Interpolation
Content for Monday, October 27, 2025
There are many cases in the analysis of social and ecological data where we might be missing data from a population or region where we hope to make inference or conduct further analysis. When the data is not spatial, we use imputation as a statistically principled approach for filling in these gaps. When the data is spatial, we use interpolation as a way of assigning values to locations where the data is missing such that we leverage the fact that most data is spatially autocorrelated. There are two general approaches for assigning these values: deterministic and probabilistic. Today we’ll take a look at deterministic approaches for interpolating missing data.
Resources
Bigger Picture
Can niche-based distribution models outperform spatial interpolation? by (Bahn and McGill 2007) illustrates the power of spatial interpolation for species distribution modeling and the potential for spurious inferences when failing to account for spatial structure in species data.
Social–ecological hotspots mapping: A spatial approach for identifying coupled social–ecological space by (Alessa et al. 2008) uses interpolation to map human values across a landscape and provides an interesting justificaiton for why we might prefer this approach over something more statistically sophisticated.
Technical Details
The Spatial Interpolation chapter of (Pebesma and Bivand 2023) provides some code for using
sfandstarsto create spatial interpolation. We’ll be replacing the raster operations withterrafunctions, but the workflow is the same.Spatial interpolation in R from Manuel Gimond provides a less statistical overview of the same workflow and uses
terrainstead ofstars.
Objectives
By the end of today you should be able to:
Describe reasons for interpolating data
Distinguish between deterministic and probabilistic methods for interpolation
Characterize the difference between distance- and spline-based interpolation
Implement two common interpolation methods in
R