Publication Details

Category Text Publication
Reference Category Journals
DOI 10.1111/j.1538-4632.2010.00777.x
Title (Primary) A wavelet-based extension of generalized linear models to remove the effect of spatial autocorrelation
Author Carl, G.; Kühn, I. ORCID logo
Source Titel Geographical Analysis
Year 2010
Department BZF
Volume 42
Issue 3
Page From 323
Page To 337
Language englisch
Abstract Biogeographical studies are often based on a statistical analysis of data sampled in a spatial context. However, in many cases standard analyses such as regression models violate the assumption of independently and identically distributed errors. In this article, we show that the theory of wavelets provides a method to remove autocorrelation in generalized linear models (GLMs). Autocorrelation can be described by smooth wavelet coefficients at small scales. Therefore, data can be decomposed into uncorrelated and correlated parts. Using an appropriate linear transformation, we are able to extend GLMs to autocorrelated data. We illustrate our new method, called the wavelet-revised model (WRM), by applying it to multiple regression with response variables conforming to various distributions. Results are presented for simulated data and real biogeographical data (species counts of the plant genus Utricularia [bladderworts] in grid cells throughout Germany). The results of our WRM are compared with those of GLMs and models based on generalized estimating equations. We recommend WRMs, especially as a method that allows for spatial nonstationarity. The technique developed for lattice data is applicable without any prior knowledge of the real autocorrelation structure.
Persistent UFZ Identifier https://www.ufz.de/index.php?en=20939&ufzPublicationIdentifier=9853
Carl, G., Kühn, I. (2010):
A wavelet-based extension of generalized linear models to remove the effect of spatial autocorrelation
Geogr. Anal. 42 (3), 323 - 337 10.1111/j.1538-4632.2010.00777.x