A Wavelet‐Based Extension of Generalized Linear Models to Remove the Effect of Spatial Autocorrelation. 基于小波扩展广义线性模型消除空间自相关的影响

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.

Less than eight (and a half) misconceptions of spatial analysis

“…It does not, however, account for SA, nor is it able to deal with nonlinear relationships (due to non-uniqueness of regression estimates) or make predictions outside the study area (Hothorn et al, 2011). Methods accounting for non-stationarity and SA include, for example, wavelet-revised regressions (Carl & Kühn, 2010) or a specific non-stationary extension of boosted regression trees (Bühlmann & Hothorn, 2007;Hothorn et al, 2011).…”

Spatio-temporal MODIS EVI gap filling under cloud cover: An example in Scotland

“…Kondrashov and Ghil, 2006) and wavelets approach (e.g. Carl and Kuehn, 2010). Borak and Jasinski (2009) compared various interpolation techniques, addressing the spatial and temporal components separately.…”

spind: an R Package to Account for Spatial Autocorrelation in the Analysis of Lattice Data

“… Dormann et al 2007 , Beale et al 2010 , Hefley et al 2017 ). Here, two methods are offered that are based on the two fundamentally different approaches of generalised estimating equations (GEE) ( Zeger and Liang 1986 , Yan and Fine 2004 , Carl and Kühn 2007 ) on the one hand and wavelet-revised methods (WRM) ( Carl and Kühn 2008 , Carl and Kühn 2010 ) on the other. These methods are extensions of the generalised linear model (GLM).…”