Geo- spatial InformationVolume 7,Issue 4Science ( Quarterly)December 2004Article ID: 1009- -5020( 2004)04- 262 -267Document code:AApplication of Integration of Spatial Statistical Analysiswith GIS to Regional Economic AnalysisCHEN Fei DU DaoshengABSTRACTThis paper summarizes a few spatial statistical analysis methods for to measuring spatial autocor-relation and spatial association, discusses the criteria for the identification of spatial association by the use ofglobal Moran Coefficient, Local Moran and Local Geary. Furthermore, a user friendly statistical module, com-bining spatial statistical analysis methods with GIS visual techniques, is developed in Areview using Avenue.An example is also given to show the usefulness of this module in identifying and quantifying the underlyingspatial association patterns between economic units.KEY WORDS spatial statistical analysis; spatial autocorrelation; spatial association; regional economic analy-siCLC NUMBER P208for a researcher who wishes to examine relation-Int roductionship between different variables， and to makestatistical decisions with geo-referenced data.Nowadays， spatial statistics can be found inTrue spatial analysis in GIS is a much longer-the fields of agriculture, geology, soils, water,term goal. In fact, since the late of 1980s， thethe environment, economy and geography and sostatistical aspect of spatial analysis has receivedon. Many researchers have conducted compre-increasing attention from the GIS community.hensive researches on spatial statistics in the lastSince spatial statistical analysis becomes moretwo decades or sol-5]， and new statisticalnecessary in many GIS analysis, researchers payapproaches have been developed.more attention to the integration of spatial sta-GIS technology, as an interactive visualizationtistical analysis and GIS. Nowadays， thoughand decision-support tool， plays an importantthere are still a lot of discussions and disagree -role in regional economic development plans asments on the integration of GIS and spatial stawell as traditional analytical systems or approa-tistical analysis, it is generally agreed that com-ches6]，especially in the decision -making proce-bining at least some spatial statistical analysisdure of economic development at local, regional .with GIS is necessary. Different researchers putand state levels. However, almost all the cur-forward different opinions, but most of them be-rent commercial GIS packages are extremely lim-lieve that the integration can occur in two totallyited in standard statistical. Many GIS provide .different but equally valid solutions: embeddingonly some of the most basic summary statisticsspatial statistical analysis function into a GIS en-about data and do not support statistical model-vironment, or embedding selected GIS functionsing required by many decision makers, let aloneinto a spatial statistical analysis environmentl'l .spatial statistical capabilities. Whereas， spatial中國(guó)煤化工ke a beneficial explo-statistical analysis is very necessary and helpful|YHC N M H Gtegration of GIS andReeived on March 30, 2004.Funded by the National Natural Science Foundation of China (N0. 40401021) and the National Social Science Foundation of China (N0. 04C]L019).CHEN Fei, Associate Professor, School of Economices and Management, Nanchang University, 235 Nanjing East Road, Nanchang 330047. China.E mail; chenfei1208@ sina. comCHEN Fei, et al. / Application of Integration of Spatial ..263spatial statistical analysis. The application in re-techniques are thrown away in spatial statistics,gional developing analysis reflects mainly the usejustly most of them are modified so that they can .in the field of social- economic development-11be used properly for spatial data analysis.For the reason that there are still some technicaldifficulty on the integration of spatial statistical1.1 Spatial weight matrixanalysis with GIS and the spatial statistical analThe topological information generated by GISysis capabilities of GIS are deficient up to now,provides the basic measure of spatial linkages orthe application of that integration in regionalproximity for spatial data analysis58.n]. A binaryeconomic analysis is still limited.spatial weight matrix W(nXn) is usually definedto represent the spatial proximity relations,1Spatial statistical analysis ap-which can be measured with adjacency or dis-proachestance criterion. Besides， a general measure ofthe weighted spatial proximity can be defined interms of the attribute value(x;) observed and theSpatial statistics is concerned with the applica-binary spatial weight matrix. According to thetion of spatial sampling in geographic situations.adjacency criterion, the elements W; of the spa-In general，a geographic phenomena or an at-tial weight matrix will be one when location i istribute value observed at one area unit is not in-adjacent to location j, and zero otherwise. Simi-dependent of the same phenomena or the samelarly，according to the distance criterion, the el-attribute values observed at adjacency areaements W; of the spatial weight matrix will beunits[1.2].Almost all kinds of spatial data haveone when the distance between location i and lo-the feature of spatial dependence or spatial auto-cation j within a given distance(d) and zero oth-correlation. The existing spatial dependence vio-erwise. For convention， all the diagonal ele-lates the basic assumption of independencements W; are set to zeros. .among the observations in classical statistical1.2， Measurement of spatial autocorrela-analysis. Most of the classical statistical meth-tion and spatial associationods, when applied to geo-referenced data, fail tocapture the spatial dependence of the data gener-Goodchild(1987) thought that in its most gen-ally. However, most of urban and regional anal-eral sense spatial autocorrelation or spatial de-ysis is conducted with discretized data aggrega-pendence concerns the degree to which objects or .ted for different geographical areas or zones.activities at some place are similar to other ob-Therefore，a set of spatial statistical analysisjects or activities located nearby. Spatial depend-methods should be identified and introduced innce can be measured on two different scales:order to handle those data efficiently. The“spa-global indicators and local indicators.tial statistics” in this paper is a narrow defini-The Moran Cofficient (MC) and Geary Ratiotion. It doesn't means all the statistical methods(GR) are two well-known global indicators offor analyzing spatial data， but means thosespatial autocorrelation. MC reflects attribute-methods suitable for handling discretized data ofsimilarity among area units that are located near-different geographical areas or zones. Thus, theby. Spatial weight matrix W; provides the meas-core of spatial statistics is the explicit recogni-urement of locational proximity and C; = (x;tion of spatial dependence or spatial autocorrela-|Y片中國(guó)煤化工ibute- similarty. Withtion among geo- referenced datal1-8]， the con-C N M H Gnd attibute- simiaritystruction of spatial weight matrix， the measure-C; both determined, the MC could be calculatedment and test of spatial autocorrelation or spatialconsequently. The calculation of GR is mainlyassociation，the identification of spatial associa-similar to the calculation of MC [1.2].tion and so on. Not all of the classical statisticalHowever, global indicators only use a single264 Geo spatial Information Science (Quarterly)value to describe autocorrelation within a certain. (there is no spatial autocorrelation between ob-given areal2， so the patterns of spatial associa-served values over the n area units) can be con-tion existing in different local map areas are dif-ducted. MC=- 1/(n 一1) or GR = 1 indicatesficult to be detected. G(d) statistics, Local Mo-a random map pattern， MC > - 1/(n- 1)orran statistics and Local Geary statistics are alter-0 < GR < 1 (MC or GR is significant too) indi-native local indicators.cates that similar values tend to cluster on a mapAccording to Reference[ 3]， a spatial statistics( positive spatial autocorrelation)，MC<- 1/(nG;(d) can be defined as follows.-1) orGR > 1(MC or GR is significant too) in-G,(d)= (2wix,)/2x,(1)dicates that dissimilar values tend to cluster on aj.j≠ij,j≠map( negative spatial autocorrelation). When nwhere x; denotes the observed attribute value atis large, the expected value of MC converges tolocation j，and the construction of symmetriczero, and a positive value is associated with posi-spatial weight matrix w is based on the distancetive spatial autocorrelation, while a negative val-criterion. For ease of interpretation， Z(G)，aue is associated with negative spatial autocorrela-standardized form of G;(d), can be defined-4.5].tion.According to Reference [5], Local Moran sta-The standardized form of G;(d) can be appliedtistics and Local Geary statistics for each loca-to either positive or negative attributes. A t- testtion i can be defined respectively as follows:can be conducted on the null hypothesis of H。:I,(Z;/S*) Zw;Z,(2)G,=0[4.可. Z(G;) does not include the observa-j≠tion i from the index. The G statistics can beC,= 2w,(Z,- Z,)2used to identify spatial clustering patterns withhigh-values or low-values. However, the G sta-where Z; and Z; are with deviations from thetistics cannot detect spatial patterns of positivemean，such as Z;=x;-下，Wi are the elementsof binary symmetric spatial weight matrix, S2 =association or negative association.Local Moran and local Geary statistics haveZ(x,- )2/(n- 1) and j≠i,W,Z; is thesome advantages over the G;(d) statistic. For aweighted average of the deviations in the sur-randomization hypothesis， the test statistics forrounding locations. Unlike Local Moran statis-I; is:tics，Local Geary statistics is the weighted sumZ(I;) = (I;- E[1,])/VVar(I)(5)of the squared differences between the deviationwhere E[ I;] and Var( I;) denote the expectedat location i and surrounding locations.value and variance of I;，respectively-sl. On thebasis of the calculated test statistics similarly,1.3 Identification of spatial associationthe significant testing on local spatial associationThe inverse relationship between Moran’s Ican be conducted.and Geary's C is basically linear in naturelaJA pseudosignificance level of I; can be obtainedwith one index we can express the other. Theby a“conditional”randomization or permutationMC is more popular and powerful statistically.approach5.9. The experimental p-value alsoHence，we implement MC to measure the globalprovides a basis for the test on the null hypothe-spatial autocorrelation in this article. Under asis Ho (all observed values are randomly distribu-normality assumption, the test statistics for MCted over the_ space).is:中國(guó)煤化工a1 Moran is similar toZ(I) = (IE[I])/Var(MC)(4)YHCNMH Gp -value (such as p0. 95)the significant test on the null hypothesis H。indicates that observation i is associated withCHEN Fei, et al. / Application of Integration of Spatial ..265relatively low values in surrounding observa-nits, and it is possible for a user to execute spa-tions.tial statistical analysis and visualization analysisThe calculation of pseudosignificance levelin the same environment. Consequently， we de-p-value of the local Geary is similar to that ofvelop a user friendly interactive spatial statisticalLocal Moran[9]. A large p-value (such as p : >analysis module with ArcView as developing er0.95) indicates a small C，in extremes, whichvironment, and realize the combination of spatialindirectly suggests a positive spatial associationstatistical technologies with a regional analysis(+ + or --) of observation i with its sur-procedure in a GIS environment. The modulerounding observations， while a small p - valueprovides a flexible and convenient tool for the(such as p<0. 05) indicates a large C;，in ex-decision-making in regional economy. The fol-tremes, which indirectly suggests a negative spa-lowing example illustrates its application in thetial association(+ 一or一十 ) of observation ifield of regional economic analysis.with its surrounding observations.3 Example analysis2 Integration of spatial analysisstatistical with GISWe take Xinjiang Uyger Autonomous Regionas research area， and utilize mean annual GDPThe key feature of GIS is that it can link differ-increasing velocity from 1978 to 1999 in differentent geo referenced data to geographic locations,counties as an analytical indicator, then calculatethat is to say， GIS represents and analyzes difglobal MC for research area and local MC forferent data from a spatial perspective. Current-each county. Those spatial outliers can also bely，researchers pay more attention to the inte-identified by the use of Local MC scatterplot.gration of spatial statistical analysis and GIS,The results show the usefulness of the module inand make a beneficial exploration into the use ofidentifying and quantifying the underlying spatialthe integration in the field of social-economic de-association patterns among economic units.velopment. The application in regional develo-To construct an adjacency spatial weight ma-ping analysis reflects the use in the field of so-trix is the first step in the procedure of spatialcial-economic development mainly-7-11.statistical analysis, in Fig. 1 for details. A two-Different researchers put forward differentdimensional matrix can be expressed as a one-opinions on the integration of GIS and spatialdimensional array by use of the“List”class. Irstatistical analysisl-11, and most of them believethe module developed by authors， a spatialthat this integration can occur in two totally dif-neighbor list table is used to represent spatiallyferent but equally valid solutions: embeddingadjacent relations among different regionalspatial statistical analysis function into a GIS en-units[10]. Fig.2 is one section of the spatial .vironment，or embedding selected GIS functionsneighbor list created in practice.into a spatial statistical analysis environment.On the basis of the spatial neighbor list createdAttention has been focused almost exclusively onand the results calculated in Fig. 3，the signifi-the former so far， while the latter has beencant testing on spatial autocorrelation can be im-largely ignored in the past[l1However, almostplemented. If choose a = 0. 05，then Zo.025 =any module developed can only offer limited1. 96. Because Z = 4.202 > 1. 96 in this exam-functions of spatial statistical analysis.中國(guó)煤化工is not true and shouldWith the research on regional economic analy-MHCNMHGthatthereisasignif-sis，embedding spatial statistical analysis apicant positive spatial autocorrelation among theproaches mentioned above into a GIS environ-values of analytical indicator of all counties.ment can meet the need of the analysis on under-Furthermore，we can investigate the underly-lying spatial association patterns between area u-ing local patterns of spatial economic association266 Geo-spatial Iformation Science (Qurerl)TEMPAre atrbute tablecant spatial association existing among differentTEMPLPOLY-RPOLYcounties. For instance, there is a positive signif-⑤3②icant spatial association between the mean annual④⑥GDP increasing velocity of Korla City and thoseindexes of Korla's surrounding counties, a nega-tive significant spatial association between Shan-a)(bshan and its surrounding counties. An examina-Polygon atribute tabletion on original data gives further help for ex-TEMP Poly Id Attnbutelplaining those underlying local spatial associationpatterns. According to those linked windows in{1010Fig.4，a local Moran scatterplot window and atable of local spatial statistics can be used to helpc)d)identify spatial outliers and underlying patternsFig.1 Constructing spatial weightsof local spatial clustering[10].matrix using Arc/ Info topologyTable 1 Local moran eofficient and its test statisticsRoighbering Polygona Liat 30xfor different counties( one section)PdlygonNeighoringPolyensCountiesIIZ- Score14 10.13.19.2025Hejing County417.161 148. 0321515 13.16.17.18.23Shanshan County5(-3.25338161517Korla City5614. 837596. 948 30171562.28.30Weili County668. 176913.84134181315.19.2327Heshou County8:13. 879016.501 1619131418.20252742Bohu County8215. 735 557. 367162011014.19.21 25.31.22110202234.42.Moryu County10. 966 435.14255Luopu County87.612 843. 57823Pishan County866.781 95 .3. 53973Hotan City886712. 253. 503 60Fig.2 Spatial neighbor list table of the spatial relationsamong regional unitsNotes: With an overall significance level of a=o. o5, the individu-al significance level a; =a/n=0.000 57 based on a Bonfer-roni criteria.Horan Coeffici entSpatal Atocrretion TestingMoran Cefficient 0.266209Mean00116279Z-score4.20201Fig.3 Global spatial autocorrelation cofficientand its significant testing statisticsamong counties in Xinjiang by calculating the lo-cal Moran statistics I, at county level. On thebasis of the module developed and that criteriafor the identification of Spatial Association men-Fig.4 A sketch map of muli- window linkages for .tioned above, we can do well for completing rel-中國(guó)煤化Ititical analysisevant calculations and analyses. See Table 1(on-MYHCNMHGly those significant testing scores listed) and4 ConclusionsFig. 4 for details. According to Local Moran Co-eficient I and its Testing 2-Score in Table 1,In many regional studies, relatively independ-there are underlying positive or negative signifi-ent economic areas comprise an important basisCHEN Fei, et al. / Application of Integration of Spatial .. 267for regional economic analysis. GIS is well sui-and applications. London: Pion.ted for the change of research area in level, like2 Goodchild M F(1986) Spatial autocorrelation. 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