Uncertainty in spatially predicted covariates: is it ignorable?

Summary.  In ecology, a common form of statistical analysis relates a biological variable to variables that delineate the physical environment, typically by fitting a regression model or one of its extensions. Unfortunately, the biological data and the physical data are frequently obtained from separate sources of data. In such cases there is no guarantee that the biological and physical data are co-located and the regression model cannot be used. A common and pragmatic solution is to predict the physical variables at the locations of the biological variables and then to use the predictions as if they were observations. We show that this procedure can cause potentially misleading inferences and we use generalized linear models as an example. We propose a Berkson error model which overcomes the limitations. The differences between using predicted covariates and the Berkson error model are illustrated by using data from the marine environment, and a simulation study based on these data.