Modeling local terrain attributes in landscape-scale site-specific data using spatially lagged independent variable via cross regression

Abstract

Analysis methods for landscape-scale site-specific agricultural datasets have been adapted from a wide range of quantitative disciplines. Due to spatial effects expected at landscape scales with respect to yield affecting factors, inference from aspatial analyses may lead to inefficient statistical inference. When spatial correlation exists within a random variable e.g. explanatory variables such as elevation or soil characteristics, spatial statistical methods can provide unbiased and efficient estimates on which to base economic analyses and farm management decisions. Simple continuous terrain variables derived from spatially lagged independent variable transformation of relative terrain position allowed models to be estimated using familiar linear aspatial models without introducing the problems associated with interpolated data in inferential spatial statistics. Using site-specific data from three example fields, cross regressive elevation variables complemented topographic attributes, rather than replacing them in a range of statistical models. Results indicated that cross regressive elevation variables, especially relative elevation, reduced estimation problems due to correlation among independent variables and bias arising from spatially interpolated data in statistical analysis.

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References

  1. Anselin, L. (1988). Spatial econometrics: Methods and models. Dordrecht, Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  2. Anselin, L. (2001). Spatial effects in econometric practice in environmental and resource economics. American Journal of Agricultural Economics, 83(3), 705–710.

    Article  Google Scholar 

  3. Anselin, L. (2002). Under the hood issues in the specification and interpretation of spatial regression models. Agricultural Economics., 27(3), 247–267.

    Article  Google Scholar 

  4. 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.

    Article  Google Scholar 

  5. Arbia, G. (2014). A primer for spatial econometrics with applications in R. New York, NY, USA: Palgrave MacMillan.

    Google Scholar 

  6. Bell, K. P., & Bockstael, N. E. (2000). Applying the generalized-moment estimation approach to spatial problems involving micro-level data. The Review of Economics and Statistics, 82(1), 72–82.

    Article  Google Scholar 

  7. Bishop, T. F. A., & McBratney, A. B. (2002). Creating field extent digital elevation models for precision agriculture. Precision Agriculture, 3(1), 37–46.

    Article  Google Scholar 

  8. Clark, R. L., & Lee, R. (1998). Development of topographic maps for precision farming with kinematic GPS. Transactions of the ASAE, 41(4), 909–916.

    Article  Google Scholar 

  9. Cliff, A. D., & Ord, J. K. (1981). Spatial processes: Models and applications. London, UK: Pion Limited.

    Google Scholar 

  10. Coble, K., Ferrell, S. L., Mishra, A., & Griffin, T. W. (2018). Big data in agriculture: A challenge for the future. Applied Economics Perspectives and Policy, 40(1), 79–96.

    Article  Google Scholar 

  11. Dubin, R. A. (2003). Robustness of spatial autocorrelation specifications: Some Monte Carlo evidence. Journal of Regional Science, 43, 221–248.

    Article  Google Scholar 

  12. Florax, R., & Folmer, H. (1992). Specification and estimation of spatial linear regression models: Monte Carlo evaluation of pre-test estimators. Regional Science and Urban Economics, 22, 405–432.

    Article  Google Scholar 

  13. Florax, R. J. G. M., Voortman, R. L., & Brouwer, J. (2002). Spatial dimensions of precision agriculture: A spatial econometric analysis of Millet yield on Sahelian Coversands. Agricultural Economics., 27(3), 425–443.

    Article  Google Scholar 

  14. Garrido, M. S., de Lacy, M. C., Ramos, M. I., Borque, M. J., & Susi, M. (2019). Assessing the accuracy of NRTK altimetric positioning for precision agriculture: Test results in an olive grove environment in Southeast Spain. Precision Agriculture, 20(3), 461–476.

    Article  Google Scholar 

  15. Greene, W. H. (2012). Econometric analysis (7th ed.). Upper Saddle River, NJ, USA: Pearson Education, Prentice Hall.

    Google Scholar 

  16. Griffin, T. W. (2010). The spatial analysis of yield data. In M. Oliver (Ed.), Geostatistical applications for precision agriculture (p. 295p). Dordrecht, Netherlands: Springer.

    Google Scholar 

  17. Griffin, T. W., Brown, J. P., & Lowenberg-DeBoer, J. (2007). Yield monitor data analysis protocol: A primer in the management and analysis of Precision Agriculture Data. Purdue University. Retrieved November 16, 2019, from https://ssrn.com/abstract=2891888.

  18. Griffin, T. W., Dobbins, C. L., Vyn, T. J., Florax, R. J. G. M., & Lowenberg-DeBoer, J. (2008). Spatial analysis of yield monitor data: Case studies of on-farm trials and farm management decision making. Precision Agriculture, 9(5), 269–283.

    Article  Google Scholar 

  19. Griffin, T. W., Mark, T. B., Dobbins, C. L., & Lowenberg-DeBoer, J. (2014). Estimating whole farm costs of conducting on-farm research: A linear programming approach. International Journal of Agricultural Management, 4(1), 21–27.

    Google Scholar 

  20. Griffin, T. W., & Yeager, E. A. (2019). How quickly do farmers adopt technology? A duration analysis. In J. V. Stafford (Ed.) Precision agriculture’19. 12th European conference on precision agriculture (pp. 843–849). Wageningen, The Netherlands: Wageningen Academic Publishers.

  21. Hartsock, N. J., Mueller, T. G., Karathanasis, A. D., & Cornelius, P. L. (2005). Interpreting soil electrical conductivity and terrain attribute variability with soil surveys. Precision Agriculture, 6(1), 53–72.

    Article  Google Scholar 

  22. 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, 30(2), 231–249.

    Google Scholar 

  23. Jiang, P., & Thelen, K. D. (2004). Effect of soil and topographic properties on crop yield in a north-central corn-soybean cropping system. Agronomy Journal, 96(1), 252–258.

    Article  Google Scholar 

  24. Kaspar, T. C., Pulido, D. J., Fenton, T. E., Colvin, T. S., Karlen, D. L., Jaynes, D. B., et al. (2004). Relationship of corn and soybean yield to soil and terrain properties. Agronomy Journal, 96(3), 700–709.

    CAS  Article  Google Scholar 

  25. Kelejian, H., & Prucha, I. (1998). A generalized spatial two stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. Journal of Real Estate Finance and Economics, 17(1), 99–121.

    Article  Google Scholar 

  26. Kelejian, H. H., & Prucha, I. R. (1999). A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review, 40, 509–533.

    Article  Google Scholar 

  27. Kelejian, H. H., & Prucha, I. R. (2010). Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics, 157(1), 53–67.

    PubMed  PubMed Central  Article  Google Scholar 

  28. Kravchenko, A. N., Bullock, D. G., & Boast, C. W. (2000). Joint multifractal analysis of crop yield and terrain slope. Agronomy Journal, 92(6), 1279–1290.

    Article  Google Scholar 

  29. 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, 579–600.

    Article  Google Scholar 

  30. LeSage, J., & Pace, R. K. (2009). Introduction to spatial econometrics (1st ed., p. 394). Boca Raton, FL, USA: Taylor & Francis.

    Google Scholar 

  31. Liu, Z., Griffin, T. W., Kirkpatrick, T. L., & Monfort, W. S. (2015). Spatial econometric approaches to site-specific nematode management strategies. Precision Agriculture, 16(5), 587–600.

    Article  Google Scholar 

  32. Long, D. S., & McCallum, J. D. (2015). On-combine, multi-sensor data collection for post-harvest assessment of environmental stress in wheat. Precision Agriculture, 16(5), 492–504.

    Article  Google Scholar 

  33. Miao, Y., Mulla, D. J., & Robert, P. C. (2006). Spatial variability of soil properties, corn quality and yield in two Illinois, USA fields: Implications for precision corn management. Precision Agriculture, 7(1), 5–20.

    Article  Google Scholar 

  34. Miller, N. J., Griffin, T. W., Ciampitti, I., & Sharda, A. (2019). Farm adoption of embodied knowledge and information intensive precision agriculture technology bundles. Precision Agriculture, 20(2), 348–361.

    Article  Google Scholar 

  35. Papadakis, J. S. (1937). Methode statistique pour des experiences sur champs [Statistical methods for field experiments]. Bulletin de l‘Institut de l’Amelioration des Plantes, Thessaloniki (Greece), 23, 1–30.

    Google Scholar 

  36. Selle, M. L., Steinsland, I., Hickey, J. M., & Gorjanc, G. (2019). Modelling spatial variation in agricultural field trials with INLA. bioRxiv. https://doi.org/10.1101/612036.

    Article  Google Scholar 

  37. Sudduth, K. A., Drummond, S. T., & Myers, D. B. (2012). Yield Editor 2.0: Software for automated removal of yield map errors. Paper no. 121338343. St. Joseph, MI, USA: ASABE. Retrieved November 16, 2019, from http://extension.missouri.edu/sare/documents/ASABEYieldEditor2012.pdf.

  38. Thomas, I. A., Jordan, P., Shine, O., Fenton, O., Mellander, P.-E., Dunlop, P., et al. (2017). Defining optimal DEM resolutions and point densities for modelling hydrologically sensitive areas in agricultural catchments dominated by microtopography. International Journal of Applied Earth Observation and Geoinformation, 54, 38–52.

    Article  Google Scholar 

  39. Trevisan, R. G., Bullock, D. S., & N. F. Martin. (2019). Site-specific treatment responses in on-farm precision experimentation. Preprints. Retrieved November 18, 2019, from https://doi.org/10.20944/preprints201902.0007.v1.

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Correspondence to Terry Griffin.

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Griffin, T., Lowenberg-DeBoer, J. Modeling local terrain attributes in landscape-scale site-specific data using spatially lagged independent variable via cross regression. Precision Agric 21, 937–954 (2020). https://doi.org/10.1007/s11119-019-09702-5

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Keywords

  • Cross regression
  • Elevation
  • Landscape position
  • Lagged independent variable