Analyzing spatial ecological data using linear regression and wavelet analysis

Original Paper

DOI: 10.1007/s00477-007-0117-2

Cite this article as:
Carl, G. & Kühn, I. Stoch Environ Res Risk Assess (2008) 22: 315. doi:10.1007/s00477-007-0117-2

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.

Keywords

Binary dataDistribution dataMultiple regressionNormal dataSpatial autocorrelation

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department Community Ecology (BZF)UFZ-Helmholtz Centre for Environmental ResearchHalleGermany
  2. 2.Virtual Institute MacroecologyHalleGermany