9,270 research outputs found
Geographically weighted regression with parameter-specific distance metrics
Geographically weighted regression (GWR) is an important local technique to model spatially varying relationships. A single distance metric (Euclidean or non-Euclidean) is generally used to calibrate a standard GWR model. However, variations in spatial relationships within a GWR model might also vary in intensity with respect to location and direction. This assertion has led to extensions of the standard GWR model to mixed (or semiparametric)GWR and to flexible bandwidth GWR models. In this article, we present a strongly related extension in fitting a GWR model with
parameter-specific distance metrics (PSDM GWR). As with mixed and flexible bandwidth GWR models, a back-fitting algorithm is used for the calibration of the PSDM GWR model. The value of this new GWR model is demonstrated using a London house price data set as a case study. The results indicate that the PSDM GWR model can clearly improve the model calibration in terms of both goodness of fit and prediction accuracy, in contrast to the model fits when only one metric is singly used. Moreover, the PSDM GWR model provides added value in understanding how a regression model’s relationships may vary at different spatial scales, according to the bandwidths and distance metrics selected. PSDM GWR deals with spatial heterogeneities in data relationships in a general way, although questions remain on its model diagnostics, distance metric specification, and computational efficiency, providing options for further research
The importance of scale in spatially varying coefficient modeling
While spatially varying coefficient (SVC) models have attracted considerable
attention in applied science, they have been criticized as being unstable. The
objective of this study is to show that capturing the "spatial scale" of each
data relationship is crucially important to make SVC modeling more stable, and
in doing so, adds flexibility. Here, the analytical properties of six SVC
models are summarized in terms of their characterization of scale. Models are
examined through a series of Monte Carlo simulation experiments to assess the
extent to which spatial scale influences model stability and the accuracy of
their SVC estimates. The following models are studied: (i) geographically
weighted regression (GWR) with a fixed distance or (ii) an adaptive distance
bandwidth (GWRa), (iii) flexible bandwidth GWR (FB-GWR) with fixed distance or
(iv) adaptive distance bandwidths (FB-GWRa), (v) eigenvector spatial filtering
(ESF), and (vi) random effects ESF (RE-ESF). Results reveal that the SVC models
designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa
and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the
most computationally efficient. Conversely GWR and ESF, where SVC estimates are
naively assumed to operate at the same spatial scale for each relationship,
perform poorly. Results also confirm that the adaptive bandwidth GWR models
(GWRa and FB-GWRa) are superior to their fixed bandwidth counterparts (GWR and
FB-GWR)
Distance metric choice can both reduce and induce collinearity in geographically weighted regression
This paper explores the impact of different distance metrics on collinearity in local regression models such as geographically weighted regression. Using a case study of house price data collected in Hà Nội, Vietnam, and by fully varying both power and rotation parameters to create different Minkowski distances, the analysis shows that local collinearity can be both negatively and positively affected by distance metric choice. The Minkowski distance that maximised collinearity in a geographically weighted regression was approximate to a Manhattan distance with (power = 0.70) with a rotation of 30°, and that which minimised collinearity was parameterised with power = 0.05 and a rotation of 70°. The results indicate that distance metric choice can provide a useful extra tuning component to address local collinearity issues in spatially varying coefficient modelling and that understanding the interaction of distance metric and collinearity can provide insight into the nature and structure of the data relationships. The discussion considers first, the exploration and selection of different distance metrics to minimise collinearity as an alternative to localised ridge regression, lasso and elastic net approaches. Second, it discusses the how distance metric choice could extend the methods that additionally optimise local model fit (lasso and elastic net) by selecting a distance metric that further helped minimise local collinearity. Third, it identifies the need to investigate the relationship between kernel bandwidth, distance metrics and collinearity as an area of further work
A Template for a New Generic Geographically Weighted R Package gwverse
GWR is a popular approach for investigating the spatial variation in relationships between response and predictor variables, and critically for investigating and understanding process spatial heterogeneity. The geographically weighted (GW) framework is increasingly used to accommodate different types of models and analyses, reflecting a wider desire to explore spatial variation in model parameters and outputs. However, the growth in the use of GWR and different GW models has only been partially supported by package development in both R and Python, the major coding environments for spatial analysis. The result is that refinements have been inconsistently included within GWR and GW functions in any given package. This paper outlines the structure of a new gwverse package, that may over time replace GW model, that takes advantage of recent developments in the composition of complex, integrated packages. It conceptualizes gwverse as having a modular structure, that separates core GW functionality and applications such as GWR. It adopts a function factory approach, in which bespoke functions are created and returned to the user based on user-defined parameters. The paper introduces two demonstrator modules that can be used to undertake GWR and identifies a number of key considerations and next steps.
Volume54, Issue
A Template for a New Generic Geographically Weighted R Package gwverse
GWR is a popular approach for investigating the spatial variation in relationships between response and predictor variables, and critically for investigating and understanding process spatial heterogeneity. The geographically weighted (GW) framework is increasingly used to accommodate different types of models and analyses, reflecting a wider desire to explore spatial variation in model parameters and outputs. However, the growth in the use of GWR and different GW models has only been partially supported by package development in both R and Python, the major coding environments for spatial analysis. The result is that refinements have been inconsistently included within GWR and GW functions in any given package. This paper outlines the structure of a new gwverse package, that may over time replace GW model, that takes advantage of recent developments in the composition of complex, integrated packages. It conceptualizes gwverse as having a modular structure, that separates core GW functionality and applications such as GWR. It adopts a function factory approach, in which bespoke functions are created and returned to the user based on user-defined parameters. The paper introduces two demonstrator modules that can be used to undertake GWR and identifies a number of key considerations and next steps
(WP 2007-02) Valuing Environmental Quality: A Space-based Strategy
This paper develops and applies a space-based strategy for overcoming the general problem of getting at the demand for non-market goods. It focuses specifically on evaluating one form of environmental quality, distance from EPA designated environmental hazards, via the single-family housing market in the Puget Sound region of Washington State. A spatial two stage hedonic price analysis is used to: (1) estimate the marginal implicit price of distance from air release sites, hazardous waste generators, hazardous waste handlers, superfund sites, and toxic release sites; and (2) estimate a series of demand functions describing the relationship between the price of distance and the quantity consumed. The analysis, which represents a major step forward in the valuation of environmental quality, reveals that the information needed to identify second-stage demand functions is hidden right in plain site — hanging in the aether of the regional housing market
On the universal structure of human lexical semantics
How universal is human conceptual structure? The way concepts are organized
in the human brain may reflect distinct features of cultural, historical, and
environmental background in addition to properties universal to human
cognition. Semantics, or meaning expressed through language, provides direct
access to the underlying conceptual structure, but meaning is notoriously
difficult to measure, let alone parameterize. Here we provide an empirical
measure of semantic proximity between concepts using cross-linguistic
dictionaries. Across languages carefully selected from a phylogenetically and
geographically stratified sample of genera, translations of words reveal cases
where a particular language uses a single polysemous word to express concepts
represented by distinct words in another. We use the frequency of polysemies
linking two concepts as a measure of their semantic proximity, and represent
the pattern of such linkages by a weighted network. This network is highly
uneven and fragmented: certain concepts are far more prone to polysemy than
others, and there emerge naturally interpretable clusters loosely connected to
each other. Statistical analysis shows such structural properties are
consistent across different language groups, largely independent of geography,
environment, and literacy. It is therefore possible to conclude the conceptual
structure connecting basic vocabulary studied is primarily due to universal
features of human cognition and language use.Comment: Press embargo in place until publicatio
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