Residual spatial autocorrelation in macroecological and biogeographical modeling: a review

Macroecologists and biogeographers continue to predict the distribution of species across space based on the relationship between biotic processes and environmental variables. This approach uses data related to, for example, species abundance or presence/absence, climate, geomorphology, and soils. Researchers have acknowledged in their statistical analyses the importance of accounting for the effects of spatial autocorrelation (SAC), which indicates a degree of dependence between pairs of nearby observations. It has been agreed that residual spatial autocorrelation (rSAC) can have a substantial impact on modeling processes and inferences. However, more attention should be paid to the sources of rSAC and the degree to which rSAC becomes problematic. Here, we review previous studies to identify diverse factors that potentially induce the presence of rSAC in macroecological and biogeographical models. Furthermore, an emphasis is put on the quantification of rSAC by seeking to unveil the magnitude to which the presence of SAC in model residuals becomes detrimental to the modeling process. It turned out that five categories of factors can drive the presence of SAC in model residuals: ecological data and processes, scale and distance, missing variables, sampling design, and assumptions and methodological approaches. Additionally, we noted that more explicit and elaborated discussion of rSAC should be presented in species distribution modeling. Future investigations involving the quantification of rSAC are recommended in order to understand when rSAC can have an adverse effect on the modeling process.This research was supported by (1) the National Science Foundation (grant numbers 0825753 and 1560907), (2) the National Research Foundation of Korea (NRF-2017R1C1B5076922), and (3) the Research Resettlement Fund for the new faculty of Seoul National University

Implementing Approximations to Extreme Eigenvalues and Eigenvalues of Irregular Surface Partitionings for use in SAR and CAR Models

-Copyright © 2015 The Authors. Published by Elsevier B.V.Good approximations of eigenvalues exist for the regular square and hexagonal tessellations. To complement this situation, spatial scientists need good approximations of eigenvalues for irregular tessellations. Starting from known or approximated extreme eigenvalues, the remaining eigenvalues may be in turn approximated. One reason spatial scientists are interested in eigenvalues is because they are needed to calculate the Jacobian term in the autonormal probability model. If eigenvalues are not needed for model fitting, good approximations are needed to give the interval within which the spatial parameter will lie

Spatial Autocorrelation and Uncertainty Associated with Remotely-Sensed Data

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

Evaluating Eigenvector Spatial Filter Corrections for Omitted Georeferenced Variables

The Ramsey regression equation specification error test (RESET) furnishes a diagnostic for omitted variables in a linear regression model specification (i.e., the null hypothesis is no omitted variables). Integer powers of fitted values from a regression analysis are introduced as additional covariates in a second regression analysis. The former regression model can be considered restricted, whereas the latter model can be considered unrestricted; this first model is nested within this second model. A RESET significance test is conducted with an F-test using the error sums of squares and the degrees of freedom for the two models. For georeferenced data, eigenvectors can be extracted from a modified spatial weights matrix, and included in a linear regression model specification to account for the presence of nonzero spatial autocorrelation. The intuition underlying this methodology is that these synthetic variates function as surrogates for omitted variables. Accordingly, a restricted regression model without eigenvectors should indicate an omitted variables problem, whereas an unrestricted regression model with eigenvectors should result in a failure to reject the RESET null hypothesis. This paper furnishes eleven empirical examples, covering a wide range of spatial attribute data types, that illustrate the effectiveness of eigenvector spatial filtering in addressing the omitted variables problem for georeferenced data as measured by the RESET

A Review of Spatial Statistical Approaches to Modeling Water Quality

We review different regression models related to water quality that incorporate spatial aspects in their model. Spatial aspects refer to the location of different sites and are usually characterized by the distance between different points and directions by which they are related to each other. We focus on spatial lag and error, spatial eigenvector-based, geographically weighted regression, and spatial-stream-network-based models. We evaluated different studies using these methods based on how they dealt with clustering (spatial autocorrelation) of response variables, incorporated those clustering in the error (residual spatial autocorrelation), used multi-scale processes, and improved the model performance. The water-quality-based regression modeling approaches are shifting from straight-line distance-based spatial relations to upstream–downstream relations. Calculation of spatial autocorrelation and residual spatial autocorrelation was dependent upon the type of spatial regression used. The weights matrix is used as available in the software and most of the studies did not attempt to modify it. Different scale processes like certain distance from rivers versus consideration of entire watersheds are dealt with separately in most of the studies. Generally, the capacity of the predictor variables to predict the response variable significantly improves when spatial regressions are used. We identify new research directions in terms of spatial considerations, weights matrix construction, inclusion of multi-scale processes, and identification of predictor variables in such models

Modeling Interregional Commodity Flows with Incorporating Network Autocorrelation in Spatial Interaction Models: An Application of the US Interstate Commodity Flows." Computers, Environment and Urban Systems 36.6 (2012

a b s t r a c t Spatial interaction models are frequently used to predict and explain interregional commodity flows. Studies suggest that the effects of spatial structure significantly influence spatial interaction models, often resulting in model misspecification. Competing destinations and intervening opportunities have been used to mitigate this issue. Some recent studies also show that the effects of spatial structure can be successfully modeled by incorporating network autocorrelation among flow data. The purpose of this paper is to investigate the existence of network autocorrelation among commodity origin-destination flow data and its effect on model estimation in spatial interaction models. This approach is demonstrated using commodity origin-destination flow data for 111 regions of the United States from the 2002 Commodity Flow Survey. The results empirically show how network autocorrelation affects modeling interregional flows and can be successfully captured in spatial autoregressive model specifications