004/ag.econ.31210
Hurvich, C. M., Simonoff, J. S., & Tsai, C. L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. Journal of the Royal Statistical Society: Series B (statistical Methodology), 60(2), 271–293. https://doi.org/10.1111/1467-9868.00125
Imran, M., Zurita-Milla, R., & Stein, A. (2013). Modeling crop yield in West-African rainfed agriculture using global and local spatial regression. Agronomy Journal, 105(4), 1177–1188. https://doi.org/10.2134/agronj2012.0370
Kerry, R., Goovaerts, P., Gimenez, D., & Oudemans, P. V. (2017). Investigating temporal and spatial patterns of cranberry yield in New Jersey fields. Precision Agriculture, 18(4), 507–524. https://doi.org/10.1007/s11119-016-9471-8
Lambert, D. M., Lowenberg-Deboer, J., & Bongiovanni, R. (2004). A comparison of four spatial regression models for yield monitor data: A case study from Argentina. Precision Agriculture, 5(6), 579–600. https://doi.org/10.1007/s11119-004-6344-3
Lambert, D. M., Lowenberg-DeBoer, J., Malzer, G. L., & Varying, N. (2007). Site-specific management of nitrogen and phosphorus in a corn/soybean rotation. Agronomy Journal, 98, 43–54.
Leung, Y., Mei, C. L., & Zhang, W. X. (2000). Statistical tests for spatial nonstationarity based on the geographically weighted regression model. Environment and Planning A, 32(1), 9–32. https://doi.org/10.1068/a3162
Liu, Y., Swinton, S. M., & Miller, N. R. (2006). Is site-specific yield response consistent over time? Does it pay? American Journal of Agricultural Economics, 88(2), 471–483. https://doi.org/10.1111/j.1467-8276.2006.00872.x
Mamo, M., Malzer, G. L., Mulla, D. J., Huggins, D. R., & Strock, J. (2003). Spatial and temporal variation in economically optimum nitrogen rate for corn. Agronomy Journal, 95(4), 958–964. https://doi.org/10.2134/agronj2003.9580
Mangiafico, S. S., & Guillard, K. (2005). Turfgrass reflectance measurements, chlorophyll, and soil nitrate desorbed from anion exchange membranes. Crop Science, 45(1), 259–265. https://doi.org/10.2135/cropsci2005.0259
Mathworks. (2018). Matlab R2018b, www.mathworks.com.
McMillen, D. P., & McDonald, J. F. (2004). Locally weighted maximum likelihood estimation: Monte Carlo evidence and an application. Advances in Spatial Econometrics (pp. 225–239). Berlin: Springer.
Meyer-Aurich, A., & Karatay, Y. N. (2019). Effects of uncertainty and farmers’ risk aversion on optimal N fertilizer supply in wheat production in Germany. Agricultural Systems, 173, 130–139. https://doi.org/10.1016/j.agsy.2019.02.010
Moeltner, K., Ramsey, A. F., & Neill, C. L. (2021). Bayesian kinked regression with unobserved thresholds: An application to the von Liebig hypothesis. American Journal of Agricultural Economics. https://doi.org/10.1111/ajae.12185
Ouedraogo, F., & Brorsen, B. W. (2018). Hierarchical Bayesian estimation of a stochastic plateau response function: Determining optimal levels of nitrogen fertilization. Canadian Journal of Agricultural Economics/revue Canadienne D’agroeconomie, 66(1), 87–102.
Páez, A., Long, F., & Farber, S. (2008). Moving window approaches for hedonic price estimation: An empirical comparison of modelling techniques. Urban Studies, 45(8), 1565–1581. https://doi.org/10.1177/0042098008091491
Pede, V. O., Florax, R. J., & Lambert, D. M. (2014). Spatial econometric STAR models: Lagrange multiplier tests, Monte Carlo simulations and an empirical application. Regional Science and Urban Economics, 49, 118–128. https://doi.org/10.1016/j.regsciurbeco.2014.07.001
Perry, E. M., Dezzani, R. J., Seavert, C. F., & Pierce, F. J. (2010). Spatial variation in tree characteristics and yield in a pear orchard. Precision Agriculture, 11(1), 42–60. https://doi.org/10.1007/s11119-009-9113-5
Rodriguez, D. G. P., Bullock, D. S., & Boerngen, M. A. (2019). The origins, implications, and consequences of yield-based nitrogen fertilizer management. Agronomy Journal, 111(2), 725–735. https://doi.org/10.2134/agronj2018.07.0479
Schabenberger, O., & Pierce, F. J. (2002). Contemporary statistical models for the plant and soil sciences. Boca Raton, FL: CRC Press.
Sihvonen, M., Hyytiäinen, K., Valkama, E., & Turtola, E. (2018). Phosphorus and nitrogen yield response models for dynamic bio-economic optimization: An empirical approach. Agronomy. https://doi.org/10.3390/agronomy8040041
Tembo, G., Brorsen, B. W., Epplin, F. M., & Tostão, E. (2008). Crop input response functions with stochastic plateaus. American Journal of Agricultural Economics, 90(2), 424–434. https://doi.org/10.1111/j.1467-8276.2007.01123.x
Trevisan, R. G., Bullock, D. S., & Martin, N. F. (2020). Spatial variability of crop responses to agronomic inputs in on-farm precision experimentation. Precision Agriculture. https://doi.org/10.1007/s11119-020-09720-8
Tumusiime, E., Brorsen, B. W., Mosali, J., Johnson, J., Locke, J., & Biermacher, J. T. (2011). Determining optimal levels of nitrogen fertilizer using random parameter models. Journal of Agricultural and Applied Economics, 43, 541–552. https://doi.org/10.22004/ag.econ.117949
Waldrop, M. (2016). The chips are down for Moore’s law. Nature, 530, 144–147. https://doi.org/10.1038/530144a
Wheeler, D. C., & Calder, C. A. (2007). An assessment of coefficient accuracy in linear regression models with spatially varying coefficients. Journal of Geographical Systems, 9(2), 145–166. https://doi.org/10.1007/s10109-006-0040-y
Wheeler, D., & Tiefelsdorf, M. (2005). Multicollinearity and correlation among local regression coefficients in geographically weighted regression. Journal of Geographical Systems, 7(2), 161–187. https://doi.org/10.1007/s10109-005-0155-6
Whelan, B. M., & McBratney, A. B. (2000). The “null hypothesis” of precision agriculture management. Precision Agriculture, 2(3), 265–279. https://doi.org/10.1023/A:1011838806489
Acknowledgements
This research was supported by the Willard Sparks Chair in Agricultural Sciences and Natural Resources and USDA National Institute of Food and Agriculture’s (NIFA) Agriculture and Food Research Initiative (AFRI) Competitive Grant #2019-68012-29888.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Lambert, D.M., Cho, W. Geographically weighted regression estimation of the linear response and plateau function. Precision Agric 23, 377–399 (2022). https://doi.org/10.1007/s11119-021-09841-8
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11119-021-09841-8