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Daniel A Griffith - One of the best experts on this subject based on the ideXlab platform.
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Negative Spatial Autocorrelation: One of the Most Neglected Concepts in Spatial Statistics
Stats, 2019Co-Authors: Daniel A GriffithAbstract:Negative Spatial Autocorrelation is one of the most neglected concepts in quantitative geography, regional science, and Spatial statistics/econometrics in general. This paper focuses on and contributes to the literature in terms of the following three reasons why this neglect exists: Existing Spatial Autocorrelation quantification, the popular form of georeferenced variables studied, and the presence of both hidden negative Spatial Autocorrelation, and mixtures of positive and negative Spatial Autocorrelation in georeferenced variables. This paper also presents details and insights by furnishing concrete empirical examples of negative Spatial Autocorrelation. These examples include: Multi-locational chain store market areas, the shrinking city of Detroit, Dallas-Fort Worth journey-to-work flows, and county crime data. This paper concludes by enumerating a number of future research topics that would help increase the literature profile of negative Spatial Autocorrelation.
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Clustering: Spatial Autocorrelation and Location Quotients
Advanced Studies in Theoretical and Applied Econometrics, 2018Co-Authors: Daniel A Griffith, Jean H. P. PaelinckAbstract:Geographic concentration of employment types frequently yields clusters exhibiting moderate-to-strong positive Spatial Autocorrelation. Such clusters based upon geographic proximity, and frequently quantified with location quotients, also can relate to local indices of Spatial Autocorrelation, such as LISA and the Getis-Ord statistics. Carroll et al. (Ann Reg Sci 42:449–463, 2008) furnish a comparison of these sets of indices. This chapter adds to that literature, but by conceptualizing location quotients as Spatially autocorrelated binomial random variables.
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Spatial Autocorrelation and the p-Median Problem
Advanced Studies in Theoretical and Applied Econometrics, 2018Co-Authors: Daniel A Griffith, Jean H. P. PaelinckAbstract:To date, relationships largely have been ignored between Spatial Autocorrelation latent in some geographic distribution of demand and corresponding solutions to a p-median problem based upon it. A small literature exploits Spatial Autocorrelation in the geographic distribution of demand having missing values, in order to calculate imputations for the missing values, so that solutions are computable. But this literature fails to address explicit relationships between such solutions and their accompanying latent level of Spatial Autocorrelation as well as its associated map pattern. The purpose of this chapter is to begin filling this literature gap.
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Spatial Autocorrelation and Uncertainty Associated with Remotely-Sensed Data
Remote Sensing, 2016Co-Authors: Daniel A Griffith, Yongwan ChunAbstract:Virtually all remotely sensed data contain Spatial Autocorrelation, which impacts upon their statistical features of uncertainty through variance inflation, and the compounding of duplicate information. Estimating the nature and degree of this Spatial Autocorrelation, which is usually positive and very strong, has been hindered by computational intensity associated with the massive number of pixels in realistically-sized remotely-sensed images, a situation that more recently has changed. Recent advances in Spatial statistical estimation theory support the extraction of information and the distilling of knowledge from remotely-sensed images in a way that accounts for latent Spatial Autocorrelation. This paper summarizes an effective methodological approach to achieve this end, illustrating results with a 2002 remotely sensed-image of the Florida Everglades, and simulation experiments. Specifically, uncertainty of Spatial Autocorrelation parameter in a Spatial autoregressive model is modeled with a beta-beta mixture approach and is further investigated with three different sampling strategies: coterminous sampling, random sub-region sampling, and increasing domain sub-regions. The results suggest that uncertainty associated with remotely-sensed data should be cast in consideration of Spatial Autocorrelation. It emphasizes that one remaining challenge is to better quantify the Spatial variability of Spatial Autocorrelation estimates across geographic landscapes.
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Spatial Autocorrelation and Art
Cybergeo: European Journal of Geography, 2016Co-Authors: Daniel A GriffithAbstract:Spatial Autocorrelation is everywhere, even in paintings by artists. This paper presents a case study supporting this contention based upon paintings by Susie Rosmarin.
William E. Kunin - One of the best experts on this subject based on the ideXlab platform.
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consequences of Spatial Autocorrelation for niche based models
Journal of Applied Ecology, 2006Co-Authors: Pedro Segurado, Miguel B. Araújo, William E. KuninAbstract:Summary 1Spatial Autocorrelation is an important source of bias in most Spatial analyses. We explored the bias introduced by Spatial Autocorrelation on the explanatory and predictive power of species’ distribution models, and make recommendations for dealing with the problem. 2Analyses were based on the distribution of two species of freshwater turtle and two virtual species with simulated Spatial structures within two equally sized areas located on the Iberian Peninsula. Sequential permutations of environmental variables were used to generate predictor variables that retained the Spatial structure of the original variables. Univariate models of species’ distributions using generalized linear models (GLM), generalized additive models (GAM) and classification tree analysis (CTA) were fitted for each variable permutation. Variation of accuracy measures with Spatial Autocorrelation of the original predictor variables, as measured by Moran's I, was analysed and compared between models. The effects of systematic subsampling of the data set and the inclusion of a contagion term to deal with Spatial Autocorrelation in models were assessed with projections made with GLM, as it was with this method that estimates of significance based on randomizations were obtained. 3Spatial Autocorrelation was shown to represent a serious problem for niche-based species’ distribution models. Significance values were found to be inflated up to 90-fold. 4In general, GAM and CTA performed better than GLM, although all three methods were vulnerable to the effects of Spatial Autocorrelation. 5The procedures utilized to reduce the effects of Spatial Autocorrelation had varying degrees of success. Subsampling was partially effective in avoiding the inflation effect, whereas the inclusion of a contagion term fully eliminated or even overcompensated for this effect. Direct estimation of probability using variable simulations was effective, yet seemed to show some residual Spatial Autocorrelation effects. 6Synthesis and applications. Given the expected inflation in the estimates of significance when analysing Spatially autocorrelated variables, these need to be adjusted. The reliability and value of niche-based distribution models for management and other applied ecology purposes can be improved if certain techniques and procedures, such as the null model approach recommended in this study, are implemented during the model-building process.
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Consequences of Spatial Autocorrelation for niche‐based models
Journal of Applied Ecology, 2006Co-Authors: Pedro Segurado, Miguel B. Araújo, William E. KuninAbstract:Summary 1Spatial Autocorrelation is an important source of bias in most Spatial analyses. We explored the bias introduced by Spatial Autocorrelation on the explanatory and predictive power of species’ distribution models, and make recommendations for dealing with the problem. 2Analyses were based on the distribution of two species of freshwater turtle and two virtual species with simulated Spatial structures within two equally sized areas located on the Iberian Peninsula. Sequential permutations of environmental variables were used to generate predictor variables that retained the Spatial structure of the original variables. Univariate models of species’ distributions using generalized linear models (GLM), generalized additive models (GAM) and classification tree analysis (CTA) were fitted for each variable permutation. Variation of accuracy measures with Spatial Autocorrelation of the original predictor variables, as measured by Moran's I, was analysed and compared between models. The effects of systematic subsampling of the data set and the inclusion of a contagion term to deal with Spatial Autocorrelation in models were assessed with projections made with GLM, as it was with this method that estimates of significance based on randomizations were obtained. 3Spatial Autocorrelation was shown to represent a serious problem for niche-based species’ distribution models. Significance values were found to be inflated up to 90-fold. 4In general, GAM and CTA performed better than GLM, although all three methods were vulnerable to the effects of Spatial Autocorrelation. 5The procedures utilized to reduce the effects of Spatial Autocorrelation had varying degrees of success. Subsampling was partially effective in avoiding the inflation effect, whereas the inclusion of a contagion term fully eliminated or even overcompensated for this effect. Direct estimation of probability using variable simulations was effective, yet seemed to show some residual Spatial Autocorrelation effects. 6Synthesis and applications. Given the expected inflation in the estimates of significance when analysing Spatially autocorrelated variables, these need to be adjusted. The reliability and value of niche-based distribution models for management and other applied ecology purposes can be improved if certain techniques and procedures, such as the null model approach recommended in this study, are implemented during the model-building process.
Yongwan Chun - One of the best experts on this subject based on the ideXlab platform.
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Spatial Autocorrelation and Uncertainty Associated with Remotely-Sensed Data
Remote Sensing, 2016Co-Authors: Daniel A Griffith, Yongwan ChunAbstract:Virtually all remotely sensed data contain Spatial Autocorrelation, which impacts upon their statistical features of uncertainty through variance inflation, and the compounding of duplicate information. Estimating the nature and degree of this Spatial Autocorrelation, which is usually positive and very strong, has been hindered by computational intensity associated with the massive number of pixels in realistically-sized remotely-sensed images, a situation that more recently has changed. Recent advances in Spatial statistical estimation theory support the extraction of information and the distilling of knowledge from remotely-sensed images in a way that accounts for latent Spatial Autocorrelation. This paper summarizes an effective methodological approach to achieve this end, illustrating results with a 2002 remotely sensed-image of the Florida Everglades, and simulation experiments. Specifically, uncertainty of Spatial Autocorrelation parameter in a Spatial autoregressive model is modeled with a beta-beta mixture approach and is further investigated with three different sampling strategies: coterminous sampling, random sub-region sampling, and increasing domain sub-regions. The results suggest that uncertainty associated with remotely-sensed data should be cast in consideration of Spatial Autocorrelation. It emphasizes that one remaining challenge is to better quantify the Spatial variability of Spatial Autocorrelation estimates across geographic landscapes.
Bradford A. Hawkins - One of the best experts on this subject based on the ideXlab platform.
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red herrings revisited Spatial Autocorrelation and parameter estimation in geographical ecology
Ecography, 2007Co-Authors: Bradford A. Hawkins, Luis Mauricio Bini, Jose Alexandre Felizola Dinizfilho, Paulo De Marco, Tim M BlackburnAbstract:There have been numerous claims in the ecological literature that Spatial Autocorrelation in the residuals of ordinary least squares (OLS) regression models results in shifts in the partial coefficients, which bias the interpretation of factors influencing geographical patterns. We evaluate the validity of these claims using gridded species richness data for the birds of North America, South America, Europe, Africa, the ex-USSR, and Australia. We used richness in 110x110 km cells and environmental predictor variables to generate OLS and simultaneous autoregressive (SAR) multiple regression models for each region. Spatial correlograms of the residuals from each OLS model were then used to identify the minimum distance between cells necessary to avoid short-distance residual Spatial Autocorrelation in each data set. This distance was used to subsample cells to generate Spatially independent data. The partial OLS coefficients estimated with the full dataset were then compared to the distributions of coefficients created with the subsamples. We found that OLS coefficients generated from data containing residual Spatial Autocorrelation were statistically indistinguishable from coefficients generated from the same data sets in which short-distance Spatial Autocorrelation was not present in all 22 coefficients tested. Consistent with the statistical literature on this subject, we conclude that coefficients estimated from OLS regression are not seriously affected by the presence of Spatial Autocorrelation in gridded geographical data. Further, shifts in coefficients that occurred when using SAR tended to be correlated with levels of uncertainty in the OLS coefficients. Thus, shifts in the relative importance of the predictors between OLS and SAR models are expected when small-scale patterns for these predictors create weaker and more unstable broad-scale coefficients. Our results indicate both that OLS regression is unbiased and that differences between Spatial and nonSpatial regression models should be interpreted with an explicit awareness of Spatial scale.
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Spatial Autocorrelation and red herrings in geographical ecology
Global Ecology and Biogeography, 2003Co-Authors: José Alexandre Felizola Diniz-filho, Luis Mauricio Bini, Bradford A. HawkinsAbstract:Aim Spatial Autocorrelation in ecological data can inflate Type I errors in statistical analyses. There has also been a recent claim that Spatial Autocorrelation generates 'red herrings', such that virtually all past analyses are flawed. We consider the origins of this phenomenon, the implications of Spatial Autocorrelation for macro-scale patterns of species diversity and set out a clarification of the statistical problems generated by its presence. Location To illustrate the issues involved, we analyse the species richness of the birds of western/central Europe, north Africa and the Middle East. Methods Spatial correlograms for richness and five environmental variables were generated using Moran's I coefficients. Multiple regression, using both ordinary least-squares (OLS) and generalized least squares (GLS) assuming a Spatial structure in the residuals, were used to identify the strongest predictors of richness. Autocorrelation analyses of the residuals obtained after stepwise OLS regression were undertaken, and the ranks of variables in the full OLS and GLS models were compared. Results Bird richness is characterized by a quadratic north-south gradient. Spatial correlograms usually had positive Autocorrelation up to c. 1600 km. Including the environmental variables successively in the OLS model reduced Spatial Autocorrelation in the residuals to non-detectable levels, indicating that the variables explained all Spatial structure in the data. In principle, if residuals are not autocorrelated then OLS is a special case of GLS. However, our comparison between OLS and GLS models including all environmental variables revealed that GLS de-emphasized predictors with strong Autocorrelation and long-distance clinal structures, giving more importance to variables acting at smaller geographical scales. Conclusion Although Spatial Autocorrelation should always be investigated, it does not necessarily generate bias. Rather, it can be a useful tool to investigate mechanisms operating on richness at different Spatial scales. Claims that analyses that do not take into account Spatial Autocorrelation are flawed are without foundation.
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Spatial Autocorrelation and red herrings in geographical
2003Co-Authors: Felizola Diniz-filho, Luis Mauricio Bini, Bradford A. HawkinsAbstract:Aim Spatial Autocorrelation in ecological data can inflate Type I errors in statistical analyses. There has also been a recent claim that Spatial Autocorrelation generates 'red herrings', such that virtually all past analyses are flawed. We consider the origins of this phenomenon, the implications of Spatial Autocorrelation for macro-scale patterns of species diversity and set out a clarification of the statistical problems generated by its presence. Location To illustrate the issues involved, we analyse the species richness of the birds of western/central Europe, north Africa and the Middle East. Methods Spatial correlograms for richness and five environ- mental variables were generated using Moran's I coefficients. Multiple regression, using both ordinary least-squares (OLS) and generalized least squares (GLS) assuming a Spatial struc- ture in the residuals, were used to identify the strongest predictors of richness. Autocorrelation analyses of the residuals obtained after stepwise OLS regression were undertaken, and the ranks of variables in the full OLS and GLS models were compared. Results Bird richness is characterized by a quadratic north- south gradient. Spatial correlograms usually had positive Autocorrelation up to c . 1600 km. Including the environmen- tal variables successively in the OLS model reduced Spatial Autocorrelation in the residuals to non-detectable levels, indicating that the variables explained all Spatial structure in the data. In principle, if residuals are not autocorrelated then OLS is a special case of GLS. However, our comparison between OLS and GLS models including all environmental variables revealed that GLS de-emphasized predictors with strong Autocorrelation and long-distance clinal structures, giving more importance to variables acting at smaller geographical scales. Conclusion Although Spatial Autocorrelation should always be investigated, it does not necessarily generate bias. Rather, it can be a useful tool to investigate mechanisms operating on richness at different Spatial scales. Claims that analyses that do not take into account Spatial Autocorrelation are flawed are without foundation.
Pedro Segurado - One of the best experts on this subject based on the ideXlab platform.
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consequences of Spatial Autocorrelation for niche based models
Journal of Applied Ecology, 2006Co-Authors: Pedro Segurado, Miguel B. Araújo, William E. KuninAbstract:Summary 1Spatial Autocorrelation is an important source of bias in most Spatial analyses. We explored the bias introduced by Spatial Autocorrelation on the explanatory and predictive power of species’ distribution models, and make recommendations for dealing with the problem. 2Analyses were based on the distribution of two species of freshwater turtle and two virtual species with simulated Spatial structures within two equally sized areas located on the Iberian Peninsula. Sequential permutations of environmental variables were used to generate predictor variables that retained the Spatial structure of the original variables. Univariate models of species’ distributions using generalized linear models (GLM), generalized additive models (GAM) and classification tree analysis (CTA) were fitted for each variable permutation. Variation of accuracy measures with Spatial Autocorrelation of the original predictor variables, as measured by Moran's I, was analysed and compared between models. The effects of systematic subsampling of the data set and the inclusion of a contagion term to deal with Spatial Autocorrelation in models were assessed with projections made with GLM, as it was with this method that estimates of significance based on randomizations were obtained. 3Spatial Autocorrelation was shown to represent a serious problem for niche-based species’ distribution models. Significance values were found to be inflated up to 90-fold. 4In general, GAM and CTA performed better than GLM, although all three methods were vulnerable to the effects of Spatial Autocorrelation. 5The procedures utilized to reduce the effects of Spatial Autocorrelation had varying degrees of success. Subsampling was partially effective in avoiding the inflation effect, whereas the inclusion of a contagion term fully eliminated or even overcompensated for this effect. Direct estimation of probability using variable simulations was effective, yet seemed to show some residual Spatial Autocorrelation effects. 6Synthesis and applications. Given the expected inflation in the estimates of significance when analysing Spatially autocorrelated variables, these need to be adjusted. The reliability and value of niche-based distribution models for management and other applied ecology purposes can be improved if certain techniques and procedures, such as the null model approach recommended in this study, are implemented during the model-building process.
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Consequences of Spatial Autocorrelation for niche‐based models
Journal of Applied Ecology, 2006Co-Authors: Pedro Segurado, Miguel B. Araújo, William E. KuninAbstract:Summary 1Spatial Autocorrelation is an important source of bias in most Spatial analyses. We explored the bias introduced by Spatial Autocorrelation on the explanatory and predictive power of species’ distribution models, and make recommendations for dealing with the problem. 2Analyses were based on the distribution of two species of freshwater turtle and two virtual species with simulated Spatial structures within two equally sized areas located on the Iberian Peninsula. Sequential permutations of environmental variables were used to generate predictor variables that retained the Spatial structure of the original variables. Univariate models of species’ distributions using generalized linear models (GLM), generalized additive models (GAM) and classification tree analysis (CTA) were fitted for each variable permutation. Variation of accuracy measures with Spatial Autocorrelation of the original predictor variables, as measured by Moran's I, was analysed and compared between models. The effects of systematic subsampling of the data set and the inclusion of a contagion term to deal with Spatial Autocorrelation in models were assessed with projections made with GLM, as it was with this method that estimates of significance based on randomizations were obtained. 3Spatial Autocorrelation was shown to represent a serious problem for niche-based species’ distribution models. Significance values were found to be inflated up to 90-fold. 4In general, GAM and CTA performed better than GLM, although all three methods were vulnerable to the effects of Spatial Autocorrelation. 5The procedures utilized to reduce the effects of Spatial Autocorrelation had varying degrees of success. Subsampling was partially effective in avoiding the inflation effect, whereas the inclusion of a contagion term fully eliminated or even overcompensated for this effect. Direct estimation of probability using variable simulations was effective, yet seemed to show some residual Spatial Autocorrelation effects. 6Synthesis and applications. Given the expected inflation in the estimates of significance when analysing Spatially autocorrelated variables, these need to be adjusted. The reliability and value of niche-based distribution models for management and other applied ecology purposes can be improved if certain techniques and procedures, such as the null model approach recommended in this study, are implemented during the model-building process.