Site‐specific prescriptions require estimating response functions to controllable inputs across the field. The methodology of applying geographically weighted regression to on‐farm precision experimentation studies opens new opportunities to study site‐specific responses to inputs in farmers' fields by locally estimating the regression coefficients. However, the effect of the experiment's spatial layout, such as plot dimensions and randomization, and spatial structure of the yield response on the experiment performance are yet to be studied. Detailed information about these effects is needed to improve trial design to detect site‐specific responses. A simulation study was conducted using 14,400 fields of 37 ha and 9‐m resolution. Coefficients from a spatial variable response function were drawn from five random fields generated by unconditional Gaussian geostatistical simulations. Four levels of nitrogen were assigned to plots using 18 systematic and randomized chessboard designs with different plot sizes. Simulated yield data was obtained by combining the coefficients, treatment, and random error. The effect of spatial structure and the designs was assessed with measures of agreement between the true and estimated maps of regression coefficients. The ability to capture or approximate the true spatial pattern of the response function increased as the underlying response function's spatial structure increases. Overall differences in performance between design were observed across the spatial structure tested, mostly related to randomization and plot dimensions. In general best results were achieved by systematic designs with small or intermediate plot sizes (r = 0.54 ± 0.05, MAE = 0.005 ± 0.0005, SDR = 0.81 ± 0.06, and CP = 0.50 ± 0.04). Our methodology provides a path for testing designs under different spatial variability scenarios.

中文翻译：

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设计农场精确实验以估计特定地点的作物响应

特定于现场的处方要求估算对整个现场可控输入的响应功能。将地理加权回归应用于农场精确性实验研究的方法为通过局部估计回归系数来研究特定地点对农民田地投入的响应提供了新的机会。但是，实验空间布局（如样点尺寸和随机化）以及产量响应的空间结构对实验性能的影响尚待研究。需要有关这些影响的详细信息，以改进试验设计以检测针对特定地点的响应。使用14400个37公顷和9m分辨率的场进行了模拟研究。来自空间变量响应函数的系数是从无条件的高斯地统计模拟生成的五个随机字段中得出的。使用18种系统化和随机化的棋盘设计（具有不同的地块大小），将四个水平的氮分配给地块。通过组合系数，处理和随机误差获得模拟的产量数据。通过回归系数的真实图和估计图之间的一致性度量来评估空间结构和设计的影响。随着底层响应函数的空间结构的增加，捕获或逼近响应函数的真实空间模式的能力也随之增强。在测试的空间结构中观察到了设计之间总体性能的差异，这主要与随机化和绘图尺寸有关。r  = 0.54±0.05，MAE = 0.005±0.0005，SDR = 0.81±0.06，CP = 0.50±0.04）。我们的方法为在不同的空间可变性场景下测试设计提供了一条途径。