An assumption of most regression analyses is that independent variables are measured without error. However, in ecological studies it is common to use independent variables that are derived from samples and therefore contain some uncertainty. For example, when assessing the assumption that energy availability on the landscape is the primary driver of duck distribution during nonbreeding seasons, investigators typically sample energy availability at sites and use the site‐level means as a covariate to predict duck abundance. This strategy ignores uncertainty in the estimates of energy availability, which should be propagated into estimates of effects and predicted values of the response variable. I used Bayesian hierarchical models to include uncertainty in site‐level covariates when modeling dabbling duck count data during the spring in northeastern Colorado, USA. I found that even after accounting for uncertainty in energy availability, it was an important predictor of dabbling duck use of sites. Counts were greater at sites with more energy available; however, credible intervals were substantially wider when uncertainty in predictor variables was included. Therefore, ignoring uncertainty leads to overly precise model outputs. Furthermore, I found that larger sites and those further east also supported more dabbling ducks. Using a sample as a covariate is common in ecological studies, and researchers can use the methods outlined here to account for this additional level of uncertainty. These case study results can be used by habitat managers and planners to guide how and where wetland restoration occurs with a more accurate idea of the uncertainty associated with various effects.

中文翻译：

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忽略预测变量的不确定性会导致对结果的错误信心：以鸭子栖息地为例

大多数回归分析的假设是独立变量的测量没有误差。但是，在生态学研究中，通常使用源自样本的自变量，因此存在一定的不确定性。例如，在评估以下假设时：在非繁殖季节，景观中的能量供应是鸭子分布的主要驱动力，研究人员通常在场所采样能量利用，并使用场所水平的平均值作为协变量来预测鸭子的丰度。该策略忽略了能源可用性估算中的不确定性，应将其传播到效果估算和响应变量的预测值中。在对美国东北科罗拉多州春季的涉水鸭子计数数据进行建模时，我使用贝叶斯分层模型在站点级协变量中包含不确定性。我发现，即使考虑到能源可用性的不确定性，它还是鸭子进食地点的重要预测指标。在具有更多可用能量的站点，计数更高；但是，当包括预测变量的不确定性时，可信区间要宽得多。因此，忽略不确定性会导致模型输出过于精确。此外，我发现更大的地点和更远的地方也支持更多的鸭子。在生态学研究中，通常使用样本作为协变量，研究人员可以使用此处概述的方法来解释这种不确定性。