ART‐P‐MAP Neural Networks Modeling of Land‐Use Change: Accounting for Spatial Heterogeneity and Uncertainty

Spatial land‐use models over large geographic areas and at fine spatial resolutions face the challenges of spatial heterogeneity, model predictability, data quality, and of the ensuing uncertainty. We propose an improved neural network model, ART‐Probability‐Map (ART‐P‐MAP), tailored to address these issues in the context of spatial modeling of land‐use change. First, it adaptively forms its own network structure to account for spatial heterogeneity. Second, it explicitly infers posterior probabilities of land conversion that facilitates the quantification of prediction uncertainty. Extensive calibration under various test settings is conducted on the proposed model to optimize its utility in seeking useful information within a spatially heterogeneous environment. The calibration strategy involves building a bagging ensemble for training and stratified sampling with varying category proportions for experimentation. Through a temporal validation approach, we examine models’ performance within a systematic assessment framework consisting of global metrics and cell‐level uncertainty measurement. Compared with two baselines, ART‐P‐MAP achieves consistently good and stable performance across experiments and exhibits superior capability to handle the spatial heterogeneity and uncertainty involved in the land‐use change problem. Finally, we conclude that, as a general probabilistic regression model, ART‐P‐MAP is applicable to a broad range of land‐use change modeling approaches, which deserves future research.     

A Comparison of Spatially Varying Regression Coefficient Estimates Using Geographically Weighted and Spatial‐Filter‐Based Techniques

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data‐generating processes by allowing regression coefficients to vary spatially. It is a widely applied technique across domains because it is intuitive and conforms to the well‐understood framework of regression. An alternative method to GWR that has been suggested is spatial filtering, which it has been argued provides a superior alternative to GWR by producing spatially varying regression coefficients that are not correlated with each other and which display less spatial autocorrelation. It is, therefore, worthwhile to examine these claims by comparing the output from both methods. We do this by using simulated data that represent two sets of spatially varying processes and examining how well both techniques replicate the known local parameter values. The article finds no support that spatial filtering produces local parameter estimates with superior properties. The results indicate that the original spatial filtering specification is prone to overfitting and is generally inferior to GWR, while an alternative specification that minimizes the mean square error (MSE) of coefficient estimates produces results that are similar to GWR. However, since we generally do not know the true coefficients, the MSE minimizing specification is impractical for applied research.     

A Multivariate Model for Spatio‐temporal Health Outcomes with an Application to Suicide Mortality

This article considers models for multivariate mortality outcomes (e.g., bivariate, trivariate, or higher dimensional) observed over a set of areas and through time. The model outlined here allows for spatially structured and white noise errors and for their intercorrelation. It also includes possible temporal continuity in such types of error via structured temporal effects. An extension to spatially varying regression effects is considered, as well as the option of nonparametric specification of priors for spatial residuals and regression effects. Allowing for spatially correlated intercepts or regression effects may alter inferences regarding the changing impact on mortality of socioeconomic or environmental predictors. The modeling framework is illustrated by an application to male and female suicide mortality in London, focusing on the impact on suicide of deprivation and social fragmentation (“anomie”) in the 33 London boroughs during three periods: 1979–83, 1984–88 and 1989–93. Suicide trends by age group are also considered and show considerable differences in the trends in impacts of deprivation and social fragmentation.     

Bayesian Spatial Filtering for Hedonic Models: An Application for the Real Estate Market

This article presents a Bayesian method based on spatial filtering to estimate hedonic models for dwelling prices with geographically varying coefficients. A Bayesian Adaptive Sampling algorithm for variable selection is used, which makes it possible to select the most appropriate filters for each hedonic coefficient. This approach explores the model space more systematically and takes into account the uncertainty associated with model estimation and selection processes. The methodology is illustrated with an application for the real estate market in the Spanish city of Zaragoza and with simulated data. In addition, an exhaustive comparison study with a set of alternatives strategies used in the literature is carried out. Our results show that the proposed Bayesian procedures are competitive in terms of prediction; more accurate results are obtained in the estimation of the regression coefficients of the model, and the multicollinearity problems associated with the estimation of the regression coefficients are solved.     

Spatially varying relationships between municipal operating expenditure and its determinants: The case of South Africa

We apply the geographically weighted regression to investigate spatial variability (nonstationarity) in the relationships between municipal operating expenditure (in total and for a separate component thereof) and the determinants of this expenditure, in South Africa. The empirical findings indicate that some of these relationships are spatially varying for the period under consideration. The global model (i.e., least square regression) cannot take account of the unequal environment in which South African municipalities operate. One implication of our findings is that a “one-size-fits-all” approach in the design of policies targeting municipal finances may not be appropriate for municipalities in South Africa, and indeed in other contexts in which such heterogeneity is found. Instead, policy formulation should explicitly consider relevant differences in local conditions.     

Exploring the Relations Between Riverbank Erosion and Geomorphological Controls Using Geographically Weighted Logistic Regression

The relations between riverbank erosion and geomorphological variables that are thought to control or influence erosion are commonly modelled using regression. For a given river, a single regression model might befitted to data on erosion and its geomorphological controls obtained along the river's length. However, it is likely that the influence of some variables may vary with geographical location (i.e., distance upstream). For this reason, the spatially stationary regression model should be replaced with a non‐stationary equivalent. Geographically weighted regression (GWR) is a suitable choice. In this paper, GWR is extended to predict the binary presence or absence of erosion via the logistic model. This extended model was applied to data obtained from historical archives and a spatially intensive field survey of a length of 42 km of the Afon Dyfi in West Wales. The model parameters and the residual deviance of the model varied greatly with distance upstream. The practical implication of the result is that different management practices should be implemented at different locations along the river. Thus, the approach presented allowed inference of spatially varying management practice as a consequence of spatially varying geomorphological process.     

Prediction of Bike-sharing Trip Counts: Comparing Parametric Spatial Regression Models to a Geographically Weighted XGBoost Algorithm

Regression models are commonly applied in the analysis of transportation data. This research aims at broadening the range of methods used for this task by modeling the spatial distribution of bike-sharing trips in Cologne, Germany, applying both parametric regression models and a modified machine learning approach while incorporating measures to account for spatial autocorrelation. Independent variables included in the models consist of land use types, elements of the transport system and sociodemographic characteristics. Out of several regression models with different underlying distributions, a Tweedie generalized additive model is chosen by its values for AIC, RMSE, and sMAPE to be compared to an XGBoost model. To consider spatial relationships, spatial splines are included in the Tweedie model, while the estimations of the XGBoost model are modified using a geographically weighted regression. Both methods entail certain advantages: while XGBoost leads to far better values regarding RMSE and sMAPE and therefore to a better model fit, the Tweedie model allows an easier interpretation of the influence of the independent variables including spatial effects.     

A Geostatistical Linear Regression Model for Small Area Data. 一种适用于小区域数据的地统计线性回归模型

We present a new linear regression model for use with aggregated, small area data that are spatially autocorrelated. Because these data are aggregates of individual‐level data, we choose to model the spatial autocorrelation using a geostatistical model specified at the scale of the individual. The autocovariance of observed small area data is determined via the natural aggregation over the population. Unlike lattice‐based autoregressive approaches, the geostatistical approach is invariant to the scale of data aggregation. We establish that this geostatistical approach also is a valid autoregressive model; thus, we call this approach the geostatistical autoregressive (GAR) model. An asymptotically consistent and efficient maximum likelihood estimator is derived for the GAR model. Finite sample evidence from simulation experiments demonstrates the relative efficiency properties of the GAR model. Furthermore, while aggregation results in less efficient estimates than disaggregated data, the GAR model provides the most efficient estimates from the data that are available. These results suggest that the GAR model should be considered as part of a spatial analyst's toolbox when aggregated, small area data are analyzed. More important, we believe that the GAR model's attention to the individual‐level scale allows for a more flexible and theory‐informed specification than the existing autoregressive approaches based on an area‐level spatial weights matrix. Because many spatial process models, both in geography and in other disciplines, are specified at the individual level, we hope that the GAR covariance specification will provide a vehicle for a better informed and more interdisciplinary use of spatial regression models with area‐aggregated data.     

ACCOUNTING FOR LOCAL SPATIAL HETEROGENEITIES IN HOUSING MARKET STUDIES

We adopt a novel method to deal with omitted spatial heterogeneities in hedonic house price analysis. A Gaussian variant of the conditional autoregressive (CAR) model is used to study the impact of spatial effects. In a general linear modeling framework, we include zone‐specific random effects that are allowed to interact spatially with neighboring zones. The results demonstrate that this estimator accounts for missing spatial information, producing more reliable results on estimated spatially related coefficients. The CAR model is benchmarked against a fixed effects model. Socioeconomic neighborhood characteristics are found to have only modest impact on spatial variation in housing prices.     

A Bayesian Approach to Modeling Binary Data: The Case of High‐Intensity Crime Areas

This paper reports the fitting of a number of Bayesian logistic models with spatially structured or/and unstructured random effects to binary data with the purpose of explaining the distribution of high‐intensity crime areas (HIAs) in the city of Sheffield, England. Bayesian approaches to spatial modeling are attracting considerable interest at the present time. This is because of the availability of rigorously tested software for fitting a certain class of spatial models. This paper considers issues associated with the specification, estimation, and validation, including sensitivity analysis, of spatial models using the WinBUGS software. It pays particular attention to the visualization of results. We discuss a map decomposition strategy and an approach that examines properties of the full posterior distribution. The Bayesian spatial model reported provides some interesting insights into the different factors underlying the existence of the three police‐defined HIAs in Sheffield.     

Spurios Spatial Regression: Some Monte Carlo Results with a Spatial Unit Root and Spatial Cointegration

In this paper I introduce the concepts of spatial unit roots and spatial cointegration, and via Monte-Carlo simulation I illustrate their implications for spatial regression. It is shown that spatial unit roots lead to spurious (spatial) regression, as in the well-known case involving time-series. Spatial cointegration is similar to its time-series counterpart, although I demonstrate that OLS estimation of spatial error-correction models is not consistent.     

EXTENDING A SMOOTH PARAMETER MODEL TO FIRM LOCATION ANALYSES: THE CASE OF NATURAL GAS ESTABLISHMENTS IN THE UNITED STATES

This paper extends recent developments in regional growth modeling that use spatial regime switching functions to a count regression model of firm location events. The smooth parameter count model (SPCM) allows for a parsimonious parameterization of locally varying coefficients while simultaneously attending to excess‐zero count events. An empirical application examines natural gas establishment growth between 2005 and 2010. The smooth parameter model appears to outperform a standard zero‐inflated count model. The SPCM may be extended to the location analysis of other industries with the identification of transition variables related to the supply or demand oriented cost structure of the sector.     

Analytical Modeling of Horizontally Curved Steel Girder Highway Bridges for Seismic Analysis

This article introduces a generic modeling approach that is suitable for static and dynamic analysis, and response assessment of highway bridges with varying levels of irregularities. The proposed approach and modeling recommendations are based on grillage modeling rules that allows explicit representation of various types of details and components. The validity and accuracy of the proposed approach is demonstrated against three-dimensional finite element models as well as experimentally recorded response various benchmark bridges. While achieving remarkable accuracy, the required analysis time was also reduced up to 80%, making the proposed approach suitable for computationally intensive studies.     

Geographical and Temporal Weighted Regression (GTWR)

Both space and time are fundamental in human activities as well as in various physical processes. Spatiotemporal analysis and modeling has long been a major concern of geographical information science (GIScience), environmental science, hydrology, epidemiology, and other research areas. Although the importance of incorporating the temporal dimension into spatial analysis and modeling has been well recognized, challenges still exist given the complexity of spatiotemporal models. Of particular interest in this article is the spatiotemporal modeling of local nonstationary processes. Specifically, an extension of geographically weighted regression (GWR), geographical and temporal weighted regression (GTWR), is developed in order to account for local effects in both space and time. An efficient model calibration approach is proposed for this statistical technique. Using a 19‐year set of house price data in London from 1980 to 1998, empirical results from the application of GTWR to hedonic house price modeling demonstrate the effectiveness of the proposed method and its superiority to the traditional GWR approach, highlighting the importance of temporally explicit spatial modeling.     

Spurious weather effects

Rainfall is exogenous to human actions and hence popular as an exogenous source of variation. But it is also spatially correlated. This can generate spurious relationships between rainfall and other spatially correlated outcomes. As an illustration, rainfall on almost any day of the year has seemingly high predictive power of electoral turnout in Norwegian municipalities. In Monte Carlo analyses, I find that standard tests reject true null hypotheses in as much as 99% of cases. Standard approaches to estimating consistent standard errors do not solve the problem. Instead, I suggest controlling for spatial and spatiotemporal trends using multidimensional polynomials.     

Bidimensional Regression

Since its invention by Francis Galton in 1877 regression analysis has been found useful in almost all disciplines. Comparison of geographic phenomena requires a two-dimensional extension of this technique. In this manner geographic maps can be compared with each other. Possible applications include geometric comparison of ancient and modern maps, or of “mental” maps, or for rubber-sheeting as used in Geographic Information Systems and in remote sensing. Other applications, for example, in biology for the comparison of shapes of leaves, fish, faces, or skulls after the manner of D'Arcy W. Thompson are also possible, as are higher-dimensional and multivariate cases. The method implements, and puts into this new context, existing models from the field of cartography. The linear case yields an easy definition of a Pearsonian-like correlation coefficient. The bidimensional case is richer in mathematical options than is the usual unidimensional version. The curvilinear case is of even greater utility. Here the regression coefficients constitute a spatially varying, but coordinate invariant, second-order tensor field defined by the matrix of partial derivatives of the transformation. This can be shown to be essentially equivalent to Tissot's Indicatrix, used in cartography to determine the properties of a map projection. In a computer implementation a nonparametric approach allows visualization of the regression by automatically plotting the pair of scatter diagrams, drawing of the displacement field, differentiable smooth interpolation of the warped coordinates and predicted image, by a diagram of the principal strains, and with contour maps of the estimated local angular, areal, and total distortion.     

Accuracy evaluation of the semi-automatic 3D modeling for historical building information models

It is stated that 3D recording and modeling of heritage buildings entail accurate building models (as-built). However, this paper presents an analysis of the 3D modeling accuracy for the creation of historical building information models (HBIM), considering the complexity and the deformations of historical buildings, using point cloud data and BIM tools. The 3D modeling processes analyzed are based on a three-stage semi-automatic approach leading to the generation of HBIM, including manual and automatic processes. The three stages consist of: (a) optical and terrestrial laser scanning; (b) meshing processes; and finally (c) 3D solid modeling to be assembled into HBIM. Next, this approach analyzed the mesh deformations generated automatically in comparison to the initial point cloud data. The deformations and the accuracy evaluation have been undertaken using different commercial software. Finally, our modeling approach shows that it can improve the accuracy of the 3D models achieved using existing BIM technologies.     

Local Forms of Spatial Analysis

Local forms of spatial analysis focus on exceptions to the general trends represented by more traditional global forms of spatial analysis. There is currently a rapid expansion in the development of such techniques but their history almost exactly parallels that of Geographical Analysis, with the first examples of local analysis appearing in the late 1960s. Indeed, Geographical Analysis has published many of the significant contributions in this field. This paper reviews the development of local forms of spatial analysis and assesses the current situation. Following a discussion on the nature and importance of local analysis, examples are given of local forms of point pattern analysis; local graphical approaches; local measures of spatial dependency; the spatial expansion method; adaptive filtering; multilevel modeling; geographically weighted regression; random coefficients models; autoregressive models; and local forms of spatial interaction models.     

Designs for Detecting Spatial Dependence

The aim of this article is to find optimal or nearly optimal designs for experiments to detect spatial dependence that might be in the data. The questions to be answered are: how to optimally select predictor values to detect the spatial structure (if it is existent) and how to avoid to spuriously detect spatial dependence if there is no such structure. The starting point of this analysis involves two different linear regression models: (1) an ordinary linear regression model with i.i.d. error terms—the nonspatial case and (2) a regression model with a spatially autocorrelated error term, a so-called simultaneous spatial autoregressive error model. The procedure can be divided into two main parts: The first is use of an exchange algorithm to find the optimal design for the respective data collection process; for its evaluation an artificial data set was generated and used. The second is estimation of the parameters of the regression model and calculation of Moran's I , which is used as an indicator for spatial dependence in the data set. The method is illustrated by applying it to a well-known case study in spatial analysis.     

Variations in the Spatial Pattern of Settlement Locations: An Analysis Based on Proportional Hazards Models

Models based on hazard functions are used to analyze spatial trends in the distance intervals separating point locations. The proportional hazards model, which has been widely applied to analyze intervals of time, is used to investigate variation in the spacing of settlements in Nebraska. This model allows spatial trends in the intervals between settlements to be investigated under very general conditions regarding the interdependence of settlement locations and permits the coordinate locations of the intervals to be treated as spatially varying covariates. An empirical analysis reveals an East-West trend in the spacing of settlements.