(1970). A Computer Movie Simulating Urban Growth in the Detroit Region. Economic Geography: Vol. 46, PROCEEDINGS International Geographical Union Commission on Quantitative Methods, pp. 234-240.

https://www.jstor.org/stable/pdfplus/143141.pdf

A Computer Movie Simulating Urban Growth in the Detroit Region

Statistics for Spatial Data.

Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species’ distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method’s implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing

/pdf/methods-to-account-for-spatial-autocorrelation-in-the-5fbbuizhqs.pdf

Methods to account for spatial autocorrelation in the analysis of species distributional data : a review

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1977.tb01615.x

Modelling Spatial Patterns

We investigate bag-of-visual-words (BOVW) approaches to land-use classification in high-resolution overhead imagery. We consider a standard non-spatial representation in which the frequencies but not the locations of quantized image features are used to discriminate between classes analogous to how words are used for text document classification without regard to their order of occurrence. We also consider two spatial extensions, the established spatial pyramid match kernel which considers the absolute spatial arrangement of the image features, as well as a novel method which we term the spatial co-occurrence kernel that considers the relative arrangement. These extensions are motivated by the importance of spatial structure in geographic data.The methods are evaluated using a large ground truth image dataset of 21 land-use classes. In addition to comparisons with standard approaches, we perform extensive evaluation of different configurations such as the size of the visual dictionaries used to derive the BOVW representations and the scale at which the spatial relationships are considered.We show that even though BOVW approaches do not necessarily perform better than the best standard approaches overall, they represent a robust alternative that is more effective for certain land-use classes. We also show that extending the BOVW approach with our proposed spatial co-occurrence kernel consistently improves performance.

/pdf/bag-of-visual-words-and-spatial-extensions-for-land-use-1zmhx2kqn4.pdf

Bag-of-visual-words and spatial extensions for land-use classification

Census enumerations are usually packaged in irregularly shaped geographical regions. Interior values can be interpolated for such regions, without specification of “control points,” by using an analogy to elliptical partial differential equations. A solution procedure is suggested, using finite difference methods with classical boundary conditions. In order to estimate densities, an additional nonnegativity condition is required. Smooth contour maps, which satisfy the volume preserving and nonnegativity constraints, illustrate the method using actual geographical data. It is suggested that the procedure may be used to convert observations from one bureaucratic partitioning of a geographical area to another.

/pdf/smooth-pycnophylactic-interpolation-for-geographical-regions-3qu6uhm4ew.pdf

Smooth Pycnophylactic Interpolation for Geographical Regions

Exploring the anchor-point hypothesis of spatial cognition

Daniel Sui has sent me a written version of comments presented by five geographers at a panel on the first law of geography organized byhim at the 2003 AAG meeting in New Orleans The comments seem

On the First Law of Geography: A Reply

The mathematics of a push-pull model are shown to incorporate many of Ravenstein's laws of migration, to be equivalent to a quadratic transportation problem, and to be related to the mathematics of classical continuous-flow models. These results yield an improved class of linear spatial interaction models. Empirical results are presented for one country.

Waldo R. Tobler

Papers

A Computer Movie Simulating Urban Growth in the Detroit Region

Smooth Pycnophylactic Interpolation for Geographical Regions

Exploring the anchor-point hypothesis of spatial cognition

On the First Law of Geography: A Reply

Push-pull migration laws