Multivariate Description
Content for Wednesday, October 22, 2025
Now that we’ve looked at describing spatial patterns using point processes and patch metrics, we’ll finish by taking a look at multivariate methods for making sense of spatial patterns. We’ll focus on two, relatively simple approaches. Principal components analysis for identifying and mapping latent gradients in quantitative data and clustering for identifying qualitative ‘groups’ in data based on quantitative data. These are just two approaches in a broader class of “dimension reduction” methods, but they are illustrative of the basic tasks of multivariate description.
Resources
Bigger Picture
Principal Component Analysis on Spatial Data: An Overview by (Demšar et al. 2013) provides a semi-technical introduction to why we might use Principle Components Analysis to identify spatial gradients and things we should consider when applying PCA to spatial data.
A latitudinal gradient in dimensionality of biodiversity by (Stevens and Tello 2018) is a nice, contemporary demonstration of PCA for ecological questions and spatial data.
Archetypical patterns and trajectories of land systems in Europe by (Levers et al. 2018) is a great reference for using cluster analysis to identify social-ecological archetypes for sustainability problems.
The American West as a social-ecological region: drivers, dynamics and implications for nested social-ecological systems by (Jones et al. 2019) is an example of a fairly simple cluster analysis that resulted from a workshop hosted here at Boise State!
Technical Details
Cluster Analysis provides a nice vignette introducing the workflow for cluster analysis. It’s done using the
rasterpackage (a precursor toterra), but the translation intoterrais straightforward.Principal Components Analysis from the online
terraworkbook provides an intro to the workflow for a simple PCA using rasters.
Objectives
By the end of today you should be able to:
Describe the motivations for dimension reduction with spatial data
Distinguish the differences between PCA and cluster analysis
Understand common metrics for assessing the quality of dimension reduction results
Implement simple PCA and cluster analysis using
R
Slides
The slides for today’s lesson are available online as an HTML file. Use the buttons below to open the slides either as an interactive website or as a static PDF (for printing or storing for later). You can also click in the slides below and navigate through them with your left and right arrow keys.