CONTEXT

Agricultural systems are generally characterised by many dependent variables that represent their management practices and performances. Parametric approaches are usually used to explore data collected from farms and relations among variables. However, these approaches are generally limited by strong assumptions about the shape of the model that relates variables to each other, which can induce bias in studies.

OBJECTIVE

To address these limitations, we investigated the potential of non-parametric kernel density estimators to help explore relations among variables that characterise farms (e.g., forage and milk production, greenhouse gas (GHG) emissions), which have the advantage of requiring no assumptions about the shape of these relations.

METHODS

Multivariate kernel density estimation analyses the probability that the values of two or more variables will simultaneously fall within a given range for each variable. The practical utility of this approach was shown by identifying subsets of a population of 96 dairy farms in 2013 in Normandy, France, that had forage production, milk production and GHG emissions that most other farms in the same population were likely to have.

RESULTS AND CONCLUSIONS

Several farms outside of the highest density regions, but which lay with the same range of grass or maize production, were able to produce 28% or 27% more milk per cow, respectively (or emit 21% or 9% less GHGs, respectively) each year than farms inside these regions. Characteristics of these farms that increase milk production (e.g., higher maize silage production, more often with majority-Holstein herds) or decrease GHG emissions (e.g., lower maize silage production, more often with majority-Normande herds) were identified.

SIGNIFICANCE

Kernel density estimation can be useful for selecting farms with particularly high or low production or environmental performances in a sample of farms as a function of multiple characteristics.

中文翻译：

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内核密度估计对奶牛场特征之间关系建模的潜力

语境

农业系统通常以许多代表其管理实践和绩效的因变量为特征。参数方法通常用于探索从农场收集的数据和变量之间的关系。然而，这些方法通常受到关于将变量相互关联的模型形状的强烈假设的限制，这可能会导致研究出现偏差。

客观的

为了解决这些限制，我们研究了非参数内核密度估计器的潜力，以帮助探索表征农场的变量之间的关系（例如，草料和牛奶生产、温室气体 (GHG) 排放），这些变量的优点是不需要假设这些关系的形状。

方法

多变量核密度估计分析两个或多个变量的值将同时落在每个变量的给定范围内的概率。通过在 2013 年确定法国诺曼底 96 个奶牛场的人口子集，证明了这种方法的实际效用，这些奶牛场的牧草产量、牛奶产量和温室气体排放量与同一人口中的大多数其他农场可能有。

结果和结论

密度最高地区以外的几个农场，但草或玉米产量相同，每头奶牛的产奶量分别增加了 28% 或 27%（或温室气体排放量分别减少了 21% 或 9%）每年比这些地区内的农场。确定了这些农场增加牛奶产量（例如，较高的玉米青贮饲料产量，更常见于大多数荷斯坦牛群）或减少温室气体排放（例如，较低的玉米青贮饲料产量，更常见于大多数诺曼底牛群）的特征。

意义

核密度估计可用于在农场样本中选择具有特别高或低产量或环境绩效的农场，作为多种特征的函数。