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## General Spatial Econometric Conclusions

### Non-standard Spatial Statistics and Spatial Econometrics (2011-01-01) 1: 243 , January 01, 2011

What should be clear from the exercises presented is that in most of them, classical “regression” has been combined with mathematical programming to obtain the desired estimators.

## A Mixed Linear-Logarithmic Specification for Lotka-Volterra Models with Endogenously Generated SDLS-Variables

### Non-standard Spatial Statistics and Spatial Econometrics (2011-01-01) 1: 179-187 , January 01, 2011

In Arbia and Paelinck (2003a, b), a Lotka-Volterra model (LVM) is applied to the convergence-divergence problem of European regions in terms of incomes per capita. As the latter have to be non-negative, a double logarithmic version may be substituted for the original specification, a modification that removes at least part of the non-linearity of LVMs; this chapter introduces this non-linearity again. Discussion begins with a general section on LVMs, to go on with a mixed linear-logarithmic specification, of which the positivity of the (possible) equilibrium solution is proved, and for which a (sufficient) stability condition is derived.

## When Space Beats Time: A Proof of Concept with Hurricane Dean

### Advances in Geocomputation (2017-01-01): 207-215 , January 01, 2017

In this research, we present an empirical case study to illustrate the new framework called “space beats time” (SBT). SBT is rooted in the expectation that predictions based on temporal autocorrelation typically outperform predictions based on spatial autocorrelation, except in the aftermath of abrupt disruptive events. Following such disruption scenarios, space is likely to outperform time, albeit often for a brief post event period. We illustrate the SBT concept by assessing the impact of Hurricane Dean on vegetation greenness using a remotely sensed spatiotemporal data series. We predict the normalized difference vegetation index (NDVI) using separate temporal-only and spatial-only models without the aid of covariates. We then compare each prediction model’s performance before and after the hurricane event. Results suggest that SBT expected behaviors are valid in general terms but that some issues require attention. Our case study shows conspicuous SBT effects in the aftermath of the hurricane event in question, including increased performance in the geographic areas where the hurricane impact was more severe. In addition, we unexpectedly find that a more limited SBT pattern is present before the hurricane. This unanticipated pattern suggests that the presence of SBT features in an empirical study may vary, depending on the strength of a disruptive event as well as on the ability of a dataset and proxy variable to capture a disruptive event and its effects.

## Introduction

### Advances in Geocomputation (2017-01-01): 1-3 , January 01, 2017

At Geocomputation 2015, a number of researchers presented their work orally or as a poster. Oral presentations included five keynote lectures by the following internationally renowned people in the field that the conference featured: Michael Batty, Scott Morehouse, Shashi Shekhar, Dana Tomlin, and Paul Torrens.

## Introduction

### Spatial Autocorrelation and Spatial Filtering (2003-01-01): 1-32 , January 01, 2003

At least since the dawn of civilization data have been analyzed as numerical figures to support a decision or to understanding a part of reality. Until the advent of the modern computer, data had to be collected manually and necessary calculations had to be done by hand, often restricting the volume of data analyzed to a very modest size. The computer has enabled the collection of vast amounts of data with greater ease and the performance of necessary data analysis calculations with far fewer mistakes and with considerably greater speed. With this transformation the new restriction to the volume of data analyzed became one based upon computer memory (RAM and ROM) and the speed of input and output devices. Initially this restriction resulted in two classes of computer: standard ones used by most scientists, mainframes and desktop PCs, and then supercomputers housed in a handful of regional centers. In recent years standard desktop PCs have become as powerful as earlier supercomputers, with differences between the two_{1}.

## Epilogue

### Evolving Geographical Structures (1983-01-01) 15: 468-469 , January 01, 1983

Considerable work has been done in recent years by geographers, spatial economists, regional scientists, and allied disciplines, on dynamic modelling. A main emphasis of this work is description of spatio-temporal paths of geographical systems. Good examples of dynamic models for spatial problems are provided in Griffith and MacKinnon (1981). Unfortunately these sorts of dynamic models tend to be linear in form, and tend to treat locations in space in an independent fashion. This latter feature is analogous to constructing a set of n time series models that are independent of one another. But spatial autocorrelation mechansims, space-time processes and the relative nature of space highlight the inappropriateness of most dynamic spatial models for most real world problems. As soon as non-linear formulations embracing interaction effects are introduced, the modelling game is dramatically changed. Movements through time become irreversible, and bifurcations of trajectories become possible, perhaps even likely.

## Introduction: Spatial Statistics

### Non-standard Spatial Statistics and Spatial Econometrics (2011-01-01) 1: 3 , January 01, 2011

A wide array of topics in spatial statistics introduce methodological controversy: aggregate versus disaggregated data inference (e.g., the ecological fallacy), modelling the spatial covariance versus the spatial inverse covariance matrix, including fixed and/or random effects terms in a model specification, spatial autocorrelation specified as part of the mean response versus part of the variance parameter, and methods for simulating spatially autocorrelated random variables.

## Front Matter - Spatial Autocorrelation and Spatial Filtering

### Spatial Autocorrelation and Spatial Filtering (2003-01-01) , January 01, 2003

## Spatial Filtering

### Spatial Autocorrelation and Spatial Filtering (2003-01-01): 91-130 , January 01, 2003

One approach to dealing with spatial autocorrelation in regression analysis involves filtering, which seeks to transform a spatially dependent variable into an independent variable by removing the spatial dependence embedded in it. In doing so, the original georeferenced attribute variable is partitioned into two synthetic variables: a filtered nonspatial variable and a residual spatial variable. Haining (1991) shows that the temporal-type filtering approach is equivalent to a spatial autocorrelation adjustment for the case of bivariate correlation. He employs one of the family of autoregressive models, such as the simultaneous (SAR), of the general form discussed in Anselin (1988) and Griffith (1988) to implement his version of spatial filtering. In essence, these models depend on one or more spatial structural matrices that remove (filter) spatial autocorrelation from the georeferenced data from which model parameters are estimated: e.g., from equation (1.3), (*I*- ρ*W*)^{-1}*Y* = μ_{Y}*1* + ε _{Y}. The filtering devices are constructed from geographic weights matrices, which are used to capture the covariation among values of one or more random variables associated with the depiction of the configuration of areal units.

## Selecting Spatial Regimes by Threshold Analysis

### Non-standard Spatial Statistics and Spatial Econometrics (2011-01-01) 1: 189-197 , January 01, 2011

The existence of differential spatial regimes has been revealed on different occasions (see for instance Arbia and Paelinck, 2003a, b; also see Chap. 14). Hence the necessity exists for developing workable specifications to compute possible frontiers or thresholds between those regimes.