Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression
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2009-01-08
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Resumo
A major focus of geographical ecology and macroecology is to understand the causes of spatially structured ecological
patterns. However, achieving this understanding can be complicated when using multiple regression, because the relative
importance of explanatory variables, as measured by regression coefficients, can shift depending on whether spatially
explicit or non-spatial modeling is used. However, the extent to which coefficients may shift and why shifts occur are
unclear. Here, we analyze the relationship between environmental predictors and the geographical distribution of species
richness, body size, range size and abundance in 97 multi-factorial data sets. Our goal was to compare standardized partial
Ecography 32: 193 204, 2009
doi: 10.1111/j.1600-0587.2009.05717.x
# 2009 The Authors. Journal compilation # 2009 Ecography
Subject Editor: Jens-Christian Svenning. Accepted 8 January 2009
193
regression coefficients of non-spatial ordinary least squares regressions (i.e. models fitted using ordinary least squares
without taking autocorrelation into account; ‘‘OLS models’’ hereafter) and eight spatial methods to evaluate the
frequency of coefficient shifts and identify characteristics of data that might predict when shifts are likely. We generated
three metrics of coefficient shifts and eight characteristics of the data sets as predictors of shifts. Typical of ecological data,
spatial autocorrelation in the residuals of OLS models was found in most data sets. The spatial models varied in the extent
to which they minimized residual spatial autocorrelation. Patterns of coefficient shifts also varied among methods and
datasets, although the magnitudes of shifts tended to be small in all cases. We were unable to identify strong predictors of
shifts, including the levels of autocorrelation in either explanatory variables or model residuals. Thus, changes in
coefficients between spatial and non-spatial methods depend on the method used and are largely idiosyncratic, making it
difficult to predict when or why shifts occur. We conclude that the ecological importance of regression coefficients cannot
be evaluated with confidence irrespective of whether spatially explicit modelling is used or not. Researchers may have little
choice but to be more explicit about the uncertainty of models and more cautious in their interpretation.
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Geographical ecology, Spatially structured ecological
Citação
BINI, L. M.; DINIZ-FILHO; RANGEL, T.; AKRE, Thomas S. B.; ALBALADEJO, Rafael G.; ALBUQUERQUE, Fabio S.; APARICIO, Abelardo; ARAÚJO, Miguel B.; BASELGA, Andrés; BECK, J.; BELLOCQ; BOHNING-GAESE; BORGES; CASTRO-PARGA; CHEY; CHOWN; DE MARCO JR., Paulo; FERRER-CASTÁN, Field; FILLOY; FLESHMAN; GÓMEZ, HORTAL; IVERSON; KERR; et al. Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression. Ecography, Copenhagen, v. 32, p. 193-204, Jan. 2009. Disponível em: <http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0587.2009.05717.x/epdf>.