On Extrapolating Past the Range of Observed Data When Making Statistical Predictions in Ecology.
Ecologists are increasingly using statistical models to predict animal abundance and occurrence in unsampled locations. The reliability of such predictions depends on a number of factors, including sample size, how far prediction locations are from the observed data, and similarity of predictive covariates in locations where data are gathered to locations where predictions are desired. In this paper, we propose extending Cook's notion of an independent variable hull (IVH), developed originally for application with linear regression models, to generalized regression models as a way to help assess the potential reliability of predictions in unsampled areas. Predictions occurring inside the generalized independent variable hull (gIVH) can be regarded as interpolations, while predictions occurring outside the gIVH can be regarded as extrapolations worthy of additional investigation or skepticism. We conduct a simulation study to demonstrate the usefulness of this metric for limiting the scope of spatial inference when conducting model-based abundance estimation from survey counts. In this case, limiting inference to the gIVH substantially reduces bias, especially when survey designs are spatially imbalanced. We also demonstrate the utility of the gIVH in diagnosing problematic extrapolations when estimating the relative abundance of ribbon seals in the Bering Sea as a function of predictive covariates. We suggest that ecologists routinely use diagnostics such as the gIVH to help gauge the reliability of predictions from statistical models (such as generalized linear, generalized additive, and spatio-temporal regression models).
National Marine Mammal Laboratory, NOAA, National Marine Fisheries Service, Alaska Fisheries Science Center, 7600 Sand Point Way NE, Seattle, WA 98115 United States of America.
Paul B
PB
Conn
National Marine Mammal Laboratory, NOAA, National Marine Fisheries Service, Alaska Fisheries Science Center, 7600 Sand Point Way NE, Seattle, WA 98115 United States of America.
Devin S
DS
Johnson
National Marine Mammal Laboratory, NOAA, National Marine Fisheries Service, Alaska Fisheries Science Center, 7600 Sand Point Way NE, Seattle, WA 98115 United States of America.
Peter L
PL
Boveng
D000413:Alaska; D000465:Algorithms; D063147:Animal Distribution; D000818:Animals; D002335:Carnivora; D003198:Computer Simulation; D003247:Conservation of Natural Resources; D004463:Ecology; D015233:Models, Statistical; D009792:Oceans and Seas; D011156:Population Density; D012044:Regression Analysis; D015203:Reproducibility of Results; D062211:Spatio-Temporal Analysis