Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression Export

@article{citeulike:4526961, 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 Alexandre and Rangel, Thiago F. L. V. B. and Akre, Thomas S. B. and Albaladejo, Rafael G. and Albuquerque, Fabio S. and Aparicio, Abelardo and Ara\'{u}jo, Miguel B. and Baselga, Andr\'{e}s and Beck, Jan and Bellocq, M. Isabel and B\"{o}hning-Gaese, Katrin and Borges, Paulo A. V. and Castro-Parga, Isabel and Chey, Vun K. and Chown, Steven L. and de Marco, Paulo and Jr and Dobkin, David S. and Ferrer-Cast\'{a}n, Dolores and Field, Richard and Filloy, Julieta and Fleishman, Erica and G\'{o}mez, Jose F. and Hortal, Joaqu\'{\i}n 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 Montoya, Daniel and Morales-Castilla, Ignacio and Moreno, Juan C. and Oberdorff, Thierry and Miguel and Pausas, Juli G. and Qian, Hong and Rahbek, Carsten and Miguel and Rueda, Marta and Ruggiero, Adriana and Sackmann, Paula and Sanders, Nathan J. and Terribile, Levi C. and Vetaas, Ole R. and Hawkins, Bradford A.}, citeulike-article-id = {4526961}, citeulike-linkout-0 = {http://dx.doi.org/10.1111/j.1600-0587.2009.05717.x}, citeulike-linkout-1 = {http://www.ingentaconnect.com/content/mksg/eco/2009/00000032/00000002/art00001}, citeulike-linkout-2 = {http://www3.interscience.wiley.com/cgi-bin/abstract/122261991/ABSTRACT}, doi = {10.1111/j.1600-0587.2009.05717.x}, issn = {1600-0587}, journal = {Ecography}, keywords = {ecological\_patterns, geographical\_distribution, multiple\_regression, ordinary\_least\_squares, regression\_coefficients, spatial\_autocorrelation, spatial\_methods, spatial\_models, spatial\_regression}, number = {2}, pages = {193--204}, posted-at = {2009-11-08 13:32:59}, priority = {2}, publisher = {Blackwell Publishing}, title = {Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression}, url = {http://dx.doi.org/10.1111/j.1600-0587.2009.05717.x}, volume = {32}, year = {2009} }

TY - JOUR ID - citeulike:4526961 L3 - citeulike-article-id:4526961 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. IS - 2 JF - Ecography SN - 1600-0587 EP - 204 TI - Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression PB - Blackwell Publishing VL - 32 SP - 193 KW - ecological_patterns KW - geographical_distribution KW - multiple_regression KW - ordinary_least_squares KW - regression_coefficients KW - spatial_autocorrelation KW - spatial_methods KW - spatial_models KW - spatial_regression AU - Bini, Mauricio AU - Alexandre AU - Rangel, Thiago AU - Akre, Thomas AU - Albaladejo, Rafael AU - Albuquerque, Fabio AU - Aparicio, Abelardo AU - Araújo, Miguel AU - Baselga, Andrés AU - Beck, Jan AU - Bellocq, Isabel AU - Böhning-Gaese, Katrin AU - Borges, Paulo AU - Castro-Parga, Isabel AU - Chey, Vun AU - Chown, Steven AU - de Marco, Paulo AU - Jr AU - Dobkin, David AU - Ferrer-Castán, Dolores AU - Field, Richard AU - Filloy, Julieta AU - Fleishman, Erica AU - Gómez, Jose AU - Hortal, Joaquín AU - Iverson, John AU - Kerr, Jeremy AU - Kissling, Daniel AU - Kitching, Ian AU - León-Cortés, Jorge AU - Lobo, Jorge AU - Montoya, Daniel AU - Morales-Castilla, Ignacio AU - Moreno, Juan AU - Oberdorff, Thierry AU - Miguel AU - Pausas, Juli AU - Qian, Hong AU - Rahbek, Carsten AU - Miguel AU - Rueda, Marta AU - Ruggiero, Adriana AU - Sackmann, Paula AU - Sanders, Nathan AU - Terribile, Levi AU - Vetaas, Ole AU - Hawkins, Bradford PY - 2009/// UR - http://dx.doi.org/10.1111/j.1600-0587.2009.05717.x ER -