Geographical Analysis最新文献

This article compares multivariate spatial analysis methods that include not only multivariate covariance, but also spatial dependence of the data explicitly and simultaneously in model design by extending two univariate autocorrelation measures, namely Moran's I and Geary's c. The results derived from the simulation datasets indicate that the standard Moran component analysis is preferable to Geary component analysis as a tool for summarizing multivariate spatial structures. However, the generalized Geary principal component analysis developed in this study by adding variance into the optimization criterion and solved as a trace ratio optimization problem performs as well as, if not better than its counterpart the Moran principal component analysis does. With respect to the sensitivity in detecting subtle spatial structures, the choice of the appropriate tool is dependent on the correlation and variance of the spatial multivariate data. Finally, the four techniques are applied to the Social Determinants of Health dataset to analyze its multivariate spatial pattern. The two generalized methods detect more urban areas and higher autocorrelation structures than the other two standard methods, and provide more obvious contrast between urban and rural areas due to the large variance of the spatial component.

Sub-national economic policies increasingly use labor market areas (LMAs) rather than administrative areas for analysis and implementation. How a set of LMAs was defined influences the results of such analyses, and so accurate policy delivery needs appropriately defined LMAs. Multinational bodies need comparable LMA definitions in many countries, calling for a definition method that is transferable across national boundaries. This article applies quantitative metrics to evaluate LMAs defined in three contrasting countries by three methods that represent the main methodological approaches. The deductive approach—based on a center and hinterland—is too inflexible to deal with differing geographical circumstances and cannot cope with statistical zones that are very small, or do not respect settlement structure. The alternative inductive methods tested define appropriate LMAs in each country, with the newer method performing slightly better in statistical terms. The article also exemplifies the usefulness of the metrics for comparisons of alternative regionalizations.

We are delighted that the RM paper has stimulated three coherent but diverse Commentaries from leading thinkers in this field (Fotheringham, 2022; Oshan, 2022; Wolf, 2022). Each of these contains robust critiques of the proposed RM and suggest alternative but diverse sets of considerations. We consider each of these in turn and provide a rejoinder by way of response.

We thank the authors of these commentaries for their efforts, and for taking the time to consider our article in detail. In general, we are pleased to see these—part of our motivation here was to initiate discussion on approaches to modeling spatial non-stationarity in regression models. By setting out one way to proceed through our RM, we intended to make an opening move. One thing we observe from these responses is that there is perhaps a spectrum for motivation for using these kind of models—at one end, an approach that is strongly motivated by underlying theories, and at the other, a more exploratory approach. One also has to consider the idea of data analysis as compromise—the reality of modern data collection is frequently that of “big data” where datasets are large, but quality and suitability assurance are not to the standards achieved by carefully designed surveys or experiments. In many cases, geographical fluctuations in models may be a consequence of this, and spatially varying coefficient methods may act as “spatial detectives” by shedding light on spatial inconsistencies and biases in the data collection, rather than direct measurements of a true underlying process. This suggests the need for a kind of “deep inference” where processes under investigation and the process of data collection are considered in equal measure, requiring consideration of underlying process theories, in addition to issues relating to the act of data exploration—perhaps suggesting that the spectrum referred to earlier is something to be scanned, rather than choosing a specific viewpoint from which to carry out analysis.

As we stated earlier, the approach outlined in the GWR RM by Comber et al. (2022a) is not intended to be a strict set of immutable rules, but more of an exemplar of what could be done to respond to a specific research context, and acknowledging that a degree of ‘fuzziness’ in modeling strategies is inevitable. The replies to our article have been useful in considering potential alternative research contexts, and how they may interact with this kind of fuzziness. We look forward to the debate advancing.

Inference procedures for spatial autocorrelation statistics assume that the underlying configurations of spatial units are fixed. However, sometimes this assumption can be disadvantageous, for example, when analyzing social media posts or moving objects. This article examines for the case of point geometries how a change from fixed to random spatial indexes affects inferences about global Moran's I, a popular spatial autocorrelation measure. Homogeneous and inhomogeneous Matérn and Thomas cluster processes are studied and for each of these processes, 10,000 random point patterns are simulated for investigating three aspects that are key in an inferential context: the null distributions of I when the underlying geometries are varied; the effect of the latter on critical values used to reject null hypotheses; and how the presence of point processes affects the statistical power of Moran's I. The results show that point processes affect all three characteristics. Inferences about spatial structure in relevant application contexts may therefore be different from conventional inferences when this additional source of randomness is taken into account.

Geographic Information Systems (GIS) and Machine Learning methods are now widely used in mass property valuation using the physical attributes of properties. However, locational criteria, such as as proximity to important places, sea or forest views, flat topography are just some of the spatial factors that affect property values and, to date, these have been insufficiently used as part of the valuation process. In this study, a hybrid approach is developed by integrating GIS and Machine Learning for mass valuation of residential properties. GIS-based Nominal Valuation Method was applied to carry out proximity, terrain, and visibility analyses using Ordnance Survey and OpenStreetMap data, than land value map of Great Britain was produced. Spatial criteria scores obtained from the GIS analyses were included in the price prediction process in which global and spatially clustered local regression models are built for England and Wales using Price Paid Data and Energy Performance Certificates data. Results showed that adding locational factors to the property price data and applying a novel nominally weighted spatial clustering algorithm for creating a local regression increased the prediction accuracy by about 45%. It also demonstrated that Random Forest was the most accurate ensemble model.

Machine learning (ML) is being applied in an increasing volume of geographical research. However, the aspects of spatial autocorrelation (SAC) in the residuals produced by ML models have been understudied compared to the benefit of ML, namely, reduction of prediction errors. In this study, we examined the relationship between predictive accuracy and the reduction in the residual SAC for 597 variables from 25 geographical socio-economic data sets using spatial and nonspatial cross-validation of three ML algorithms such as random forests, support vector machine, and artificial neural network (ANN) to provide an extensive empirical diagnosis—but not a definitive theory—of the relationship between SAC and ML. Our results highlighted that the ML algorithms with tuned hyperparameters yielded marginal predictive accuracy gains and the minimal decreases in residual SAC. ANN revealed lower accuracy and higher reduction in the residual SAC than others. This implies ML algorithms in geographical research in socio-economic domains would not always result in higher prediction accuracy. We suggest that ML in geographical research should be cautiously employed when the main objective is related to the residual SAC. We also showed that spatial cross-validation neither improves predictive accuracy substantially nor reduce the residual SAC effectively.

The present work pursues theoretical and empirical objectives. With regards to the former, it is demonstrated that the natural tendency to uniformity of both the probability distribution of a city to have a certain number of inhabitants and that of a person to reside in a town of a given number of citizens leads to a competition between their information entropies, which provides the power law distribution as the most probable one for city size. It is also shown that Zipf's law reflects the significant control of the existence of interconnections between cities on the self-organization of their size. With regards to the empirical objectives, based on population data of European countries and Italian municipalities, the theoretical approach proposed is validated. At the Italian scale, city distribution is shown to be a power law for cities above 10,000 inhabitants. In the 20 Italian regions, the breakpoint in the distribution is generally lower. Finally, the geographical control on city distribution is discussed based on the results achieved in some regions.

The development of “route maps” for spatial analytical methods is a pursuit with important ramifications. Comber et al. propose a route map to guide applications of geographically weighted regression consisting of a three-step primary pathway and a series of secondary arterials. This comment first highlights some concerns about the underlying “map” (i.e., experimental setup and assumptions) and then with the proposed “route” (i.e., core decisions and evaluation criteria). It closes by suggesting a more general focus on identifying modeling issues with the highest impact and facilitating consensus-building, which could improve the future production of route maps for navigating the methodological landscape in spatial analysis.

Comber et al. provide an important contribution to the future of quantitative geography and Geographical Analysis. The contribution is chiefly in their development of a “GWR Route Map,” a diagram showing the sequence of analytical steps that “successful” specification searches in local modeling tend to follow. Geographically weighted techniques have been rapidly expanding, both in terms of complexity, users, and disciplinary reach. With geographically weighted methods now in so many more analysts' hands, any new rule of thumb will have a major imprint. But, by what right does the thumb rule the analysts? That is, what “counts” as valid knowledge about local models in general? In the following comment, I argue that we probably should use theory, not route maps to decide specifications. But, if we are pressed to build route maps, we sorely need better epistemological foundations for them. I discuss a few previous examples of strongly grounded route maps and offer a few paths to these better grounds as well as two ways to the exit.