Coefficient shifts in geographical ecology

An empirical evaluation of spatial and non-spatial regression

L. Mauricio Bini, J. Alexandre F Diniz-Filho, Thiago F L V B Rangel, Thomas S B Akre, Rafael G. Albaladejo, Fabio Suzart de Albuquerque, Abelardo Aparicio, Miguel B. Araújo, Andrés Baselga, Jan Beck, M. Isabel Bellocq, Katrin Böhning-Gaese, Paulo A V Borges, Isabel Castro-Parga, Vun Khen Chey, Steven L. Chown, Paulo De Marco, David S. Dobkin, Dolores Ferrer-Castán, Richard Field & 26 others Julieta Filloy, Erica Fleishman, Jose F. Gómez, Joaquín Hortal, John B. Iverson, Jeremy T. Kerr, W. Daniel Kissling, Ian J. Kitching, Jorge L. León-Cortés, Jorge M. Lobo, Daniel Montoya, Ignacio Morales-Castilla, Juan C. Moreno, Thierry Oberdorff, Miguel Á Olalla-Tárraga, Juli G. Pausas, Hong Qian, Carsten Rahbek, Miguel Á Rodríguez, Marta Rueda, Adriana Ruggiero, Paula Sackmann, Nathan J. Sanders, Levi Carina Terribile, Ole R. Vetaas, Bradford A. Hawkins

Research output: Contribution to journalArticle

195 Citations (Scopus)

Abstract

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 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.

Original languageEnglish (US)
Pages (from-to)193-204
Number of pages12
JournalEcography
Volume32
Issue number2
DOIs
StatePublished - Apr 2009
Externally publishedYes

Fingerprint

ecology
autocorrelation
least squares
macroecology
model uncertainty
spatial data
geographical distribution
range size
modeling
multiple regression
evaluation
methodology
body size
species richness
researchers
method
species diversity

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics

Cite this

Bini, L. M., Diniz-Filho, J. A. F., Rangel, T. F. L. V. B., Akre, T. S. B., Albaladejo, R. G., Suzart de Albuquerque, F., ... Hawkins, B. A. (2009). Coefficient shifts in geographical ecology: An empirical evaluation of spatial and non-spatial regression. Ecography, 32(2), 193-204. https://doi.org/10.1111/j.1600-0587.2009.05717.x

Coefficient shifts in geographical ecology : An empirical evaluation of spatial and non-spatial regression. / Bini, L. Mauricio; Diniz-Filho, J. Alexandre F; Rangel, Thiago F L V B; Akre, Thomas S B; Albaladejo, Rafael G.; Suzart de Albuquerque, Fabio; Aparicio, Abelardo; Araújo, Miguel B.; Baselga, Andrés; Beck, Jan; Bellocq, M. Isabel; Böhning-Gaese, Katrin; Borges, Paulo A V; Castro-Parga, Isabel; Chey, Vun Khen; Chown, Steven L.; De Marco, Paulo; Dobkin, David S.; Ferrer-Castán, Dolores; Field, Richard; Filloy, Julieta; Fleishman, Erica; Gómez, Jose F.; Hortal, Joaquín; Iverson, John B.; Kerr, Jeremy T.; Kissling, W. Daniel; Kitching, Ian J.; León-Cortés, Jorge L.; Lobo, Jorge M.; Montoya, Daniel; Morales-Castilla, Ignacio; Moreno, Juan C.; Oberdorff, Thierry; Olalla-Tárraga, Miguel Á; Pausas, Juli G.; Qian, Hong; Rahbek, Carsten; Rodríguez, Miguel Á; Rueda, Marta; Ruggiero, Adriana; Sackmann, Paula; Sanders, Nathan J.; Terribile, Levi Carina; Vetaas, Ole R.; Hawkins, Bradford A.

In: Ecography, Vol. 32, No. 2, 04.2009, p. 193-204.

Research output: Contribution to journalArticle

Bini, LM, Diniz-Filho, JAF, Rangel, TFLVB, Akre, TSB, Albaladejo, RG, Suzart de Albuquerque, F, Aparicio, A, Araújo, MB, Baselga, A, Beck, J, Bellocq, MI, Böhning-Gaese, K, Borges, PAV, Castro-Parga, I, Chey, VK, Chown, SL, De Marco, P, Dobkin, DS, Ferrer-Castán, D, Field, R, Filloy, J, Fleishman, E, Gómez, JF, Hortal, J, Iverson, JB, Kerr, JT, Kissling, WD, Kitching, IJ, León-Cortés, JL, Lobo, JM, Montoya, D, Morales-Castilla, I, Moreno, JC, Oberdorff, T, Olalla-Tárraga, MÁ, Pausas, JG, Qian, H, Rahbek, C, Rodríguez, MÁ, Rueda, M, Ruggiero, A, Sackmann, P, Sanders, NJ, Terribile, LC, Vetaas, OR & Hawkins, BA 2009, 'Coefficient shifts in geographical ecology: An empirical evaluation of spatial and non-spatial regression', Ecography, vol. 32, no. 2, pp. 193-204. https://doi.org/10.1111/j.1600-0587.2009.05717.x
Bini, L. Mauricio ; Diniz-Filho, J. Alexandre F ; Rangel, Thiago F L V B ; Akre, Thomas S B ; Albaladejo, Rafael G. ; Suzart de Albuquerque, Fabio ; Aparicio, Abelardo ; Araújo, Miguel B. ; Baselga, Andrés ; Beck, Jan ; Bellocq, M. Isabel ; Böhning-Gaese, Katrin ; Borges, Paulo A V ; Castro-Parga, Isabel ; Chey, Vun Khen ; Chown, Steven L. ; De Marco, Paulo ; Dobkin, David S. ; Ferrer-Castán, Dolores ; Field, Richard ; Filloy, Julieta ; Fleishman, Erica ; Gómez, Jose F. ; Hortal, Joaquín ; Iverson, John B. ; Kerr, Jeremy T. ; Kissling, W. Daniel ; Kitching, Ian J. ; León-Cortés, Jorge L. ; Lobo, Jorge M. ; Montoya, Daniel ; Morales-Castilla, Ignacio ; Moreno, Juan C. ; Oberdorff, Thierry ; Olalla-Tárraga, Miguel Á ; Pausas, Juli G. ; Qian, Hong ; Rahbek, Carsten ; Rodríguez, Miguel Á ; Rueda, Marta ; Ruggiero, Adriana ; Sackmann, Paula ; Sanders, Nathan J. ; Terribile, Levi Carina ; Vetaas, Ole R. ; Hawkins, Bradford A. / Coefficient shifts in geographical ecology : An empirical evaluation of spatial and non-spatial regression. In: Ecography. 2009 ; Vol. 32, No. 2. pp. 193-204.
@article{40eb23db04374976bc28078c43ee4dad,
title = "Coefficient shifts in geographical ecology: An empirical evaluation of spatial and non-spatial regression",
abstract = "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 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.",
author = "Bini, {L. Mauricio} and Diniz-Filho, {J. Alexandre F} and Rangel, {Thiago F L V B} and Akre, {Thomas S B} and Albaladejo, {Rafael G.} and {Suzart de Albuquerque}, Fabio and Abelardo Aparicio and Ara{\'u}jo, {Miguel B.} and Andr{\'e}s Baselga and Jan Beck and Bellocq, {M. Isabel} and Katrin B{\"o}hning-Gaese and Borges, {Paulo A V} and Isabel Castro-Parga and Chey, {Vun Khen} and Chown, {Steven L.} and {De Marco}, Paulo and Dobkin, {David S.} and Dolores Ferrer-Cast{\'a}n and Richard Field and Julieta Filloy and Erica Fleishman and G{\'o}mez, {Jose F.} and Joaqu{\'i}n Hortal and Iverson, {John B.} and Kerr, {Jeremy T.} and Kissling, {W. Daniel} and Kitching, {Ian J.} and Le{\'o}n-Cort{\'e}s, {Jorge L.} and Lobo, {Jorge M.} and Daniel Montoya and Ignacio Morales-Castilla and Moreno, {Juan C.} and Thierry Oberdorff and Olalla-T{\'a}rraga, {Miguel {\'A}} and Pausas, {Juli G.} and Hong Qian and Carsten Rahbek and Rodr{\'i}guez, {Miguel {\'A}} and Marta Rueda and Adriana Ruggiero and Paula Sackmann and Sanders, {Nathan J.} and Terribile, {Levi Carina} and Vetaas, {Ole R.} and Hawkins, {Bradford A.}",
year = "2009",
month = "4",
doi = "10.1111/j.1600-0587.2009.05717.x",
language = "English (US)",
volume = "32",
pages = "193--204",
journal = "Ecography",
issn = "0906-7590",
publisher = "Wiley-Blackwell",
number = "2",

}

TY - JOUR

T1 - Coefficient shifts in geographical ecology

T2 - An empirical evaluation of spatial and non-spatial regression

AU - Bini, L. Mauricio

AU - Diniz-Filho, J. Alexandre F

AU - Rangel, Thiago F L V B

AU - Akre, Thomas S B

AU - Albaladejo, Rafael G.

AU - Suzart de Albuquerque, Fabio

AU - Aparicio, Abelardo

AU - Araújo, Miguel B.

AU - Baselga, Andrés

AU - Beck, Jan

AU - Bellocq, M. Isabel

AU - Böhning-Gaese, Katrin

AU - Borges, Paulo A V

AU - Castro-Parga, Isabel

AU - Chey, Vun Khen

AU - Chown, Steven L.

AU - De Marco, Paulo

AU - Dobkin, David S.

AU - Ferrer-Castán, Dolores

AU - Field, Richard

AU - Filloy, Julieta

AU - Fleishman, Erica

AU - Gómez, Jose F.

AU - Hortal, Joaquín

AU - Iverson, John B.

AU - Kerr, Jeremy T.

AU - Kissling, W. Daniel

AU - Kitching, Ian J.

AU - León-Cortés, Jorge L.

AU - Lobo, Jorge M.

AU - Montoya, Daniel

AU - Morales-Castilla, Ignacio

AU - Moreno, Juan C.

AU - Oberdorff, Thierry

AU - Olalla-Tárraga, Miguel Á

AU - Pausas, Juli G.

AU - Qian, Hong

AU - Rahbek, Carsten

AU - Rodríguez, Miguel Á

AU - Rueda, Marta

AU - Ruggiero, Adriana

AU - Sackmann, Paula

AU - Sanders, Nathan J.

AU - Terribile, Levi Carina

AU - Vetaas, Ole R.

AU - Hawkins, Bradford A.

PY - 2009/4

Y1 - 2009/4

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=62249098547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62249098547&partnerID=8YFLogxK

U2 - 10.1111/j.1600-0587.2009.05717.x

DO - 10.1111/j.1600-0587.2009.05717.x

M3 - Article

VL - 32

SP - 193

EP - 204

JO - Ecography

JF - Ecography

SN - 0906-7590

IS - 2

ER -