A Spatially Adjusted ANOVA Model

Environment and Nation: Geographical Factors in the Cultural and Political History of Europe. By Griffith Taylor, Professor of Geography, The University of Toronto. (Chicago: University of Chicago Press. 1936. Pp. 571. $4.00.) Environment and Nation: Geographical Factors in the Cultural and Political History of Europe. By Taylor Griffith, Professor of Geography, The University of Toronto. (Chicago: University of Chicago Press. 1936. Pp. 571. $4.00.) John K. Wright John K. Wright American Geographical Society Search for other works by this author on: Oxford Academic Google Scholar The American Historical Review, Volume 42, Issue 4, July 1937, Pages 700–702, https://doi.org/10.1086/ahr/42.4.700 Published: 01 July 1937

Arthritis is a public health issue that is of global concern. Arthritis is one of the chronic diseases with a high incidence of middle-aged and older adults. The patients have paid a heavy price for this and caused a substantial economic burden on society. In this study, we used spatial autocorrelation, spatial cluster analysis, multiple logistic regression, and random forest models to analyze the spatial distribution and possible risk factors for arthritis in elderly Chinese and assess arthritis risk. Global spatial autocorrelation analysis and significance test results show that Moran's I of arthritis spatial autocorrelation in 2011, 2013, and 2015 are statistically significant, so there is significant spatial autocorrelation three years. The results of local spatial autocorrelation and spatial clustering analysis show that the aggregation areas of arthritis patients are mainly in the southwest, northwest, and central China. Multivariate logistic regression analysis showed that gender, age, education level, Body Mass Index (BMI), Center for Epidemiologic Studies Depression Scale score (CES-D), altitude, region, weather temperature, hypertension, lung, liver, heart, stroke, digestive, and kidney disease were all arthritis affects factors (P <; 0.05). Compared with the multi-factor Logistic regression model, the random forest model better assesses performance and higher fit. The fitting accuracy is 82.2% in the random forest model, which is better than the multi-factor Logistic regression model (66.6%). According to the assessment risk map generated by the random forest model, Northeast, Southwest, Northwest, South, and Central are high-risk areas for arthritis. These results provide benchmark data for the control and prevention of arthritis diseases.

Geographical AnalysisVolume 15, Issue 3 p. 205-211 Free Access Majority Voting and the Location of Salutary Public Facilities Fred M. Shelley, Fred M. Shelley Fred M. Shelley is assistant professor of geography, University of Oklahoma.Search for more papers by this authorMichael F. Goodchild, Michael F. Goodchild Michael F. Goodchild is professor of geography, University of Western Ontario. The helpful comments of Daniel Fesenmaier, Diane Whalley, Frank Stetzer, Sally McLafferty, Avijit Ghosh, and two anonymous referees on earlier drafts of this paper are gratefully acknowledged.Search for more papers by this author Fred M. Shelley, Fred M. Shelley Fred M. Shelley is assistant professor of geography, University of Oklahoma.Search for more papers by this authorMichael F. Goodchild, Michael F. Goodchild Michael F. Goodchild is professor of geography, University of Western Ontario. The helpful comments of Daniel Fesenmaier, Diane Whalley, Frank Stetzer, Sally McLafferty, Avijit Ghosh, and two anonymous referees on earlier drafts of this paper are gratefully acknowledged.Search for more papers by this author First published: July 1983 https://doi.org/10.1111/j.1538-4632.1983.tb00782.xCitations: 2 Michael F. Goodchild is professor of geography, University of Western Ontario. The helpful comments of Daniel Fesenmaier, Diane Whalley, Frank Stetzer, Sally McLafferty, Avijit Ghosh, and two anonymous referees on earlier drafts of this paper are gratefully acknowledged. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED Black, D. (1948). “On the Rationale of Group Decision Making. Journal of Political Economy, 56, 23– 34. Hansen, P., and J.-E Thisse (1981). “Outcomes of Voting and Planning: Condorcet, Weber, and Rawls Locations. Journal of Public Economics, 16, 1– 15. Kramer, G. (1973). “On a Class of Equilibrium Conditions for Majority Rule. Econometrica, 41, 255– 97. Rushton, G., S. L. McLafferty, and A. Ghosh (1981). “Optimum Locations for Public Services: Individual Preferences and Social Choice. Geographical Analysis, 13, 196– 202. Sen, A. (1977). “Social Choice Theory: A Re-Examination. Econometrica, 45, 53– 89. Tellier, L.-N. (1972). “The Weber Problem: Solution and Interpretation. Geographical Analysis, 4, 215– 33. Wendell, R. E., and R. D. McKelvey (1981). “New Perspectives in Competitive Location Theory. European Journal of Operational Research, 6, 174– 82. Citing Literature Volume15, Issue3July 1983Pages 205-211 ReferencesRelatedInformation

Geographical AnalysisVolume 14, Issue 1 p. 72-78 Free Access Pattern Change and Distance Variation in the Square Arthur Getis, Arthur Getis Arthur Getis is professor of geography, University of Illinois at Urbana-Champaign. The author has benefited from comments made by Tames O. Huff and computer programming by Marc Armstrong, both of the Department of Geography, University of Illinois, and Ralph Lenz of Wittenberg University.Search for more papers by this author Arthur Getis, Arthur Getis Arthur Getis is professor of geography, University of Illinois at Urbana-Champaign. The author has benefited from comments made by Tames O. Huff and computer programming by Marc Armstrong, both of the Department of Geography, University of Illinois, and Ralph Lenz of Wittenberg University.Search for more papers by this author First published: January 1982 https://doi.org/10.1111/j.1538-4632.1982.tb00056.xCitations: 4 Arthur Getis is professor of geography, University of Illinois at Urbana-Champaign. The author has benefited from comments made by Tames O. Huff and computer programming by Marc Armstrong, both of the Department of Geography, University of Illinois, and Ralph Lenz of Wittenberg University. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED Dacey, M. F. (1965). “Numerical Measures of Random Sets.” Research Report,16. Evanston., Ill: Department of Geography, Northwestern University. Dacey, M. F. (1975). “Evaluation of the Poisson Approximation to Measures of the Random Pattern in the Square.” Geographical Analysis, 7: 351– 67. Gaile, G. L., and J. E. Burt (1980). “Directional Statistics.” Concepts and Techniques in Modem Geography (CATMOG), No. 25. London: Institute of British Geographers. Getis, A., and B. Boots (1978). Models of Spatial Processes: An Approach to the Study of Point, Line and Area Patterns. Cambridge: Cambridge University Press. Ghosh, B. (1951). “Random Distances within a Rectangle and between Two Rectangles.” Bulletin of the Calcutta Mathematical Society. 43: 17– 24. Horowitz, M. (1965). “Probability of Random Paths across Elementary Geometrical Shapes.” Journal of Applied Probability, 2: 169– 77. Taylor, P. J. (1971). “Distances within Shapes: An Introduction to a Family of Finite Frequency Distributions.” Geografiska Annaler, 53: 40– 53. Tobler, W. (1977). “Bidimensional Regression.” Santa Barbara, Calif.: Department of Geography, University of California. Tobler, W. (1978). “Comparison of Plane Forms.” Geographical Analysis, 10: 154– 62. Citing Literature Volume14, Issue1January 1982Pages 72-78 ReferencesRelatedInformation

The high importance of bathymetric character for many processes on reefs means that high-resolution bathymetric models are commonly needed by marine scientists and coastal managers. Empirical and optimisation methods provide two approaches for deriving bathymetry from multispectral satellite imagery, which have been refined and widely applied to coral reefs over the last decade. This paper compares these two approaches by means of a geographical error analysis for two sites on the Great Barrier Reef: Lizard Island (a continental island fringing reef) and Sykes Reef (a planar platform reef). The geographical distributions of model residuals (i.e., the difference between modelled and measured water depths) are mapped, and their spatial autocorrelation is calculated as a basis for comparing the performance of the bathymetric models. Comparisons reveal consistent geographical properties of errors arising from both models, including the tendency for positive residuals (i.e., an under-prediction of depth) in shallower areas and negative residuals in deeper areas (i.e., an over-prediction of depth) and the presence of spatial autocorrelation in model errors. A spatial error model is used to generate more reliable estimates of bathymetry by quantifying the spatial structure (autocorrelation) of model error and incorporating this into an improved regression model. Spatial error models improve bathymetric estimates derived from both methods.

Geographical AnalysisVolume 13, Issue 2 p. 95-116 Free Access Maximum Entropy Spectra and the Spatial and Temporal Dimensions of Economic Fluctuations in an Urban System Claude Marchand, Claude Marchand The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. Claude Marchand is assistant professor of geography, University of Montreal.Search for more papers by this author Claude Marchand, Claude Marchand The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. Claude Marchand is assistant professor of geography, University of Montreal.Search for more papers by this author First published: April 1981 https://doi.org/10.1111/j.1538-4632.1981.tb00719.xCitations: 17 Claude Marchand is assistant professor of geography, University of Montreal. The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED Bartels, C. P. A. (1977). “The structure of Regional Unemployment in the Netherlands. Regional Science and Urban Economics, 7, 103– 5. Bartels, C. P. A., M. Booleman, and W. H. Peters (1978). “A Statistical Analysis of Regional-Unemployment Series. Environment and Planning A, 10, 937– 54. Bennett, R. J. (1979). Spatial Time Series: Analysis—Forecasting—Control. London: Pion. Brechling, F. (1967). “Trends and Cycles in British Regional Unemployment. Oxford Economic Papers, 19, 1– 21. Burg, J. P. (1968). A New Analysis Technique for Time Series Data. Netherlands: Advanced Study Institute in Signal Processing. Bums, F., and W. Mitchell (1947). Measuring Business Cycles. New York: National Bureau of Economic Research. Cho, D. W., and D. S. McDougall (1978). “Regional Cyclical Patterns and Structure, 1954-1975. Economic Geography, 54, 66– 74. Fishman, G. S. (1969). Spectral Methods in Econometrics. Cambridge, Mass.: Harvard University Press. Granger, C. W. J. (1966). “The Typical Spectral Shape of an Economic Variable. Econometrica, 24, 150– 61. Granger, C. W. J., and M. Hatanaka (1964). Spectral Analysis of Economic Time Series, Princeton, N. J.: Princeton University Press. Haggett, P. (1975). “ Time Series Comparison: Unemployment. In Elements of Spatial Structure, edited by A. D. Cliff et al, Cambridge: Cambridge University Press. Hanna, F. A. (1954). “Cyclical and Secular changes in State per Capita Incomes, 1920-1950. Review of Economics and Statistics, 36, 320– 30. Hansen, A. H. (1951). Business Cycles and the National Income, New York: W. W. Norton. Harris, C. P., and A. P. Thirlwall (1968). “Interregional Variations in Cyclical Sensitivity to Unemployment in the U.K. 1949-1964. Bulletin of the Oxford University Institute of Economics and Statistics, 55– 66. Hepple, L. (1975). “ Spectral Techniques and the Study of Interregional Economic Cycles.” In Processes in Physical and Human Geography, edited by R. Peel, M. Chisholm, and P. Haggett, pp. 392– 408. London: Heinmann. Jeffrey, D. (1974). “Regional Fluctuations in Unemployment Within the Australian Urban Economic System: A Study of the Spatial Impact of Short Term Economic Change. Economic Geography, 50. Jeffrey, D. and D. J. Webb (1972). “Economic Fluctuations in the Australian Regional System 1955-70. Australian Geographical Studies, 10, 141– 60. Jenkins, G. M., and D. G. Watts (1968). Spectral Analysis and its Applications, San Francisco: Holden-Day. Kanasewich, E. R. (1973). Time Sequence Analysis in Geophysics. Edmonton: The University of Alberta Press. King, L., E. Casetti, and D. Jeffrey (1969). “Economic Impulses in a Regional System of Cities: A Study of Spatial Interaction. Regional Studies, 3, 213– 18. King, L., E. Casetti, and D. Jeffrey (1974). “Cyclical Fluctuations in Unemployment Levels in the U.S. Metropolitan Areas. Tidjdschrift Voor Economische en Social Geographie, 50, 345– 52. King, L. J., and G. R. Clark (1978). “Regional Unemployment Patterns and the Spatial Dimensions of Macro-Economic Policy: The Canadian Experience 1966-1975. Regional Studies, 12, 283– 96. Lacoss, R. T. (1971). “Data Adaptative Spectral Analysis Methods. Geophysics, 36, 661– 75. Schumpeter, J. (1935). “The Analysis of Economic Change. Review of Economic Statistics, 17, 1– 10. Thompson, W. R. (1965). A Preface to Urban Economics. Baltimore: Johns Hopkins University Press. Thompson, W. R. (1975). “ Internal and External Factors in the Development of Urban Economies.” In Regional Policy: Readings in Theory and Applications, edited by J. Friedman and W. Alonso, pp. 210– 20. Cambridge, Mass.: M. I. T. Press. Tiebout, T. M. (1975). “ Exports and Regional Economic Growth.” In Regional Policy: Readings in Theory and Applications, edited by J. Friedman and W. Alonso, pp. 348– 52. Cambridge, Mass.: M. I. T. Press. Citing Literature Volume13, Issue2April 1981Pages 95-116 ReferencesRelatedInformation

Fundamental to most classical data collection sampling theory development is the random drawings assumption requiring that each targeted population member has a known sample selection (i.e., inclusion) probability. Frequently, however, unrestricted random sampling of spatially autocorrelated data is impractical and/or inefficient. Instead, randomly choosing a population subset accounts for its exhibited spatial pattern by utilizing a grid, which often provides improved parameter estimates, such as the geographic landscape mean, at least via its precision. Unfortunately, spatial autocorrelation latent in these data can produce a questionable mean and/or standard error estimate because each sampled population member contains information about its nearby members, a data feature explicitly acknowledged in model-based inference, but ignored in design-based inference. This autocorrelation effect prompted the development of formulae for calculating an effective sample size (i.e., the equivalent number of sample selections from a geographically randomly distributed population that would yield the same sampling error) estimate. Some researchers recently challenged this and other aspects of spatial statistics as being incorrect/invalid/misleading. This paper seeks to address this category of misconceptions, demonstrating that the effective geographic sample size is a valid and useful concept regardless of the inferential basis invoked. Its spatial statistical methodology builds upon the preceding ingredients.

DO SPATIAL EFFECFS REALLY MATTER IN REGRESSION ANALYSIS?

Abstracts of papers presented at the annual meeting of the Canadian Phytopathological Society McGill University, Montreal 9-13 July 1988

Statistics is a branch of mathematics concerned with the collection, quantification, analysis, interpretation, and presentation of real-world data, and the use of probability theory to estimate population parameters with these data. Spatial statistics is a subset of statistics that is concerned with handling the special problems associated with geographically distributed data, which include spatial point patterns, regional and lattice measurement aggregations, irregularly spaced site-specific measurements on a surface, and image analysis. Meanwhile, econometrics is concerned with the application of statistical methods to the study of economic data and problems. When coining the term spatial econometrics in 1979, Paelinck and Klaassen characterized it as a subset of econometrics that is concerned with the role of spatial dependence in regional economic model response and explanatory variables, asymmetries in spatial relationships, the specification of geographic structure governing spatial interactions, and the explicit modeling of space. We outline and discuss principal similarities (e.g., testing for the presence of spatial autocorrelation) and differences (e.g., map generalization) between spatial statistics and spatial econometrics. In doing so, our goal is to help clarify past, present, and future relationships between these two subfields.

A test for robust detection of residual spatial autocorrelation with application to mortality rates in Sweden

Notes on Contributors

©, 2014, Editorial Office of Journal of Shenzhen University. All right reserved. Based on the establishment of Shenzhen service enterprises geographic database, spatial analysis is adopted to develop empirical research on Shenzhen service industry spatial distribution and autocorrelation patterns. Conclusions are drawn as follows: dot density rendering and centrographic statistics estimate the spatial distribution characteristics of geographic factors on the whole. Shenzhen service enterprises distribute with a strong trickle-down trend from the city center to the periphery. The weighted mean centers of Shenzhen service industries display an obviously western offset from the geometry center. Indicated by Moran's I verifications, Shenzhen service industries have different global spatial autocorrelations. Also Shenzhen services with high proportion of added values (≥3%) show diversified local spatial autocorrelations on agglomerative subdistricts. Regional industrial division has been formed, which is the result of cooperative effect of location condition, economic ties, and government planning. Furthermore, it would be necessary to keep customized spatial development policies for the specific service industry, because of the existence of urban regional differences and industrial heterogeneity.

Analysis of spatial panel data is of great importance and inter est in spatial econometrics. Here we consider cigarette demand in a spatial panel of 46 states of the US over a 30-year period. We construct a de mand equation to examine the elasticity of per pack cigarette price and per capita disposable income. The existing spatial panel models account for both spatial autocorrelation and state-wise heterogeneity, but fail to account for temporal autocorrelation. Thus we propose new spatial panel models and adopt a fully Bayesian approach for model parameter inference and predic tion of cigarette demand at future time points using MCMC. We conclude that the spatial panel model that accounts for state-wise heterogeneity, spa tial dependence, and temporal dependence clearly outperforms the existing models. Analysis based on the new model suggests a negative cigarette price elasticity but a positive income elasticity.

Statistical models of environment‐abundance relationships may be influenced by spatial autocorrelation in abundance, environmental variables, or both. Failure to account for spatial autocorrelation can lead to incorrect conclusions regarding both the absolute and relative importance of environmental variables as determinants of abundance. We consider several classes of statistical models that are appropriate for modeling environment‐abundance relationships in the presence of spatial autocorrelation, and apply these to three case studies: 1) abundance of voles in relation to habitat characteristics; 2) a plant competition experiment; and 3) abundance of Orbatid mites along environmental gradients. We find that when spatial pattern is accounted for in the modeling process, conclusions about environmental control over abundance can change dramatically. We conclude with five lessons: 1) spatial models are easy to calculate with several of the most common statistical packages; 2) results from spatially‐structured models may point to conclusions radically different from those suggested by a spatially independent model; 3) not all spatial autocorrelation in abundances results from spatial population dynamics; it may also result from abundance associations with environmental variables not included in the model; 4) the different spatial models do have different mechanistic interpretations in terms of ecological processes – thus ecological model selection should take primacy over statistical model selection; 5) the conclusions of the different spatial models are typically fairly similar – making any correction is more important than quibbling about which correction to make.