Presence Of Spatial Autocorrelation Research Articles

Accounting for Spatial Autocorrelation in the 2004 Presidential Popular Vote: A Reassessment of the Evidence

Ordinary least squares econometric approaches to estimating election vote outcomes potentially ignore spatial dependence (or autocorrelation) in the data that may affect estimates of voting behavior. The presence of spatial autocorrelation in the data can yield biased or inconsistent point estimates when ordinary least squares is used inappropriately. Therefore, this paper puts forward a spatial econometric model to estimate the vote outcomes in the 2004 presidential election. We contribute to the literature in two ways. One, we extend the voting behavior literature by considering newly developed spatial specification tests to determine the proper econometric model. The results of two different spatial specification tests suggest that a spatial Durbin model provides a better fit to the data. Two, we offer a richer interpretation of the spatial effects, which differ from standard ordinary least squares estimates, of the county-level vote outcome for the 2004 presidential election.

A Spatially Autocorrelated Weights of Evidence Model

One of the most important features of spatial datasets is that they often exhibit spatial autocorrelation, where locational similarities are observed jointly with similarities in values. Both logistic regression (LR) modelling and weights of evidence (WE) modelling are methods commonly applied in binary pattern recognition. While a spatially autocorrelated variant of the LR model, the so-called autologistic regression (ALR) model, exists in the literature, a spatially autocorrelated variant of the WE model does not exist. In this paper, a spatially autocorrelated weights of evidence (SACWE) model will be proposed. It will be demonstrated that the new model contains the same amount of spatial information as does an ALR model, and it is easy to program and implement. Via a simulation study, it will be shown that, in the presence of spatial autocorrelation, both in terms of in-sample fit and out-of-sample predictions the SACWE model is on par with the ALR model, while significantly outperforming the conventional WE model.

Spatial Autocorrelation and Impacts on Criminology

Despite criminology's widespread application of geography, the full implications of Cliff and Ord's article have yet to be realized. In this essay the major types of spatial studies in criminology are outlined, followed by a depiction of the context of criminological research at the time the article was published. Next the major changes to the field occurring after the publication of Cliff and Ord's paper, focusing on technology advances and theory, are set out. Fortunately these changes mean the discipline is well placed to move beyond seeing the presence of spatial autocorrelation as a methodological issue that needs to be explained away.

Comparison of Methods for Defining Geographical Connectivity for Variables of Trip Generation Models

The four-step procedure for travel demand modeling is ubiquitously used in the United States and elsewhere due to institutional and financial requirements. Trip generation analysis, which is the first step, is based on traffic analysis zones which are geographical units. Therefore, the zonal trip generation totals are observations measured at different geographical locations. Spatial distribution of the observations limits the methods that can be applied in analyzing the data and influences the final conclusions that can be reached. Most past efforts of incorporating spatial effects in trip generation models have been using contiguity of the zones as the major criterion for defining spatial relationship of the observations. In this study, we tested for the presence of spatial autocorrelation in both trip attraction and trip production variables. We found significant spatial autocorrelation in trip attraction variables but insignificant spatial autocorrelation in trip production variables for the data collected from the Las Vegas valley. We evaluated four alternative methods for defining geographical connectivity: (1) contiguity, (2) separation, (3) combined contiguity and separation, and (4) economic linkage (accessibility measure). Comparison of the trip attraction model indicated that the model estimated using geographical connectivity matrix with elements defined by separation (distance between centroids of the zones) was the best fitted. A further comparison indicated that this model outperformed the one without spatial variables by minimizing deviation of the modeled trips from observed trips. We recommend using separation between the zones to define spatial connectivity as opposed to contiguity only. Contiguity only excludes zones that may have an impact on the observation under consideration.

The detection of spatial structure in populations and communities: An empirical case study

The presence of spatial autocorrelation in abundance and richness patterns has been recognised for some time. Evaluation of the tools to quantify patterning often uses simulated data that may be unrealistic or empirical field data where the presence and cause of structuring are unknown. We examine the efficacy of spatial pattern analysis for detecting pattern in empirical data at a fine scale using a field-based mesocosm experiment of a Drosophilidae community associated with decaying fruit. The mesocosm comprised 2 microclimate treatments that generated a particular expected spatial pattern in abundance and species richness. The magnitude of Moran's autocorrelation coefficients (I) was < 0.3 (i.e., low). However, the detected pattern was unaffected. Low Moran's I values did not result from low sample sizes, neither was the significance of Moran's I falsely inflated by large sample sizes. Examination of published I values revealed that autocorrelation values between 0.1 and 0.3 are common in empirical data, particularly at fine (lag distance ≤ 1 m) spatial scales. Pooling temporal samples strengthened the detected output without affecting the form of spatial pattern. We conclude that “weak” responses provide a valuable basis for mechanistic hypothesis generation, especially at fine spatial scales, and that the strength of spatial structure is likely to be determined by the spatial scale of the study.

Interpretation of electrical conductivity patterns by soil properties and geological maps for precision agriculture

Precision farming needs management rules to apply spatially differentiated treatments in agricultural fields. Digital soil mapping (DSM) tools, for example apparent soil electrical conductivity, corrected to 25°C (EC25), and digital elevation models, try to explain the spatial variation in soil type, soil properties (e.g. clay content), site and crop that are determined by landscape characteristics such as terrain, geology and geomorphology. We examined the use of EC25 maps to delineate management zones, and identified the main factors affecting the spatial pattern of EC25 at the regional scale in a study area in eastern Germany. Data of different types were compared: EC25 maps for 11 fields, soil properties measured in the laboratory, terrain attributes, geological maps and the description of 75 soil profiles. We identified the factors that influence EC25 in the presence of spatial autocorrelation and field-specific random effects with spatial linear mixed-effects models. The variation in EC25 could be explained to a large degree (R 2 of up to 61%). Primarily, soil organic matter and CaCO3, and secondarily clay and the presence of gleyic horizons were significantly related to EC25. Terrain attributes, however, had no significant effect on EC25. The geological map unit showed a significant relationship to EC25, and it was possible to determine the most important soil properties affecting EC25 by interpreting the geological maps. Including information on geology in precision agriculture could improve understanding of EC25 maps. The EC25 maps of fields should not be assumed to represent a map of clay content to form a basis for deriving management zones because other factors appeared to have a more important effect on EC25.

Diversity and employment growth in sub-regions of Great Britain

This article presents evidence from an empirical study of employment growth across 203 sub-regions of Great Britain using OLS and maximum likelihood spatial econometric techniques. The results suggest a positive relationship between diversity and local employment growth implying that cross-sector externalities may be of considerable importance to the local growth process. The presence of spatial autocorrelation in the data suggests the existence of substantive interactions across contiguous sub-regions.

Spatial analysis of Neospora caninum distribution in dairy cattle from Sweden

The national herd prevalence and spatial distribution of Neospora caninum infected dairy herds in Sweden were investigated. The study was based on a bulk milk survey comprising samples from 2,978 herds. Test-positive herds were found in all parts of Sweden and the overall prevalence of test-positive herds was 8.3% (95% confidence interval = 7.3-9.3%). The presence of spatial autocorrelation was tested using the Moran's I test. Possible clusters of test-positive herds were identified by applying the local indicator of spatial association (LISA) test statistic and the spatial scan statistic. Analysis based on data aggregated by postal code areas as well as analysis based on exact coordinates identified significant clusters of high prevalence in the middle parts of Sweden and low prevalence in the south. This was not expected considering the results from other European studies of N. caninum in cattle. However, the findings are supported by the distribution of previously known case herds.

Prostorová autokorelace - všudypřítomný jev při analýze prostorových dat?

The article deals with one of the big analytical issues in spatial data analysis: spatial autocorrelation. This phenomenon is described as a key con- cept and potential problem of spatial analysis, but especially as a method of spatial analysis. The method is introduced fi rst by reviewing the basic meth- odological framework including some related issues (the choice of spatial weighting system etc.) and second by presenting empirical examples of its application. Spatial autocorrelation statistics detect the presence of interde- pendence between the values of data at neighbouring locations. In addition to global spatial autocorrelation, measuring the overall degree of clustering, and calculated, for example, by Moran's I, emphasis is placed on the local analysis of spatial autocorrelation. This local form of spatial autocorrelation is based on the premise that the presence of spatial autocorrelation can vary across the study area, and it is fully in line with contemporary developments in spa- tial analysis. The results of LISA (local indicators of spatial association, local Moran) can be mapped for the purpose of identifying clusters. The empirical examples based on aggregate statistical data at the municipal level highlight the relevance and usefulness of analysis of spatial autocorrelation and show how these analyses can be used in social research and can improve our under- standing of spatial processes.

Income Distribution Dynamics and Cross-Region Convergence in Europe: Spatial Filtering and Novel Stochastic Kernel Representations

This paper suggests an empirical framework for analysing income distribution dynamics and cross-region convergence in the European Union of 27 member states, 1995-2003. The framework lies in the research tradition that allows the state income space to be continuous, puts emphasis on both shape and intra-distribution dynamics and uses stochastic kernels for studying transition dynamics and implied long-run behaviour. In this paper stochastic kernels are described by conditional density functions, estimated by a product kernel estimator of conditional density and represented by means of novel visualisation tools. The technique of spatial filtering is used to account for spatial effects, in order to avoid misguided inferences and interpretations caused by the presence of spatial autocorrelation in the income distributions. The results reveal a slow catching-up of the poorest regions and a process of polarisation, with a small group of very rich regions shifting away from the rest of the cross-section. This is well evidenced by both, the unfiltered and the filtered ergodic density view. Differences exist in detail, and these emphasise the importance to properly deal with the spatial autocorrelation problem.

Malaria seasonality and rainfall seasonality in Sri Lanka are correlated in space

Correlation in space between seasonality of malaria and seasonality of rainfall was studied in Sri Lanka. A simple seasonality index was developed by making use of the bimodal seasonality of both malaria and rainfall. The malaria seasonality index was regressed against the rainfall seasonality index taking spatial autocorrelation into account. Despite the presence of spatial autocorrelation, the coefficient for the rainfall seasonality index in explaining the malaria seasonality index was found to be significant. The results suggest that rainfall is an important driver of malaria seasonality.

Analyzing spatial autocorrelation in species distributions using Gaussian and logit models

Analyses of spatial distributions in ecology are often influenced by spatial autocorrelation. While methods to deal with spatial autocorrelation in Normally distributed data are already frequently used, the analysis of non-Normal data in the presence of spatial autocorrelation are rarely known to ecologists. Several methods based on the generalized estimating equations (GEE) are compared in their performance to a better known autoregressive method, namely spatially simultaneous autoregressive error model (SSAEM). GEE are further used to analyze the influence of autocorrelation of observations on logistic regression models. Originally, these methods were developed for longitudinal data and repeated measures models. This paper proposes some techniques for application to two-dimensional macroecological and biogeographical data sets displaying spatial autocorrelation. Results are presented for both computationally simulated data and ecological data (distribution of plant species richness throughout Germany and distribution of the plant species Hydrocotyle vulgaris). While for Normally distributed data SSAEM perform better than GEE, GEE provide far better results than frequently used autologistic regressions and remove residual spatial autocorrelation substantially when having binary data.

Red herrings revisited: spatial autocorrelation and parameter estimation in geographical ecology

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 110×110 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.

All Together Now? An Empirical Study of the Voting Behaviors of Homeowner Association Members in St. Louis County

AbstractHomeowner associations (HOAs), by design, collect homogenous members of a community into a residential development with defined boundaries and contain at least some very active individuals. This implies that HOAs may lower the transaction costs involved with voting resulting in HOA membership increasing voter participation. Further, as more HOAs provide goods and services to their members as substitutes for goods and services provided by the public sector, one would expect HOA members to vote more conservatively and in support of more privatization. Using a detailed population database constructed for Saint Louis County, Missouri, and results from the November 2004 general election, this article analyzes the effect that living in an HOA has on voter participation and on the results of several election issues. Following a similar study by the Public Policy Institute of California, the results show that, once population characteristics are controlled for, there is no HOA effect on the likelihood of HOA members to vote Republican. Unlike previous work, this study shows that if the vote reporting districts are broken into five mutually exclusive categories rather than using the 60% rule used in other studies, areas with more HOAs do show an increase in participation rates and an increased likelihood to vote against property tax increases. The results hold up even after the presence of spatial autocorrelation is confirmed and controlled for.

Relating geographical variation in pollination types to environmental and spatial factors using novel statistical methods

The relative frequencies of functional traits of plant species show notable spatial variation, which is often related to environmental factors. Pollination type (insect-, wind- or self-pollination) is a critical trait for plant reproduction and provision of ecosystem services. Here, we mapped the distribution of pollination types across Germany by combining databases on plant distribution and plant pollination types. Applying a new method, we modelled the composition of pollination types using a set of 12 environmental variables as predictors within a Bayesian framework which allows for the analysis of compositional data in the presence of spatial autocorrelation. A clear biogeographical pattern in the distribution of pollination types was revealed which was adequately captured by our model. The most striking relationship was a relative increase in insect-pollination and a corresponding decrease of selfing with increasing altitude. Further important factors were wind speed, geology and land use. We present a powerful tool to analyse the distribution patterns of plant functional types such as pollination types and their relationship with environmental parameters in a spatially explicit framework.

Behavior of Vegetation Sampling Methods in the Presence of Spatial Autocorrelation

Spatial autocorrelation in vegetation has been discussed extensively, but little is yet known about how standard plant sampling methods perform when confronted with varying levels of patchiness. Simulated species maps with a range of total abundance and spatial autocorrelation (patchiness) were sampled using four methods: strip transect, randomly located quadrats, the non-nested multiscale modified Whittaker plot and the nested multiscale North Carolina Vegetation Survey (NCVS) plot. Cover and frequency estimates varied widely within and between methods, especially in the presence of high patchiness and for species with moderate abundances. Transect sampling showed the highest variability, returning estimates of 19–94% cover for a species with an actual cover of 50%. Transect and random methods were likely to miss rare species entirely unless large numbers of quadrats were sampled. NCVS plots produced the most accurate cover estimates because they sampled the largest area. Total species richness calculated using semilog species-area curves was overestimated by transect and random sampling. Both multiscale methods, the modified Whittaker and the NCVS plots, overestimated species richness when patchiness was low, and underestimated it when patchiness was high. There was no clear distinction between the nested NCVS or the non-nested modified Whittaker plot for any of the measures assessed. For all sampling methods, cover and especially frequency estimates were highly variable, and depended on both the level of autocorrelation and the sampling method used. The spatial structure of the vegetation must be considered when choosing field sampling protocols or comparing results between studies that used different methods.

Analysis of meso scaled spatial distribution of dab Limanda limanda in the German Bight: does the type of fishing gear matter?

In the North Sea, studies are carried out to assess the effect of offshore windmills on the spatial distributions of various fish species, based on data often obtained from different fishing gears. In this study, spatial analysis of three size classes of dab Limanda limanda in the German Bight was undertaken and the effect of different fishing gear type on analyzing spatial patterns are assessed, using geostatistics. In an area equal in size to a wind park (with ≈200 windmills), a comparative fishing experiment was carried out, where a 7 m-beam trawl and an otter trawl were employed. Structural analyses showed a presence of spatial autocorrelation in the catch data in all cases. The use of an efficient sampling gear led to an improved resolution of spatial structuring, but did not necessarily result in reduction of nugget variability. Ecological parameters derived from a spatial analysis were in good agreement in cases of high abundance and similar gear efficiency. Thus, it is shown that the type of gear matters in cases of low species abundance. Therefore, to achieve reliable results of a structural analysis and an accurate spatial assessment of fisheries data, it is recommended that the abundance of the target species (biological group) and efficiency of the sampling gear are considered.

Effective Geographic Sample Size in the Presence of Spatial Autocorrelation

As spatial autocorrelation latent in georeferenced data increases, the amount of duplicate information contained in these data also increases. This property suggests the research question asking what the number of independent observations, say , is that is equivalent to the sample size, n, of a data set. This is the notion of effective sample size. Intuitively speaking, when zero spatial autocorrelation prevails, ; when perfect positive spatial autocorrelation prevails in a univariate regional mean problem, . Equations are presented for estimating based on the sampling distribution of a sample mean or sample correlation coefficient with the goal of obtaining some predetermined level of precision, using the following spatial statistical model specifications: (1) simultaneous autoregressive, (2) geostatistical semivariogram, and (3) spatial filter. These equations are evaluated with simulation experiments and are illustrated with selected empirical examples found in the literature.

The secret assumption of transfer functions: problems with spatial autocorrelation in evaluating model performance

The estimation of the predictive power of transfer functions assumes that the test sites are independent of the modelling sites. Cross-validation in the presence of spatial autocorrelation seriously violates this assumption. This assumption and the consequences of its violation have not been discussed before. We show, by simulation, that the expected r 2 of a transfer function model from an autocorrelated environment can be high, and is not near zero as commonly assumed. We investigate a foraminiferal sea surface temperature training set for the North Atlantic, for which, with cross-validation, the modern analogue technique (MAT) and artificial neural networks (ANN) outperform transfer function methods based on a unimodal species-environment response model. However, when a spatially independent test set, the South Atlantic, is used, all models have a similar predictive power. We show that there is a spatial structure in the foraminiferal assemblages even after accounting for temperature, presumably due to autocorrelations in other environmental variables. Since the residuals from MAT show little spatial structure, in contrast to the residuals of unimodal response models, we contend that MAT has inappropriately internalized the non-temperature spatial structure to improve its performance. We argue that most, if not all, estimates of the predictive power of MAT and ANN models for sea surface temperatures hitherto published are over-optimistic and misleading.

An Evaluation of Spatial Dependency in Juvenile Loblolly Pine Stands Using Stem Diameter

Abstract A simultaneous autoregressive model (SAR) was used to evaluate the amount of spatial influence juvenile loblolly pine (Pinus taeda L.) stems in a plantation have on one another. The presence of spatial autocorrelation between stems in a stand indicates that the characteristics of one stem are related to the characteristics of neighboring stems. The stands evaluated in this study had planting densities that varied from 747 to 6,727 trees per hectare. The SAR model contains a spatial dependency parameter that captures the inter-tree influences. Analysis on detrended diameter data showed that across ages 2 to 5 for groundline diameter measurements and ages 5 to 11 for breast height diameter measurements, the simultaneous autoregressive model indicated significant spatial dependency parameters in 23.2% of the plots (alpha-level = 0.10). A generally increasing trend in the occurrence of significant spatial influence from 18.2% to 28.4% was noted with an increase in planting density from 747 to 3,364 trees per hectare, beyond which the trend decreased. Estimation of the spatial dependency parameter will aid in describing juvenile competition processes and developing a more precise representation of juvenile forest stands. FOR. SCI. 51(2):102–108.