Spatial functional data modeling of plant reflectances
Philip A. White, Henry Frye, Michael F. Christensen, Alan E. Gelfand, John A. Silander
The Annals of Applied Statistics · 2022 · Volume 16 · Issue 3
Abstract
Plant reflectance spectra, the profile of light reflected by leaves across different wavelengths, supply the spectral signature for a species at a spatial location to enable estimation of functional and taxonomic diversity for plants. We consider leaf spectra as “responses” to be explained spatially. These reflectance spectra are also functions over wavelength that respond to the environment. Our motivating data are gathered for several plant families from the Greater Cape Floristic Region (GCFR) in South Africa and lead us to develop rich novel spatial models that can explain spectra for genera within families. Wavelength responses for an individual leaf are viewed as a function of wavelength, leading to functional data modeling. Local environmental features become covariates. We introduce a wavelength, covariate interaction, since the response to environmental regressors may vary with wavelength, as may variance. Formal spatial modeling enables prediction of reflectances for genera at unobserved locations with known environmental features. We incorporate spatial dependence, wavelength dependence, and space–wavelength interaction (in the spirit of space–time interaction). We implement out-of-sample validation for model selection, finding that the model features above are informative for the functional data analysis. We supply ecological interpretation of the results under the selected model.
Keywords
Environmental regressors, Functional data analysis, Heterogeneity, hierarchical model, interaction, kernel weighting, reflectance, spatial confounding
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