Ignoring uncertainty in predictor variables leads to false confidence in results: a case study of duck habitat use

Abstract

Abstract 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.