Submitted to: Journal of Agricultural, Biological, and Environmental Statistics
Publication Type: Peer reviewed journal
Publication Acceptance Date: 1/14/2007
Publication Date: 12/1/2008
Citation: Holan, S., Wang, S., Arab, A., Sadler, E.J., Stone, K.C. 2008. Semiparametric Geographically Weighted Response Curves with Application to Site Specific Agriculture. Journal of Agricultural, Biological, and Environmental Statistics. 13(4):424-439. Interpretive Summary: Analyzing data from typical experiments is well understood, but any statistical results obtained are for the whole experiment, averaged across the area being studied. In most fields, trends in soil productivity exist, but are averaged out. In the emerging field of precision agriculture, these trends are very important, so statistical methods are needed that simultaneously explain both the treatments and the soil variation. A method was developed that accomplishes this goal and also provides estimates of the uncertainty in the result. This is demonstrated with an example of corn yield data obtained under site-specific irrigation. This method can be implemented using many standard statistical software packages. Although the methodology is quite flexible and can be used in many different settings, it will be especially useful for practitioners in precision agricultural research.
Technical Abstract: Lack of basic knowledge about spatial and treatment varying crop response to irrigation hinders irrigation management and economic analysis for site-specific agriculture. One model that has been postulated for relating crop-specific economic quantities to irrigation is a quadratic response curve of yield as a function of irrigation. Although this model has far reaching economic interpretations it does not account for spatial variation or possible nitrogen - irrigation interactions. To this end we propose a spatially - treatment varying coefficient model that alleviates these limitations while providing measures of uncertainty for the estimated coefficient surfaces as well as other derived quantities of interest. The modeling framework we propose is of independent interest and can be utilized in many different applications. Finally, an example involving site-specific agricultural data from the U.S. Department of Agriculture - Agricultural Research Service demonstrates the applicability of this methodology.