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Screening for spatial dependence in regression analysis
Abstract
ABSTRACT A technique of analysis is presented that is designed to circumvent the problem of finding wasy to estimate parameters of spatially stochastic independent variables. It is based on 1) a type of second-order analysis that describes the spatial association among weighted observations, and 2) a screening procedure that removes most of the spatial dependence in the dependent variable. The approach is illustrated by a study of the incidence of certain crimes in 49 districts of Columbus, Ohio. It is concluded that spatial justaposition of observations plays a large role in regression analyses that are based on spatial series.
... An alternative approach in order to deal with spatial autocorrelation in regression analysis involves the filtering of variables allowing the elimination of the spatial effects. The most well-known filtering procedures are those proposed by Getis (1990Getis ( , 1995 based on the statistic of local association (Getis and Ord, 1992) and the Griffith's (1996Griffith's ( , 2000 alternative procedure based on the eigenfunction decomposition associated with the Moran statistic. ...
... i G Since one of the main problems in spatial regressions is related to the presence of stochastic regressors, leading to biased Ordinary Least Squares (OLS) estimations, Getis (1990) develops a new procedure, based on the decomposition of a variable into two components (spatial and non-spatial) through the use of a filter or screen which removes the spatial component of each of the considered variables. ...
... In this work we consider this screening procedure as a decomposition technique previous to further analyses. The spatial filtering developed by Getis (1990) is based on the consideration of a spatial vector S: ≈ ρ S W (1.15) which takes the place of both the spatial weights matrix and the auto-regressive coefficient ρ. ...
The aim of this work is to analyze the influence of the spatial effects in the evolution of the regional employment, thus improving the explanation of the existing differences. With this aim, two non-parametric techniques are proposed: spatial shift-share analysis and spatial filtering. Spatial shift-share models allow the identification and estimation of the spatial effects, as shown in Mayor and López (2005). On the other hand, the spatial filtering techniques can be used in order to remove the effects of the spatial correlation, thus allowing the decomposition of the employment variation into two components, respectively related to the spatial and structural effects. The application of both techniques to the spatial analysis of the regional employment in Spain leads to some interesting findings, also showing the main advantages and limitations of each of the considered procedures and allowing the quantification of their sensibility with regard to the considered weights matrix.
... We note from the start that our intention is not to make a causal statement, but simply to use this correlation to validate the value of the information contained in our measures of urban perception. Because of the spatial nature of the dataset, we use Getis Spatially Filtered Regression (GSFR) [45][46], rather than an Ordinary Least Square (OLS) regression. In spatial datasets is not appropriate to use OLS regressions because of the existence of spatial auto correlations. ...
... Finally, a GSFR regression is an OLS regression where each variable x is replaced by its spatially filtered x* and varying component L x . More details about this statistical technique can be found in [45]. To illustrate what the method doe consider the income of a zip code. ...
... pvalue = 0.82), indicating that the model is not underspecified and can be used for statistical inference. Hence, the results cannot be interpreted as the result of a missing variable, such as policing or race [45][46]. ...
A traveler visiting Rio, Manila or Caracas does not need a report to learn that these cities are unequal; she can see it directly from the taxicab window. This is because in most cities inequality is conspicuous, but also, because cities express different forms of inequality that are evident to casual observers. Cities are highly heterogeneous and often unequal with respect to the income of their residents, but also with respect to the cleanliness of their neighborhoods, the beauty of their architecture, and the liveliness of their streets, among many other evaluative dimensions. Until now, however, our ability to understand the effect of a city's built environment on social and economic outcomes has been limited by the lack of quantitative data on urban perception. Here, we build on the intuition that inequality is partly conspicuous to create quantitative measure of a city's contrasts. Using thousands of geo-tagged images, we measure the perception of safety, class and uniqueness; in the cities of Boston and New York in the United States, and Linz and Salzburg in Austria, finding that the range of perceptions elicited by the images of New York and Boston is larger than the range of perceptions elicited by images from Linz and Salzburg. We interpret this as evidence that the cityscapes of Boston and New York are more contrasting, or unequal, than those of Linz and Salzburg. Finally, we validate our measures by exploring the connection between them and homicides, finding a significant correlation between the perceptions of safety and class and the number of homicides in a NYC zip code, after controlling for the effects of income, population, area and age. Our results show that online images can be used to create reproducible quantitative measures of urban perception and characterize the inequality of different cities.
... The spatial filtering techniques alluded to by Cliff and Ord (1981) and Gujarati (1992), and dscussed by Getis (1990Getis ( , 1995, convert variables that are spatially autocorrelated into spatially independent variables in an OLS regression framework. The conversion requires spatial filtering procedures, two of which are compared in this paper. ...
... The conversion requires spatial filtering procedures, two of which are compared in this paper. The first, devised by Getis (1990Getis ( , 1995, is a multistep procedure based upon Ripley's second-order statistic (1978)-now called the K function-and the Gi spatial statistic developed by Getis and Ord (1992). The second, devised by Griffith (1996Griffith ( , 2000a, exploits an eigenfunction decomposition associated with Moran's I ( M I ) statistic, a decomposition in part explicated by Tiefelsdorf and Boots (1995). ...
... In the sections that follow, each of these approaches first is outlined, then is applied to a data set, and finally the results are discussed. The Getis approach is summarized here since two articles outline its characteristics (Getis 1990(Getis , 1995. More attention is given to the Griffith approach simply because several new types of analysis are presented. ...
One approach to dealing with spatial autocorrelation in regression analysis involves the filtering of variables in order to separate spatial effects from the variables’ total effects. In this paper we compare two filtering approaches, both of which allow spatial statistical analysts to use conventional linear regression models. Getis’ filtering approach is based on the autocorrelation observed with the use of the Gi local statistic. Griffith's approach uses an eigenfunction decomposition based on the geographic connectivity matrix used to compute a Moran's I statistic. Economic data are used to compare the workings of the two approaches. A final comparison with an autoregressive model strengthens the conclusion that both techniques are effective filtering devices, and that they yield similar regression models. We do note, however, that each technique should be used in its appropriate context.
... An alternative approach to deal with spatial autocorrelation in regression analysis involves the filtering of variables allowing the elimination of the spatial effects. The most well-known filtering procedures are those proposed by Getis (1990Getis ( , 1995 based on the statistic of local association G i (Getis and Ord 1992and Griffith's 1996, 2000 alternative procedure based on the eigenfunction decomposition associated with the Moran statistic. According to Getis and Griffith (2002), both nonparametric spatial filtering approaches lead to similar solutions in the context of regression models but each procedure must be applied in the appropriate context and its different origin must be considered. ...
... Since one of the main problems in spatial regressions is related to the presence of stochastic regressors, leading to biased ordinary least squares (OLS) estimations, Getis (1990) develops a new procedure, based on the decomposition of a variable into two components (spatial and non-spatial) through the use of a filter or screen which removes the spatial component of each of the considered variables. ...
... In this paper we consider this screening procedure as a decomposition technique previous to further analyses. The spatial filtering developed by Getis (1990) is based on the consideration of a spatial vector S: ...
The aim of this work is to analyse the influence of spatial effects in the evolution of regional employment, thus improving
the explanation of the existing differences. With this aim, two non-parametric techniques are proposed: spatial shift-share
analysis and spatial filtering. Spatial shift-share models based on previously defined spatial weights matrix allow the identification
and estimation of the spatial effects. Furthermore, spatial filtering techniques can be used in order to remove the effects
of spatial correlation, thus allowing the decomposition of the employment variation into two components, respectively related
to the spatial and structural effects. The application of both techniques to the spatial analysis of regional employment in
Spain leads to some interesting findings and shows the main advantages and limitations of each of the considered procedures,
together with the quantification of their sensitivity with regard to the considered weights matrix.
... At first, two spatial solutions were offered. Getis (1990) used the term "screening" to represent the alteration of variables to eliminate spatial autocorrelation. His method was broadened and made more relevant to spatial analysts in 1995 (Getis 1995). ...
... Models not taking nearness into account, therefore, must be biased. The Getis (1990Getis ( , 1995 solution became known as Getis spatial filtering (GSF). It is based on the nearest neighbor analysis methodology that was popular in the late 1950s and early 1960s (see such work as Clark and Evans (1954) and Pielou (1977) in biology, Dacey (1960) and Getis and Boots (1978) in geography, and more recent work in this area, such as by Ripley (1981) and Getis and Franklin (1987)). ...
... At first, two spatial solutions were offered. Getis (1990) used the term "screening" to represent the alteration of variables to eliminate spatial autocorrelation. His method was broadened and made more relevant to spatial analysts in 1995 (Getis 1995). ...
... Models not taking nearness into account, therefore, must be biased. The Getis (1990Getis ( , 1995 solution became known as Getis spatial filtering (GSF). It is based on the nearest neighbor analysis methodology that was popular in the late 1950s and early 1960s (see such work as Clark and Evans (1954) and Pielou (1977) in biology, Dacey (1960) and Getis and Boots (1978) in geography, and more recent work in this area, such as by Ripley (1981) and Getis and Franklin (1987)). ...
... The principal aim of using ESF is to avoid SAC-based regression misspecification. The topology-based approach (Griffith, 2000(Griffith, , 2012 has several advantages compared to other filtering techniques (Getis, 1990;Griffith & Peres-Neto, 2006). For example, Getis's (1990) approach is restricted to: a) positive SAC, b) the variables must have a natural and positive origin, and c) each variable must be filtered separately. ...
... The topology-based approach (Griffith, 2000(Griffith, , 2012 has several advantages compared to other filtering techniques (Getis, 1990;Griffith & Peres-Neto, 2006). For example, Getis's (1990) approach is restricted to: a) positive SAC, b) the variables must have a natural and positive origin, and c) each variable must be filtered separately. In contrast, Griffith's (2008) approach is not limited in this respect, and, more importantly, it can be extended to model geographically varying relationships. ...
... Again for all cases, the statistical values appear very high, leading to a rejection of the null hypothesis about a random pattern in the spatial distribution of data.The next step in our empirical application is now dropping from these variables the linear spatial dependence structure. In order to do so, we apply the filtering technique usually employed in the spatial econometrics literature, namely theGetis (1990Getis ( , 1995) proposal 3 . ...
... Among the most commonly applied spatial filtering techniques we find theGetis (1990Getis ( , 1995) proposal, as well as theGriffith (1996Griffith ( , 2003) eigenvector spatial filtering approach. A recent empirical comparison of that two filtering techniques, spatial lag regression and Getis filtred, has shown that both approaches are almost equally equipped for removing the spatial effects from geographically organized variables (Getis and Griffith, 2002). ...
Accounting for spatial structures in econometric studies is becoming
an issue of special interest, given the presence of spatial dependence and spatial
heterogeneity problems arising in data. Generally, researchers have been employing
parametric tests for detecting spatial dependence structures: Moran’s I and LM tests
in spatial regressions are the most popular approaches employed in literature.However,
this approach remains misleading in the presence of nonlinear spatial structures,
inducing important biases in the estimation of the parameters of the model.
In this paper we illustrate that issue by applying three non-parametrical proposals
when testing for spatial structure in data. Empirical findings for the regions of the
European Union show important failures of traditional parametric tests if nonlinearities
characterise geo-referenced data. Our results clearly recommend employing new
families of tests, beyond parametrical ones, when working in such environments.
... In the multivariate case, multivariate spatial correlation enables correlation to be assessed between two measurements allowing for the fact that either measure may itself be autocorrelated within the space. Getis (1990) has also developed a type of second order analysis, based on an extension of K-function concepts to attribute data, for describing the spatial association between weighted observations. Such methods are of use in a general exploratory sense to summarize the overall existence of pattern in attribute data and to establish the validity of various stationarity assumptions prior to modelling. ...
... The potential benefits in terms of visualization of outputs in conjunction with maps is less convincing, unless dynamic links can be generated between contributions to the correlogram or variogram and areas in the map. The study of variogram clouds (Chauvet, 1982)-plots of the average squared difference between each pair of values against their separation-might provide a basis for this as well as the second order techniques described by Getis (1990). ...
... Following the recommendations of Isaaks & Srivastava (1989), 12 nearest neighbours were used to estimate the values with weights inversely proportional to the square of the distance from the estimated cell. (iii) Partial regression analysis Partial regression analysis is one of several techniques that can be used when attempting to model data showing spatial dependence (see Clifford & Richardson 1985; Clifford, Richardson & Hémon 1989; Getis 1990; Legendre 1993; Carroll & Pearson 1998; Legendre & Legendre 1998; for applications and reviews of the available techniques). Following the methodology suggested by Legendre (1993), we used the method to estimate how much variation in leaf-miner densities can be attributed to regional climatic variation and altitude once the effect of spatial location has been taken into account. ...
... At a smaller, regional scale, in a study of the factors that affect the species composition of oribatid mite communities, Borcard et al. (1992) found that two-thirds of the variation explained by environmental variables could equally well be predicted by spatial position. Kitron et al. (1996) used the method proposed by Getis (1990) in their analysis of tsetse fly distribution using remotely sensed environmental data. They also found that the spatial component of their environmental data contributed more to explaining fly catches than the nonspatial component. ...
The local population density structure of a phytophagous insect, the holly leaf‐miner Phytomyza ilicis Curtis, was examined across its natural geographical range in Europe.
The frequency distribution of the number of sample sites at which the leaf‐miner attained different densities per tree was strongly right‐skewed, with the species being absent from a large number of sites at which its host occurred, particularly in southern regions.
There was a decline in the spatial autocorrelation of leaf‐miner densities with increasing distance between sample sites, with negative autocorrelation at long lags resulting in part from high densities being attained at the north‐eastern range limits and low densities at the southern range limits.
Partial regression analysis was used to model leaf‐miner densities in terms of spatial position within the geographical range and the broad climate experienced at the sample localities. This accounted for between 40 and 65% of the variation in densities, dependent upon how the leaf‐miner’s geographical range was defined.
While overall these results are at odds with common and intuitively appealing assertions about the abundance structure of geographical ranges, they can readily be interpreted in terms of a simple modification of a general model of such structures.
... Griffith and Getis (2016) furnish a historical overview of its development and extension to spatial autocorrelation (SA) situations, highlighting their respective individual contributions to this more specialized geography-oriented methodology. Their particular publication supplements their earlier one that builds upon Getis (1990Getis ( , 1995, in which they compare their respective contributions (Getis and Griffith 2002). Reflecting a limited focal point of that time, their initial specifications are exclusively for positive SA (PSA) settings. ...
The dual achievements of this paper are: establishing that the Getis spatial filtering technique can uncover latent PSA–NSA mixtures, and uncovering this very mixture property in geospatial agricultural datasets, acknowledging omitted variable complications attributable to its presence. This methodological extension derives from published comments by Getis himself, whereas this agricultural data category augments the existing set comprising georeferenced socio-economic/demographic and disease data. Puerto Rico space–time datasets—for milk, plantain, and sugarcane production—constitute the analyzed empirical specimens, adding consistency across sequential periods in time to the current repertoire of already recognized focal data features that include geographic resolution and scale as well as geographic landscape diversity. This paper also presents comparisons between the proposed novel Getis spatial filtering decomposition with both spatial autoregressive and Moran eigenvector spatial filtering specifications, credibly concluding that, to some degree, all are capable of identifying PSA–NSA mixtures in geotagged data. Its other prominent general conclusion is that PSA–NSA mixtures tend to be latent in geospatial agricultural datasets.
... In addition to the spatial effects contained in the Ψ k , k ∈ {1, 2}, where k is used to denote the category ordering, our interest also lies in the within-location effects, contained in Θ E = Σ −1 E , the precision matrix of E. In order to obtain these within-location effects, a so-called spatial filter is required. Let Ψ = {Ψ 1 , Ψ 2 }, the model specification in (2) allows for the construction of such a filter R(Ψ)vec(X) = vec(E), where R(Ψ) = I np − 2 k=1 Ψ T k ⊗ W k is the spatial filter matrix, filtering out the spatial effects on the observations as vec(X) − 2 k=1 Ψ T k ⊗ W k vec(X) = vec(E), resulting in the within-location data, assuming that all spatial dependencies are accurately captured by the W k (Getis, 1990;Millo, 2014). This result is straightforwardly obtained from the data generating process, vec(X) = R(Ψ) −1 vec(E), with np × np identity matrix I np , which in turn is obtained by vectorising (2). ...
Within the statistical literature, there is a lack of methods that allow for asymmetric multivariate spatial effects to model relations underlying complex spatial phenomena. Intercropping is one such phenomenon. In this ancient agricultural practice multiple crop species or varieties are cultivated together in close proximity and are subject to mutual competition. To properly analyse such a system, it is necessary to account for both within- and between-plot effects, where between-plot effects are asymmetric. Building on the multivariate spatial autoregressive model and the Gaussian graphical model, the proposed method takes asymmetric spatial relations into account, thereby removing some of the limiting factors of spatial analyses and giving researchers a better indication of the existence and extend of spatial relationships. Using a Bayesian-estimation framework, the model shows promising results in the simulation study. The model is applied on intercropping data consisting of Belgian endive and beetroot, illustrating the usage of the proposed methodology. An R package containing the proposed methodology can be found on https:// CRAN.R-project.org/package=SAGM.
... The first one is a spatial model that captures the relationship between crime and income and housing value for 49 neighborhoods in Columbus, Ohio. The data are listed in Table 12.1, p.189 of Anselin (1988) and have been used in a number of papers to benchmark different estimators and specification tests, see for instance, Getis (1990), McMillen (1992, Anselin et al. (1996), LeSage (1997, Griffith (2000) Elhorst (2014, pp. 27-32). ...
... Instead of treating space as a vacuum in which all that matters is the mass of attraction between any two places that are somehow isolated from other places, we instead adopt a system-wide perspective and allow for the inter-connections between places through migration flows. Although the importance of spatial dependency has been stressed in multiple fields of social science (Fingleton 1986;Getis 1990;Leorato and Mezzetti 2016), it has not received comparable attention in migration studies. To fill this empirical gap, we propose multilevel modelling extensions to the traditional linear regression formulation of the gravity model of migration. ...
This paper proposes a novel multilevel gravity model of migration to study the under-researched topic of urban to urban migration in China. Many previous studies have looked at rural to urban migration in the context of urbanisation and economic development, and at return migration. Very few have looked at what is becoming more important in increasingly urbanised countries, which is the movement from one urban location to another. In the study, we develop a new method that allows for the interconnections between migration flows: between those that share an origin, those that share a destination, and where there is a reciprocal flow between places. A conventional gravity model of migration ignores those connections, risking erroneous estimation of the regression parameters and of their statistical significance. It also ignores that those connections are of substantive interest—they reveal the interconnections between places regarding the numbers of migrants that they send and receive. We motivate and illustrate the advantages of our approach using 2010 interprovincial migration census data for China. The results obtained from the model confirm the effect of distance, of population size and of regional income levels. They show that there is greater variation in the numbers of migrants received by provinces than there is in the numbers sent, and that reciprocal migration between pairs of provinces is an important feature of what is happening in China, especially between the neighbouring provinces of Sichuan and Tibet.
... This study attempted to eliminate the negative influence of spatial autocorrelation on landslide susceptibility assessments by introducing eigenvector spatial filtering (ESF) into logistic regression. Spatial filtering, as discussed by Getis [21,22] and Griffith [23], was considered to be an effective approach for addressing spatial autocorrelation. The ESF method proposed by Griffith, utilizes eigenvectors generated from a given spatial connectivity matrix to account for redundant locational information resulting from spatial autocorrelation [24]. ...
Logistic regression methods have been widely used for landslide research. However, previous studies have seldom paid attention to the frequent occurrence of spatial autocorrelated residuals in regression models, which indicate a model misspecification problem and unreliable results. This study accounts for spatial autocorrelation by implementing eigenvector spatial filtering (ESF) into logistic regression for landslide susceptibility assessment. Based on a landslide inventory map and 11 landslide predisposing factors, we developed the eigenvector spatial filtering-based logistic regression (ESFLR) model, as well as a conventional logistic regression (LR) model and an autologistic regression (ALR) model for comparison. The three models were evaluated and compared in terms of their prediction capability and model fit. The ESFLR model performed better than the other two models. The overall predictive accuracy of the ESFLR model was 90.53%, followed by the ALR model (76.21%) and the LR model (74.76%), and the areas under the ROC curves for the ESFLR, ALR and LR models were 0.957, 0.828 and 0.818, respectively. The ESFLR model adequately addressed the spatial autocorrelation of residuals by reducing the Moran's I value of the residuals to 0.0270. In conclusion, the ESFLR model is an effective and flexible method for landslide analysis.
... 10 A description of these models is to be found in Anselin (1988), Anselin and Hudak (1992) and LeSage and Pace (2009), among others. 11 Other methods of spatial filtering include those of Getis (1990Getis ( , 1995, which uses (footnote continued) the G-statistic and Borcard and Legendre (2002), which uses the eigenvectors of a truncated distances matrix. The Getis method requires all the variables to have a natural origin and to be positive, so its use is limited to situations of these characteristics, and it is not applicable to the variables studied in this paper. ...
The financial crisis that set in at the end of 2007 and the ensuing years of recession have had devastating effects on the labor markets. This has led us to research into employment thresholds -Verdoorn's law - and unemployment - Okun's law - from the perspective of the Spanish provinces. We use a spatial SUR model which allows us to link the panel data with analysis of spatial dependence in order to obtain efficient and robust results about the stability of the Verdoorn and Okun coefficients. We remove the spatial dependence by using spatial filtering techniques from the semiparametric method of vector decomposition. The results show that thresholds vary over time and the output growth required for a rise in employment is well below the level necessary to reduce the unemployment rate.
... The points analysed for the spatial association of ADV seroprevalence were the geographic centres of municipalities (i.e., municipality centroids). The use of centroids for these purposes has been previously reported (Getis, 1990;Hungerford, 1991;Austin and Weigel, 1992). ...
La proliferación de sistemas de producción cinegética cada vez más intensivos, semejantes a la ganadería, conlleva graves riesgos sanitarios. Esta tesis evalúa el impacto del manejo cinegético del jabalí sobre sus enfermedades víricas, tomando como modelo la enfermedad de Aujeszky (EA). Se presentan a continuación los resultados obtenidos de mayor relevancia.
El virus de la EA (VEA) está ampliamente difundido en las poblaciones de jabalíes del centro-sur peninsular, estando su epidemiología determinada por factores ecológicos y por los sistemas de producción cinegética: mayores prevalencias a mayor densidad y manejo más artificial.
El diagnóstico serológico no es suficiente para determinar el estado de los jabalíes con respecto al VEA, debido a la presencia de un 45% de animales infectados sin niveles de anticuerpos detectables en suero. Ello tiene implicaciones en el control de granjas y traslados.
Los sistemas de producción intensiva de jabalíes tienen un efecto negativo sobre la reproducción de esta especie, y además generan una mayor tasa de contacto con agentes patógenos que la observada en poblaciones naturales.
El análisis de las interacciones epidemiológicas entre cerdo y jabalí con respecto al VEA en el centro-sur peninsular reveló una ausencia de relación entre la epidemiología del virus en las explotaciones de cerdos y en las poblaciones de jabalíes.
Finalmente, se observó que la vacunación con cepas atenuadas comerciales del VEA produce una respuesta inmune en los jabalíes similar o superior a la descrita en el cerdo, lo que induce a pensar que la vacunación podría ser un método de control de la infección en poblaciones de jabalíes en semi-cautividad o ante traslados.
... Step 3 comes in when the time series data are also spatially autocorrelated, extending the traditional LTM to geographical analysis with considerable spatial autocorrelation. In handling spatial autocorrelation, it is common that some spatial neighborhood or dependence (e.g., through defining spatial lag, spatial weights matrix, or whatever local neighborhood) is considered in various spatial error, spatial lag, or autoregressive models (Griffith 1988;Getis 1990;Fotheringham, Charlton, and Brundson 2002;Getis and Griffith 2002;Anselin 2003;LeSage and Fischer 2008;Elhorst 2012). The ESF has no exception in this regard. ...
This article introduces latent trajectory models (LTMs), an approach often employed in social sciences to handle longitudinal data, to the arena of GIScience, particularly space-time analysis. Using the space-time data collected at county level for the whole United States through webpage search on the keyword “climate change,” we show that LTMs, when combined with eigenvector filtering of spatial dependence in data, are very useful in unveiling temporal trends hidden in such data: the webpage-data derived popularity measure for climate change has been increasing from December 2011 to March 2013, but the increase rate has been slowing down. In addition, LTMs help reveal potential mechanisms behind observed space-time trajectories through linking the webpage-data derived popularity measure about climate change to a set of socio-demographic covariates. Our analysis shows that controlling for population density, greater drought exposure, higher percent of people who are 16 years old or above, and higher household income are positively predictive of the trajectory slopes. Higher percentages of Republicans and number of hot days in summer are negatively related to the trajectory slopes. Implications of these results are examined, concluding with consideration of the potential utility of LTMs in space-time analysis and more generally in GIScience.
... With the parameter r estimated solely from a variable Y, a prewhiten dependent variable is generated by ðI À rCÞY. Second, Getis's G i -based method converts each spatially correlated variable into two variates, one capturing SA and the other containing nonspatial systematic and random effects (Getis 1990). Regression with spatial and nonspatial variates enables a separation of SA components from trend and white noise components. ...
... Les exemples les plus communs sont des résidus structurés en fonction de l'espace et/ou du temps, on parle alors d'autocorrélation spatiale et/ou temporelle résiduelle (Griffith 1987). Le problème que pose l'autocorrélation d'une variable a depuis longtemps était mis en évidence (voir Hooker 1905) et a conduit à un développement faramineux de la méthodologie à son égard au cours du siècle dernier (Student <Gosset> 1914 ;Yule 1921 ;Bartlett 1935 ;Wold 1938 ;Von Neumann et al. 1941 ;Cochrane & Orcutt 1949 ;Moran 1950 ;Durbin & Watson 1950Whittle 1953 ;Anderson 1954 ;Geary 1954 ;Box & Pearce 1970 ;Cliff & Ord 1972 ;Cressie & Hawkins 1980a, b ;Anselin 1988 ;Haining 1990 ;Getis 1990 ;Cressie 1993 ;Diggle et al. 1998 ;Cressie & Huang 1999 ;Griffith 2000 ;Diggle 2003 ;Cressie & Wikle 2011). La structure des résidus est vraisemblablement liée à la non prise en compte de certaines variables qui sont elles-mêmes structurées dans l'espace et/ ou dans le temps. ...
In the context of global biodiversity loss, more and more surveys are done at a broad spatial extent and during a long time period, which is done in order to understand processes driving the distribution, the abundance and the trends of populations at the relevant biological scales. These studies allow then defining more precise conservation status for species and establish pertinent conservation measures. However, the statistical analysis of such datasets leads some concerns. Usually, generalized linear models (GLM) are used, trying to link the variable of interest (e.g. presence/absence or abundance) with some external variables suspected to influence it (e.g. climatic and habitat variables). The main unresolved concern is about the selection of these external variables from a spatial dataset. This thesis details several possibilities and proposes a widely usable method based on a cross-validation procedure accounting for spatial dependencies. The method is evaluated through simulations and applied on several case studies, including datasets with higher than expected variability (overdispersion). A focus is also done for methods accounting for an excess of zeros (zeroinflation). The last part of this manuscript applies these methodological developments for modelling the distribution, abundance and trend of raptors breeding in France.
... The first implemented attempt at spatial filtering, following earlier work by Tobler, is by Griffith (1978). Getis (1990Getis ( , 2010 argues for transforming a spatial autocorrelation-effected variable by splitting it into its actual variable effect without spatial autocorrelation and its related spatial component. Technically, he proposes a combination of K d ð Þ-functions and local G-statistics. ...
Crime intelligence analysis and criminal investigations are increasingly making use of geospatial methodologies to improve tactical and strategic decision-making. However, the full potential of geospatial technologies is yet to be exploited. In particular, geospatial technology currently applied by law enforcement is somewhat limited in handling the increasing volume of police recorded and relatively unstructured narrative crime reports, such as observations and interviews of eyewitnesses, the general public, or other relevant persons. The main objective of this research is to promote text mining, particularly the self-organizing map algorithm and its visualization capabilities, in combination with point pattern analysis, to explore the value of otherwise hidden information in a geographical context and to gain further insight into the complex behavior of the geography of crime. This methodological approach is applied to a high-profile and still unsolved homicide series in the city of Jennings, Louisiana. In a collaborative effort with the Jennings Police Task Force, the analysis is based upon a range of information sources, including email correspondence, transcribed face-to-face interviews, and phone calls that have been stored as “Information Packages” in the Orion database, which is maintained by the Federal Bureau of Investigation. Close to 200 individual information packages related to Necole Guillory, the eighth and last victim whose dead and dumped body was discovered in August 2009, are analyzed and resulted in new geographic patterns and relationships previously unknown to the Task Force.
... Second, spatial filtering methods have been applied to account for spatial autocorrelation (Getis, 1990(Getis, , 1995Griffith, 1996bGriffith, , 2000Haining, 1991). Spatial filtering focuses on isolating spatial effects from the standard regression model. ...
... The first implemented attempt at spatial filtering, following earlier work by Tobler, is by Griffith (1978). Getis (1990Getis ( , 2010 argues for transforming a spatial autocorrelation-effected variable by splitting it into its actual variable effect without spatial autocorrelation and its related spatial component. Technically, he proposes a combination of K d ð Þ-functions and local G-statistics. ...
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... Besides these approaches, spatial filtering approaches have been developed by quantitative geographers as the "third way" to model spatial autocorrelation (e.g., Getis 1990;Griffith 2000Griffith , 2003Griffith , 2012Getis and Griffith 2002;Tiefelsdorf and Griffith 2007). These approaches are used particularly in the field of ecology , but they also have many social science applications. ...
Eigenvector-based spatial filtering is one of the often used approaches to model spatial autocorrelation among the observations or errors in a regression model. In this approach, a subset of eigenvectors extracted from a modified spatial weight matrix is added to the model as explanatory variables. The subset is typically specified via the selection procedure of the forward stepwise model, but it is disappointingly slow when the observations n take a large number. Hence, as a complement or alternative, the present article proposes the use of the least absolute shrinkage and selection operator (LASSO) to select the eigenvectors. The LASSO model selection procedure was applied to the well-known Boston housing data set and simulation data set, and its performance was compared with the stepwise procedure. The obtained results suggest that the LASSO procedure is fairly fast compared with the stepwise procedure, and can select eigenvectors effectively even if the data set is relatively large (n = 104), to which the forward stepwise procedure is not easy to apply.
... Ordinary Least Square (OLS) is a commonly used method in regression analysis. However, when dealing with spatial data, the existence of spatial autocorrelation often leads to violations of the basic assumptions for OLS (Tobler, 1970;Hubert et al., 1981;Getis, 1990).The eigenvector-based spatial filtering (ESF) service provides an effective spatial regression model to handle with spatial autocorrelations. The effect of the variables in the regression model is divided into two parts: spatial influence and non-spatial influence. ...
Web service can bring together applications running on diverse platforms, users can access and share various data, information and
models more effectively and conveniently from certain web service platform. Cloud computing emerges as a paradigm of Internet
computing in which dynamical, scalable and often virtualized resources are provided as services. With the rampant growth of massive
data and restriction of net, traditional web services platforms have some prominent problems existing in development such as
calculation efficiency, maintenance cost and data security. In this paper, we offer a spatial statistics service based on Microsoft cloud.
An experiment was carried out to evaluate the availability and efficiency of this service. The results show that this spatial statistics
service is accessible for the public conveniently with high processing efficiency.
... 1 （1 武汉大学测绘遥感信息工程国家重点实验室，武汉市珞喻路 129 号，430079） （2 武汉大学资源与环境科学学院，武汉市珞喻路 129 号，430079） 摘 要：针对现有的特征函数空间滤值方法存在算法复杂，计算效率低下，难以满足当前海量空间数据应用需求等问题，本 文提出了一种特征函数空间滤值并行化方法,基于主从模型（Master/Slave 模型）和 MPI+OpenMP 混合编程模式，充分挖掘多 核集群下计算机的性能，并在多核集群平台上与纯 MPI 算法分别进行了对比实验。实验结果表明，基于 MPI+OpenMP 的方 法能够获得更高的并行加速比和计算效率。 关键字：空间滤值；特征函数；多核；集群；并行计算 特征函数空间滤值方法利用统计量 Moran 系数分解，有效地处理回归分析中的空间自相关问题 [1][2] ...
Based on the master/slave model, we present a hybrid MPI+OpenMP parallel implementation for the eigenfunction-base spatial filtering on the multi-core cluster. There are two different implementations of the algorithm: one based on MPI and the other based on a hybrid parallel paradigm with MPI+OpenMP. The experimental results show that MPI+OpenMP method can cut down the process-time effectively and improve the filtering efficiency.
... The approach developed by Griffith (1996 Griffith ( , 2004) is adopted in our study. This approach is preferred in our case study to the one by Getis (1990 Getis ( , 1995), which requires variables with a natural origin. This limitation would not allow us to apply the same method to the analysis of other labour market variables, such as employment growth rates. ...
Socio-economic interrelationships among regions can be measured in terms of economic flows, migration, or physical geographically-based measures, such as distance or length of shared areal unit boundaries. In general, proximity and openness tend to favour a similar economic performance among adjacent regions. Therefore, proper forecasting of socio-economic variables, such as employment, requires an understanding of spatial (or spatio-temporal) autocorrelation effects associated with a particular geographic configuration of a system of regions. Several spatial econometric techniques have been developed in recent years to identify spatial interaction effects within a parametric framework. Alternatively, newly devised spatial filtering techniques aim to achieve this end as well through the use of a semi-parametric approach. The experiments presented in this paper deal with the analysis of and accounting for spatial autocorrelation by means of spatial filtering techniques for data pertaining to regional unemployment in Germany. The available dataset comprises information about the share of unemployed workers in 439 German districts (the NUTS- III regional aggregation level). In this paper, various results based upon an eigenvector spatial filter model formulation (that is, the use of orthogonal map pattern components), constructed for the 439 German districts, are presented, with an emphasis on their consistency over several observation years. New insights obtained by applying spatial filtering to the database about the German regional labour markets also are discussed.
... Similar to the idea of filtering seasonality out of time series data spatial filtering techniques convert variables that are spatially autocorrelated into spatially independent variables and a residual -purely spatial -component. Among the commonly applied spatial filtering techniques is the Getis (1990Getis ( , 1995 as well as the Griffith (1996Griffith ( , 2003 Eigenvector spatial filtering approach. A recent empirical comparison of both filtering techniques has shown that both approaches are almost equally equipped for removing spatial effects from geographically organized variables (see e.g. ...
a dynamic panel data model for German internal migration flows since re-unification. So far, a capacious account of spatial patterns in German migration data is still missing in the empirical literature. In the context of this paper, network dependencies are associated with correlations of migration flows strictly attributable to proximate flows in geographic space. Using the neoclassical migration model, we start from its a spatial specification and show by means of residual testing that network dependency effects are highly present. We then construct spatial weighting matrices for our system of interregional flow data and apply spatial regression techniques to properly handle the underlying space-time interrelations. Besides spatial extensions to the Blundell-Bond (1998) system GMM estimator in form of the commonly known spatial lag and unconstrained spatial Durbin model, we also apply system GMM to spatially filtered variables. Finally, combining both approaches to a mixed spatial filtering regression specification shows a remarkably good performance in terms of capturing spatial dependence in our migration equation and at the same time qualify the model to pass essential IV diagnostic tests. The basic message for future research is that space-time dynamics is highly relevant for modeling German internal migration flows.
... There have been several suggestions for identifying δ , but in this paper we adopt the Getis filtering approach (see Getis 1990Getis , 1995 which is based on the local spatial autocorrelation statistic i G (Getis and Ord 1992) to be evaluated at a series of increasing distances until no further spatial autocorrelation is evident. As distance increases from an observation (region ), i the -value i G also increases if spatial autocorrelation is present. ...
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.
... Spatial filtering techniques (Getis 1990(Getis , 1995Griffith 2000Borcard and Legendre 2002;Getis and Griffith 2002) allow spatial analysts to employ traditional regression techniques while insuring that regression residuals behave according to the traditional model assumption of no spatial autocorrelation in these residuals. One spatial filtering method exploits an eigenfunction decomposition associated with the MC. ...
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.
... If the data display this property, least squares estimators are biased and inconsistent. The spatial aspects underpinning many social phenomenaoften influence the results obtained in multivariate regression (Getis 1990). Spatial autocorrelation between variables in a regression framework has to be identified and addressed. ...
This paper comparatively analyzes the association between urban neighborhood socioeconomic markers and ambient air pollution
in Vancouver and Seattle, the two largest urban regions in the Georgia Basin-Puget Sound (GB-PS) international airshed. Given
their similarities and common airshed, Vancouver and Seattle are useful comparators addressing not only whether socioeconomic
gradients exist in urban environmental quality but also identifying clues to differences in these gradients between Canadian
and American cities. Large air quality sampling campaigns and pollution regression mapping provide the pollution data, in
this case nitrogen dioxide—a marker of traffic emissions considered the most important air pollutant for human health in the
typical North American city. Pollution data are combined with neighborhood census data for regression and spatial analyses.
Median household income is the most consistent correlate of air pollution in both cities, including their most polluted neighborhoods,
although neighborhoods marked by immigrant populations do not correlate with high pollution levels in Vancouver as they do
in Seattle.
KeywordsTransboundary-Environmental justice-Land use regression-Spatial dependency-Lagrange multiplier-Generalized additive model
... The remedial options available when a spatial linear model shows significant residual autocorrelation have always included the respecifications of the substantive aspects of the model by adding and/or removing and/or transforming its variables (Miron 1984). However more recently greater attention has been given to the following four approaches: (i) the estimation of spatial lag, spatial autoregressive error, or spatial Durbin models; (ii) the FGLS estimation of models that incorporate spatial structure via a previous parametric estimation of the error's variance-covariance matrix; (iii) the correction of the degrees of freedom to compensate for the partial redundancy of the observations due to the spatial autocorrelation; and (iv) spatial filtering (Getis 1990;Getis and Griffith 2002;Getis and Ord 1995;Griffith 2003;Fischer and Griffith 2008). Reviews of these four approaches to remedy spatial dependency are in Rangel and Diniz-Filho (2006), de Smith (2007), and Dorman et al. (2007. ...
The body of this chapter consists of three sections: expansion method, dependency, and multimodeling. In the first section
the expansion method is defined, discussed, illustrated by an example, and pertinent literature items are briefly showcased.
In the second section it is shown that when an estimated model’s residuals show significant spatial dependency the expansion
method can provide a course of action to remedy this dependence. In the third section an expansion based multimodeling approach
to remedying spatial dependence is presented and demonstrated. The themes addressed in these sections are briefly outlined
hereafter.
... A limited number of implementations of this methodology currently exist for georeferenced data analysis purposes, and include autoregressive linear operators (à la Cochrane-Orcutt type of prewhitening), Getis's G i -based specification (Getis 1990(Getis , 1995, linear combinations of eigenvectors extracted from distance-based principal coordinates of neighboring matrices (PCNM; Borcard et al. 2002Borcard et al. , 2004Dray et al. 2006), and topology-based spatial weights matrix eigenfunctions (Griffith 2000(Griffith , 2002(Griffith , 2003(Griffith , 2004. The first of these is written in terms of a variance component, whereas the other three are written in terms of a mean response component, allowing especially the last two to be incorporated into generalized linear model (GLM) specifications. ...
In spatial statistics and spatial econometrics, spatial filtering is a general methodology supporting more robust findings
in data analytic work, and is based upon a posited linkage structure that ties together georeferenced data observations. Constructed
mathematical operators are applied to decompose geographically structured noise from both trend and random noise in georeferenced
data, enhancing analysis results with clearer visualization possibilities and sounder statistical inference. In doing so,
nearby/adjacent values are manipulated to help analyze attribute values at a given location. Spatial filtering mathematically
manipulates data in order to correct for potential distortions introduced by such factors as arbitrary scale, resolution and/or
zonation (i.e., surface partitioning).
Eigenvector spatial filtering (ESF) is a relatively new technique that considers spatial autocorrelation. It is a practical technique that can be easily implemented using standard statistical software packages and can be easily combined with other statistical methods such as general linear model, mixed effect model and so on, and so, applications of ESF is expanding more and more. However, ESF is restrictive in that it cannot consider continuity of space, and therefore, it cannot be applied to spatially continuous variables consistently. In this study, we extend ESF so as to consider the continuity of space. The extended method is practical as same as conventional ESF. To confirm the effectiveness of our method, our method, linear regression model, and kriging (a geostatistical method) are compared using a case study of land price modeling.
This article presents a Bayesian method based on spatial filtering to estimate hedonic models for dwelling prices with geographically varying coefficients. A Bayesian Adaptive Sampling algorithm for variable selection is used, which makes it possible to select the most appropriate filters for each hedonic coefficient. This approach explores the model space more systematically and takes into account the uncertainty associated with model estimation and selection processes. The methodology is illustrated with an application for the real estate market in the Spanish city of Zaragoza and with simulated data. In addition, an exhaustive comparison study with a set of alternatives strategies used in the literature is carried out. Our results show that the proposed Bayesian procedures are competitive in terms of prediction; more accurate results are obtained in the estimation of the regression coefficients of the model, and the multicollinearity problems associated with the estimation of the regression coefficients are solved.
Objective
This article attempts to analyze tax evasion as a fundamental element of tax morale in the European countries from the perspective of spatial dependence. This research focuses on the contextual differences using country‐level and cross‐sectional European Value Survey data for the year 2008 to estimate the factors that affect the rejection of tax evasion.
Method
The application of a generalized linear model using spatial filtering allowed us to observe robust results on the role of contextual variables in explaining different patterns of the rejection of tax evasion in the European countries.
Results
The results confirm the influence exerted by spatial dependence, economies of agglomeration, income inequality, economic imbalances, and perceived corruption on the variable “rejection of tax evasion.” A novel finding is the fact that income distribution is key in explaining the rejection of tax evasion.
Conclusion
This study indicate that there is interaction of the rejection of tax evasion between neighboring countries, so that low/high levels of rejection of tax evasion at home are associated with low/high levels of rejection in a neighboring country. Therefore, policymakers should establish coordinated tax awareness measures in the supranational policies (e.g., European Union), since the rejection of tax evasion depends on internal factors of the country in which one lives and those of neighboring countries. Fiscal behavior (social norm) of individuals from neighboring countries affects the behavior of individuals in the country.
The fact that in Spain there are no official statistics of gross disposable income in the municipalities together with the need to know the economic and social situation of the different territories for the planning of a balanced development in each of them, has led to an increase of work on the ground municipal to cover the information gap of one of the main features economic, as is the gross disposable income of households (GgDIiH), to assess and analyze the economic and social progress of the different local territories. This work intended to provide a reliable statistical information of such macromagnitud, through the estimate of a model space of the income in the geographical scope municipal using techniques of econometrics space incorporating the characteristics of interdependence and spatial heterogeneity and, therefore, with more robust compared to the techniques of econometrics conventional.
The aim of this work is to implement a convergence analysis of social expenditure on disability and other social measures (e.g. families and children, disabled people, substances, old age, immigrants and nomadic people, poverty adult problems and homelessness, multineeds, total), taking into account spatial effects. To this purpose, we develop a two-step analysis focusing on Italian regional data for the period 2003–2008. In the first phase, we perform a descriptive analysis and a joint application of a measure of inequality and of the degree of spatial autocorrelation. We subsequently apply the beta and sigma convergence analysis to per capita expenses on social issues, with special emphasis on expenses on disability, broadly defined. The results show that Italian regions do tend to converge in total, and also specific items of per capita social expenditures. In addition, we observe that the discrepancy among per capita expenditures for social actions and services have not been reduced over time, and that spatial effects differ according to the various types of social expenses. Policy considerations are discussed.
This paper summarizes the literature on spatial filtering (SF) for analysis of spatial data. Given the scarcity of its application in transportation and its fledgling nature, preliminary case studies were conducted using continuous and discrete response data sets, for land values and land use, in comparison with results from spatial autoregressive (SAR) models with distance decay parameters estimated using Bayesian techniques. For both the continuous land value and binary land use cases, the SF approach demonstrates great potential as a worthy competitor to more conventional SAR-based models. In addition to offering high fit statistics, somewhat shorter computing times, and more straightforward computations, the SF approach makes explicit the patterns of spatial dependency in the land value and land use data. By controlling for these spatial relationships, the SF approach yields more reliable marginal effects of policy variables of interest. Model results confirm the important role of transportation access (as quantified using distances to a region's central business district, and various roadway types).
Eigenvector spatial filtering (ESF) is becoming a popular way to address spatial dependence. Recently, a random effects specification of ESF (RE-ESF) is receiving considerable attention because of its usefulness for spatial dependence analysis considering spatial confounding. The objective of this study was to analyze theoretical properties of RE-ESF and extend it to overcome some of its disadvantages. We first compare the properties of RE-ESF and ESF with geostatistical and spatial econometric models. There, we suggest two major disadvantages of RE-ESF: it is specific to its selected spatial connectivity structure, and while the current form of RE-ESF eliminates the spatial dependence component confounding with explanatory variables to stabilize the parameter estimation, the elimination can yield biased estimates. RE-ESF is extended to cope with these two problems. A computationally efficient residual maximum likelihood estimation is developed for the extended model. Effectiveness of the extended RE-ESF is examined by a comparative Monte Carlo simulation. The main findings of this simulation are as follows: Our extension successfully reduces errors in parameter estimates; in many cases, parameter estimates of our RE-ESF are more accurate than other ESF models; the elimination of the spatial component confounding with explanatory variables results in biased parameter estimates; efficiency of an accuracy maximization-based conventional ESF is comparable to RE-ESF in many cases.
The Gravity Model is the workhorse for empirical studies in International
Economies and it is commonly used in explaining the trade flow
between countries. Recently, several studies have showed the importance
of taking into account the spatial effect. Spatial Econometric techniques
meet this matter, proposing the specification of a set of models and estimators.
We will make use of these Spatial Econometric techniques in
order to estimate a Spatial Gravity of Trade for a 22-year-long panel of
the OECD countries. The aim, therefore, is twofold: on one hand, we are
going to use the newest Spatial Econometric techniques in a field where
they aren't widely applicated. On the other hand, we provide an updated
interpretation of the behaviour of the International Trade in an OECD
context, taking into account potential spatial spillover effect due to the
third country dependence, and the effects of the migratory phenomenon.
Recent advances in spatial data analysis are making their way into a variety of applied research settings. Once purely the domain of specialists, increased availability of both spatial data and the software with which to handle them, spatial analysis techniques are diffusing into other areas of research. This article first details the rationale and need for spatial considerations in hedonic price models and focuses on the link between the context of the housing market and the statistical considerations necessary when dealing with spatial data. These issues are then explored via an application to the housing market of Cuyahoga County, Ohio. It was found, first, that explicit modeling of space is not always warranted. One of our two models shows no substantial signs of spatial misspecification. However, in the second model, where diagnostic tests call for the explicit modeling of space, some drastic differences were found between the space-neglected model and the more correctly specified spatial hedonic model. This highlights the need to include spatial diagnostics as part of the standard model-fitting procedure for hedonic house price applications.
Data on the geographic distribution of swine herds tested for pseudorabies virus (PRV) in the state of Illinois (USA) were analyzed to determine whether the prevalence of PRV-infected herds was clustered geographically at the county level. Second-order analysis of spatial dependence indicated there was a spatial clustering of counties of high PRV prevalence rates and that this clustering was greater than the observed clustering of counties with a large number of swine herds. The clustering of county PRV prevalence rates was most apparent within a radius of 120 km (on the average, approximately two couties away). The association of county PRV prevalence rates with average herd size, geographic density of swine herds in the country and regional (within 120 km) density of PRV-infected herds was analyzed using multiple linear regression. The primary factor affecting county PRV prevalence rates was the regional PRV density, which interacted with the other model variables. For counties with a low regional density of PRV infection, county PRV prevalence rates charged little with a change in county herd density or average herd size. In contrast, for counties with a high regional density of PRV infection, PRV prevalence within a county increased with increasing average herd size and increasing geographic density of swine herds in the county. The results of the current and previous studies implicate an important role for the geographic proximity of infected herds in the spread of PRV among swine herds.
Ordinary least squares linear regression models are frequently used to analyze and model spatial phenomena. These models are useful and easily interpreted, and the assumptions, strengths, and weaknesses of these models are well studied and understood. Regression models applied to spatial data frequently contain spatially autocorrelated residuals, however, indicating a misspecification error. This problem is limited to spatial data (although similar problems occur with time series data), so it has received less attention than more frequently encountered problems. A method called spatial filtering with eigenvectors has been proposed to account for this problem. We apply this method to ten real-world data sets and a series of simulated data sets to begin to understand the conditions under which the method can be most usefully applied. We find that spatial filtering with eigenvectors reduces spatial misspecification errors, increases the strength of the model fit, frequently increases the normality of model residuals, and can increase the homoscedasticity of model residuals. We provide a sample script showing how to apply the method in the R statistical environment. Spatial filtering with eigenvectors is a powerful geographic method that should be applied to many regression models that use geographic data.
Sommario Nel lavoro è definita e discussa una zonizzazione delle province italiane secondo i differenti livelli di sviluppo rurale. Lo scopo è di individuare i principali sistemi macro-regionali che sono un importante elemento di riferimento al fine di garantire il coordinamento dei livelli programmatori regionali e sub-regionali nell'istanza nazionale. I sistemi territoriali individuati sono 9: 4 riguardano l'Italia settentrionale, 3 i sistemi montani e collinari e 2 le regioni meridionali. La zonizzazione è il risultato dell'applicazione di una metodica, largamente sperimentata dagli autori, imperniata sul binomio GWR e cluster analysis che permette di pervenire ad apprezzabili risultati anche con un numero ridotto di indicatori. Questi fattori candidano la metodologia a porsi come un possibile strumento di ausilio per le scelte dei decisori pubblici. Infine è presentato un nuovo strumento di analisi che può fornire utili avanzamenti conoscitivi nelle analisi sullo sviluppo territoriale.
The geographical distribution and persistence of regional/local unemployment rates in heterogeneous economies (such as Germany) have been, in recent years, the subject of various theoretical and empirical studies. Several researchers have shown an interest in analysing the dynamic adjustment processes of unemployment and the average degree of dependence of the current unemployment rates or gross domestic product from the ones observed in the past. In this paper, we present a new econometric approach to the study of regional unemployment persistence, in order to account for spatial heterogeneity and/or spatial autocorrelation in both the levels and the dynamics of unemployment. First, we propose an econometric procedure suggesting the use of spatial filtering techniques as a substitute for fixed effects in a panel estimation framework. The spatial filter computed here is a proxy for spatially distributed region-specific information (e.g., the endowment of natural resources, or the size of the ‘home market’) that is usually incorporated in the fixed effects parameters. The advantages of our proposed procedure are that the spatial filter, by incorporating region-specific information that generates spatial autocorrelation, frees up degrees of freedom, simultaneously corrects for time-stable spatial autocorrelation in the residuals, and provides insights about the spatial patterns in regional adjustment processes.We present several experiments in order to investigate the spatial pattern of the heterogeneous autoregressive parameters estimated for unemployment data for German NUTS-3 regions. We find widely heterogeneous but generally high persistence in regional unemployment rates.
IntroductionHedonic price modelling – the conceptual frameworkUrban externalities and the functional form issue – measuring proximity effectsHedonic modelling and accessibility to urban servicesSpatial dependence – how to deal with itConcluding comments on hedonics in an appraisal contextAcknowledgementsReferences
In this chapter we review the concept of spatial autocorrelation and its attributes. Our purpose is to outline the various
formulations and measures of spatial autocorrelation and to point out how the concept helps assess the spatial nature of georeferenced
data. For a fuller treatment of the subject, a number of texts, written at various junctures in the development of the concept
and at differing levels of mathematical sophistication, spell out many of the details not discussed here (Cliff and Ord 1973,
1981; Miron 1984; Upton and Fingleton 1985; Goodchild 1986; Odland 1988; Anselin 1988; Haining 1990a; Legendre 1993; Dubin
1998; Griffith 1987, 1988, 2003). In addition, and as background to this chapter, Haining’s contribution in this volume (see
Chapter B.1) gives a clear view of the nature of georeferenced data. Our goal is to briefly describe the literature on this
subject so that the spatial autocorrelation concept is accessible to those who (i) are new to dealing with georeferenced data
in a research framework or (ii) have worked with georeferenced data previously but without explicit knowledge of how the concept
can be beneficial to them in their research. We are constrained by space and, as a result, our plan is to be short on explanations
but identify key literature where the reader will find further details.
While the geography of crime has been a focal concern in criminology from the very start of the discipline, the development
and use of statistical methods specifically designed for spatially referenced data has evolved more recently. This chapter
gives an overview of the application of such methods in research on crime and criminal justice, and provides references to
the general literature on geospatial statistics, and to instructive and innovative applications in the crime and criminal
justice literature.The chapter consists of three sections. The first section introduces the subject matter and delineates
it from descriptive spatial statistics and from visualization techniques (“crime mapping.”) It discusses the relevance of
spatial analysis, the nature of spatial data, and the issues of sampling and choosing a spatial unit of analysis. The second
section deals with the analysis of spatial distributions. We discuss the specification of spatial structure, address spatial
autocorrelation, and review a variety of spatially informed regression models and their applications. The third section addresses
the analysis of movement, including spatial interaction models, spatial choice models, and the analysis of mobility triads,
in the field of crime and criminal justice.
An important policy question concerns the impact that changing urban land uses have on the provision of local public goods. This questions has been investigated by Heikkila and Craig (1991, Journal of Regional Science 31, 65–81) for the case of policing services in Vancouver, Canada. However, their empirical analysis does not allow for the possibility of a spatially dependent error structure in the model, although it has been well established in both theory and practice that spatial autocorrelation can lead to inefficient estimators in regression analysis. Using the same data employed by Heikkila and Craig, we find that spatial effects are indeed present but do not affect our measures of impact in any important way. We conclude that spatial effects may be more important where one's emphasis is on ascertaining the parameters of the underlying model, but less important where the focus of enquiry is on fiscal impact.
A technique based on second-order methods, called second-order neighborhood analysis, is used to quantify clustering at various spatial scales. The theoretical model represents the degree of clustering in a Poisson process from the perspective of each individual point. The method is applied to point location data for a sample of ponderosa pine (Pinus ponderosa) trees, and shows that heterogeneity within the forest is clearly a function of the scale of analysis. © The American Society of Tropical Medicine and Hygiene. All rights reserved.
This paper is divided into six main parts. The first section starts by defining 'spatial autocorrelation' and outlining the traditional distinction between 'contiguity' and 'autocorrelation'. Processes are constructed that display the nature of this property. After this, it is shown how general and model-specific tests are carried out, and the present performance of the available tests is evaluated. Interpretation of test results is also discussed. The final sections focus particularly on the importance of spatial autocorrelation in inferential and model-building contexts. -after Author
Reviews second-order theory for map-pattern analysis and sets forth an approach for the study of interaction where spatial structure is implicitly built into various pattern models. The models are models of clustering when all members of the cluster are centered at one point. A density analysis is proposed where spatial autocorrelation may be discerned. An example using population distribution in East Anglia, 1971, is given along with comparisons to a central place model.-AuthorEast Anglia population distribution central place model map pattern model