Abstract Composite variables are variables derived from measurable traits. They are commonly used in agronomy: two well-known examples being the harvest index and the relative water content. There are two approaches for finding estimated averages of such variables that are derived from direct measurements: They can be found either based on a calculation using individual measurements (“pre-processing”) or from a calculation using averages or estimates (“after-fitting”). The former needs to be done prior to fitting a statistical model whereas the latter is carried out after a statistical model has been fitted to the original measurements. We show that the commonly used pre-processing approach results in biased estimates. Moreover, the bias depends on both the correlation between and the uncertainty associated with the variables used for the composite variable. This finding is shown in two examples and a simulation study.

中文翻译：

---

收获指数和相对含水量的估计——农学中复合变量的两个例子

摘要 复合变量是源自可测量特征的变量。它们常用于农学：两个众所周知的例子是收获指数和相对含水量。有两种方法可以找到从直接测量得出的这些变量的估计平均值：它们可以基于使用单个测量的计算（“预处理”）或使用平均值或估计的计算（“拟合后” ”）。前者需要在拟合统计模型之前完成，而后者是在将统计模型拟合到原始测量值之后进行的。我们表明，常用的预处理方法会导致估计有偏差。而且，偏差取决于用于复合变量的变量之间的相关性和不确定性。这一发现显示在两个例子和一个模拟研究中。