Contents Search. Autocorrelation, Spatial. How to cite. Synonyms Spatial correlation; Spatial dependence; Spatial inter-dependence.
This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access.
Moore, D. Devary, J. Diniz, J. Geary, R. Haining, R. Hoboken, N. A comparison of spatial autocorrelation indices and landscape metrics in measuring urban landscape fragmentation.
Landscape and Urban Planning , , — Spatial autocorrelation in uptake of antenatal care and relationship to individual, household and village-level factors: results from a community-based survey of pregnant women in six districts in western Kenya. International Journal of Health Geographics , 12 1 , Spatial Econometrics: Methods and Models. Dordrecht: Springer Netherlands. Links between language diversity and species richness can be confounded by spatial autocorrelation : Table 1.
Statistical bias correction for daily precipitation in regional climate models over Europe. Growth pole theory of regional economic development is another example of this externality field effect. Haag and Weidlich have tied it to self- organizing spatial systems.
Haining has used it to depict gasoline price competition. O'Neill has coupled it with stream evolution processes similar special linear cases include digitization of sequences of points, and sequential field measurement. In each of these situations, the phenomena in question need to be represented by nonlinear mathematical formulae, and tend to be stochastic in nature. These exemplars also tend to be consistent with defining spatial autocorrelation as a spillover effect. The meaning of spatial autocorrelation in this setting can be referenced to the second connotation put forth by Haining et al.
A given map is a single realization of some spatial process. If one could obtain p»n such realizations, that were independent, then each vector of areal unit values could be treated like a variable, and the. Spatial autocorrelation, then, is some common correlation amongst these areal unit variables. Once again this description is reminiscent of Q-mode factor analysis studies, where geographic distributions of various attributes are treated like repeated independent realizations of the same geographic process.
Because of change through time, available resources, or feasibility constraints, in practice spatial analysts are unable to acquire bona fide multiple replications of the outcome of a single process, except when conducting simulation experiments.
In some sense, then, most of spatial statistical analysis is conducted with a sample of size one. Therefore, spatial autocorrelation may be defined as an average correlation between observations based upon replicated realizations of the geographic distribution of some attribute.
An additional analogy helps to synthesize the foregoing discussion. One example most academics can relate to pertains to classroom testing. The instructor wishes to measure the amount of knowledge each student has of designated subject matter, in some independent fashion.
Because an exhaustive testing of the material is impossible, the instructor draws a sample of questions to administer to students. Because the class is taught by the same instructor and from the same book, similarities will occur across students in test responses. These commonalities must be acknowledged, to avoid specification error, in pairwise comparisons of test answers. Groups of students that study together will have a common kernel of knowledge, which may cause their test answers to be correlated.
More than likely the classroom seating choices of these groups of students will cluster. This is similar to the missing variable interpretation of spatial autocorrelation.
Students who copy from their neighbors will display certain common knowledge, which will cause their test answers to be correlated. This is the spillover interpretation of spatial autocorrelation. In fact, because this cheating is geo- referenced, it constitutes a spatial autocorrelation mechanism.
If two students collaborate on all answers and submit identical responses to the test, then no new information is gained once one of the test papers is graded. Spatial processes. Summary and conclusions. This is the information content interpretation of spatial autocorrelation.
Moreover, the two students should be aggregated into a single test unit resulting in the loss of one degree of freedom. In conclusion, a clear, simple, and concise definition of spatial autocorrelation can not be found in most of the literature on this subject. It is inherently geographical. But its meaning is contextual, and multifaceted, as treatments by Gatrell and Haining attest to. It can be defined as. This is what the literature implies is the meaning of spatial autocorrelation.
Anselin L. Spatial Econometrics: Methods and Models. Dordrecht: Martinus Nijhoff. Arbia G. Boston: Kluwer. Bartlett M. The Statistical Analysis of Spatial Pattern. London: Chapman and Hall.
Cliff A. Spatial Autocorrelation. London: Pion. Spatial Processes. Island Community. Cambridge: Cambridge University Press.
Curry L. Fisher W. Regional and Urban Economics, 1, p. Gatrell A. Environment and Planning A, 11 p. Geary R. Incorporated Statistician, 5 p. Goodchild M. Panel discussion, Baltimore, 85th Annual Meeting. Gould P. Griffith D. Washington, D. Advanced Spatial Statistics. The Hague: Martinus Nijhoff. Haag G. Griffith and A.
The Hague: Martinus Nijhoff, p. Haining R. Herbert and R. Johnston, p. London: Wiley. Geographical Analysis, 15, p. Matern B. Berlin: Springer- Verlag. Moran P. Journal of the Royal Statistical Society, 10B, p. Odland J. O'Neill M. Meandering Channel Patterns: Analysis and Interpretation. Openshaw S.
Paelinck J. Spatial Econometrics. Farnborough: Saxon House. Richardson S. Griffith, p. Ripley B. Spatial Statistics. New York: Wiley. Statistical Inference for Spatial Processes. Sen A. Sokal R. American Naturalist, , p. Stephan F. Journal of the American Statistical Association, 29, p. Student Biometrika, 10, p. Switzer P. Thomas E. Berry and D. Tobler W. Upton G. Spatial Data Analysis by Example, vol. Whittle P. Biometrika, 43, p. Wolpert J. Aitken S. The Professional Geographer, 41, p.
Journal of Regional Science, 28, p. Boots B. The Canadian Geographer, 33, p. Cox N. Journal of Geography in Higher Education, 13, p. Progress in Human Geography, 13, p. Geography, 74, p. Reflections on the past 25 years of spatial statistics [article] Daniel A.
Plan Introduction [link] Background [link] The information content perspective [link] The model specification error perspective [link] The modifiable areal unit perspective [link] Spatial processes [link] Summary and conclusions [link] Bibliographie [link]. Liste des illustrations Fig. Reflections on the past 25 years of spatial statistics Daniel A. Introduction A generic way of describing the concept of spatial autocorrelation, frequently encountered in the literature, refers to either similar or dissimilar values clustering, rather than being randomly located, on a map see fig.
Spatial autocorrelation was noticed in passing here, too, with spatial data being characterized by a modified urn model, where sample selections appear to more closely resemble an experiment in which clusters of grapes, rather than 13 16 23 38 A 19 26 41 55 27 50 75 78 38 58 83 84 50 83 19 78 B 27 26 84 58 23 16 75 55 38 38 13 41 41 26 75 38 C 27 83 13 78 55 16 84 19 38 58 23 50 Positive Spatial Autocorrelation similar values clustering Zero Spatial Autocorrelation random 6.
Negative Spatial Autocorrelation dissimilar values clustering Fig. Background Spatial autocorrelation may be defined in a literal sense by dissecting the phrase. Odland introduces spatial autocorrelation in a succinct, readable fashion, commenting on why objects are autocorrelated in space, but never defining the concept in a clear, simple, and concise manner.
Among other features, this book gives an excellent presentation of spatial heterogeneity issues affiliated with spatial dependence. The information content perspective One reason researchers became interested in spatial autocorrelation is because the locational information of geo- referenced data is not captured by classical statistics; traditional estimators are not statistically sufficient i. Griffith and Jones Daniel Griffith The information content perspective.
Models used to date are summarized by Upton and Fingleton The model specification error perspective At times spatial autocorrelation is defined as an artifact of specification error in spatial modelling. This expression reduces to the previous, simpler one, only if p y which corresponds to a spatially stationary mean. In this latter case the appropriate statistical model has a term like Daniel Griffith The model specification error perspective.
An analysis of MC in this way suggests that if one posits a constant mean when a variable mean is true, then specification error could lead to the detection of spatial autocorrelation when in fact it does not exist in the geo-referenced data. The detection of spatial autocorrelation here is a mistake, an artifact of specification error. Accordingly, spatial autocorrelation functions as a diagnostic concept.
This idea constitutes part of the thrust of Odland's monograph. It also is the notion illustrated by Haining in his formulation of a model of High Plains agriculture. But this Table H Data for and residuals from simple linear regressions: positive and negative spatial autocorrelation examples. The modifiable areal unit perspective As was mentioned earlier, Arbia has produced an impressive, imaginative, and innovative piece discussing the modifiable areal unit problem.
Although theoretically there appear to be an infinite number of ways in which a study region can be areally divided, the critical question here has to do with determining the number of groups of those elements constituting the geographical distribution under study, not slight changes in areal unit boundaries, which might affect nothing more than the shape or planar surface area of units.
Daniel Griffith The modifiable areal unit perspective. Table in The number of ways eight items can be allocated to a given number of areal units. Table IV Pseudo-random numbers generated for the simulated geographic distribution. Three different judiciously chosen surface partitionings have been superimposed upon this geographic landscape, and the individual attribute values summed for objects captured by each of the four resulting areal units.
0コメント