Analyzing spatial ecological data using linear regression and wavelet analysis |
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| Authors: | Gudrun Carl Ingolf Kühn |
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| Institution: | (1) Department Community Ecology (BZF), UFZ-Helmholtz Centre for Environmental Research, Theodor-Lieser-Strasse 4, 06120 Halle, Germany;(2) Virtual Institute Macroecology, Theodor-Lieser-Strasse 4, 06120 Halle, Germany |
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| Abstract: | Spatial (two-dimensional) distributions in ecology are often influenced by spatial autocorrelation. In standard regression
models, however, observations are assumed to be statistically independent. In this paper we present an alternative to other
methods that allow for autocorrelation. We show that the theory of wavelets provides an efficient method to remove autocorrelations
in regression models using data sampled on a regular grid. Wavelets are particularly suitable for data analysis without any
prior knowledge of the underlying correlation structure. We illustrate our new method, called wavelet-revised model, by applying
it to multiple regression for both normal linear models and logistic regression. Results are presented for computationally
simulated data and real ecological data (distribution of species richness and distribution of the plant species Dianthus carthusianorum throughout Germany). These results are compared to those of generalized linear models and models based on generalized estimating
equations. We recommend wavelet-revised models, in particular, as a method for logistic regression using large datasets. |
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| Keywords: | Binary data Distribution data Multiple regression Normal data Spatial autocorrelation |
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