ABSTRACT
Chapter 7 introduces the many complex topics that arise when including covariates in a spatial model. To do so, it first highlights the difference between extrapolation (when predicting sampling units that are similar to those that are fitted) and counter-factual prediction (where the relationship among covariates might differ systematically from those that are fitted). Using vocabulary from graphical modelling, it shows that standard regression methods can perform well for extrapolation but still poorly for counter-factual prediction, while structural equation models can in some cases resolve the difficulties arising with counter-factual prediction. The chapter then highlights the distinction between habitat covariates (which affect the target variable being estimated) vs. detectability covariates (which affect the sampling process). It first uses a simulated case study to highlight that density covariates can improve statistical performance for extrapolation in a spatial model. Next, it uses a real-world case study involve multiple sampling gears for red snapper in the Gulf of Mexico to highlight how detectability covariates can be used to integrate multiple data sets in a spatial model.
