Nationwide Freight Generation Models: A Spatial Regression Approach

This paper investigates the application of linear regression models and modeling techniques in predicting freight generation at the national level within the U.S. Specifically, the paper seeks to improve the performance and fit of linear regression models of freight generation. We provide insight into different variable transformation techniques, evaluate the use of spatial regression variables, and apply a spatial regression modeling methodology to correct for spatial autocorrelation. We conclude that the spatial regression model is the preferred specification for freight generation at the national level. The proliferation of Geographic Information Systems (GIS) within planning agencies affords more widespread use of spatial regression and our results indicate this technique would provide improvement to models that have been traditionally limited by insufficient data.     

基于最小拟合误差平方和准则的空间聚类

在一些回归分析问题中，数据来自于空间对象的非空间属性．许多问题中不用考虑空间属性，而直接分析非空间属性．如果在整个问题空间中，对象空间差异较大，需要将空间对象划分为若干子空间，子空间对应的局域回归模型，可以减小空间差异性的影响．针对子空间连通性约束情况下空间对象的局域回归分析问题，提出基于最小拟合误差平方和准则的空间划分方法，从一个空间的初始划分开始，按照拟合误差平方和下降的原则调整子空间边界，获得新的空间划分和对应的回归模型，不断迭代直到准则函数收敛．     

An empirical evaluation of spatial regression models

Conventional statistical methods are often ineffective to evaluate spatial regression models. One reason is that spatial regression models usually have more parameters or smaller sample sizes than a simple model, so their degree of freedom is reduced. Thus, it is often unlikely to evaluate them based on traditional tests. Another reason, which is theoretically associated with statistical methods, is that statistical criteria are crucially dependent on such assumptions as normality, independence, and homogeneity. This may create problems because the assumptions are open for testing. In view of these problems, this paper proposes an alternative empirical evaluation method. To illustrate the idea, a few hedonic regression models for a house and land price data set are evaluated, including a simple, ordinary linear regression model and three spatial models. Their performance as to how well the price of the house and land can be predicted is examined. With a cross-validation technique, the prices at each sample point are predicted with a model estimated with the samples excluding the one being concerned. Then, empirical criteria are established whereby the predicted prices are compared with the real, observed prices. The proposed method provides an objective guidance for the selection of a suitable model specification for a data set. Moreover, the method is seen as an alternative way to test the significance of the spatial relationships being concerned in spatial regression models.     

Bayesian modelling strategies for spatially varying regression coefficients: A multivariate perspective for multiple outcomes

The modelling of spatially varying regression effects for multivariate mortality count outcomes is investigated. Alternative approaches to spatial regression heterogeneity are considered: the multivariate normal conditional autoregressive (MCAR) model is contrasted with a flexible set of priors based on the multiple membership approach. These include spatial factor priors and a non-parametric approach based on the Dirichlet process. A case study considers varying regression effects for a bivariate suicide outcome, namely male and female suicides in 354 English local authorities with social deprivation, social fragmentation and rurality as predictors.     

A systematic investigation of geostatistical image fusion for the improvement of the spectral fidelity and spatial detail in Landsat MS imagery

This is the first systematic investigation into the assumptions of image fusion using regression Kriging (RK) – a geostatistical method – illustrated with Landsat MS (multispectral) and SPOT (Satellite Pour l’Observation de la Terre) panchromatic images. The efficiency of different linear regression and Kriging methods in the fusion process is examined by visual and quantitative indicators. Results indicate a trade-off between spectral fidelity and spatial detail preservation for the GLS (generalized least squares regression) and OLS (ordinary least squares regression) methods in the RK process: OLS methods preserve more spatial detail, while GLS methods retain more spectral information from the MS images but at a greater computational cost. Under either OK (ordinary Kriging) or UK (universal Kriging) with either OLS or GLS, the spherical variogram improves spatial details from the panchromatic image, while the exponential variogram maintains more spectral information from the MS image. Overall, RK-based fusion methods outperform conventional fusion approaches from both the spectral and spatial point of view.     

Spatial contextual classification and prediction models for mining geospatial data

Modeling spatial context (e.g., autocorrelation) is a key challenge in classification problems that arise in geospatial domains. Markov random fields (MRF) is a popular model for incorporating spatial context into image segmentation and land-use classification problems. The spatial autoregression (SAR) model, which is an extension of the classical regression model for incorporating spatial dependence, is popular for prediction and classification of spatial data in regional economics, natural resources, and ecological studies. There is little literature comparing these alternative approaches to facilitate the exchange of ideas. We argue that the SAR model makes more restrictive assumptions about the distribution of feature values and class boundaries than MRF. The relationship between SAR and MRF is analogous to the relationship between regression and Bayesian classifiers. This paper provides comparisons between the two models using a probabilistic and an experimental framework.     

基于地理加权回归克里金的中国PM_(2.5)浓度空间制图方法北大核心CSCD

空气细颗粒物健康暴露风险等研究需要准确的PM_(2.5)浓度时空分布信息作为健康评估的重要输入。然而,由于监测台站稀疏分布,通常需要融合遥感等辅助信息,通过空间制图模型得到PM_(2.5)浓度的分布状况。如何在估计模型中将PM_(2.5)浓度的空间分布特征融入制图模型将是提高PM_(2.5)制图精度的关键。发展了一种融合地理加权回归和克里金插值方法的混合模型:地理加权回归克里金(Geographically Weighted Regression-Kriging,GWRK),地理加权回归模型考虑PM_(2.5)浓度分布的空间异质性,克里金模型对回归后的残差中存在的空间自相关性进行建模。基于该方法,利用中国空气质量监测站数据,采用遥感、模式模拟数据作为辅助信息,对2017年中国逐月的PM_(2.5)浓度分布进行估计空间制图。交叉验证结果表明,GWRK相较于传统制图方法(最小二乘回归、地理加权回归、回归克里金)具有更高的精度,决定系数R2为0.824,平均绝对误差为6.96μg/m3,均方根误差为10.94μg/m3。2017年逐月的PM_(2.5)浓度制图结果显示,在时间上,冬季是PM_(2.5)污染最严重的时段,夏季最轻,空间上,东部经济较为发达的城市如长三角地区是污染严重区,西南地区污染程度较轻。     

Mapping the richness and composition of British breeding birds from coarse spatial resolution satellite sensor imagery

Remote sensing has great potential as a source of information on biodiversity over large areas. Past studies have generally focused on species richness, used aspatial statistical techniques and highlighted scale‐dependent results. Here, a fuller assessment of avian biodiversity, considering species richness and composition, was undertaken for breeding bird species in Great Britain from NDVI and temperature data derived from NOAA AVHRR imagery. Broad classes of bird species composition defined by an ordination analysis exhibited a high degree of separability, with classification accuracies (based on training data) of up to 77.3% observed. Although only 18.1% of the variance in species richness could be explained by a conventional aspatial regression analysis it was apparent from geographically weighted regression analyses that the relationship between species richness and the remotely sensed response was significantly non‐stationary. Relative to the standard regression, geographically weighted analyses yielded models that provided stronger relationships and highlighted the spatial dependence of the relationship. Marked spatial variation in the regression model parameters and explanatory power were evident within and between scales. The results indicated the ability to characterize aspects of biodiversity from coarse spatial resolution remote sensing data and highlight the need to accommodate for the effects of spatial non‐stationarity in the relationship.     

Data augmentation strategies for the Bayesian spatial probit regression model

The well known latent variable representation of the Bayesian probit regression model due to Albert and Chib (1993) allows model fitting to be performed using a simple Gibbs sampler. In addition, various types of dependence among categorical outcomes not explained by covariate information can be accommodated in a straightforward manner as a result of this latent variable representation of the model. One example of this is the spatial probit regression model for spatially-referenced categorical outcomes. In this setting, commonly used covariance structures for describing residual spatial dependence in the normal linear model setting can be imbedded into the probit regression model. Capturing spatial dependence in this way, however, can negatively impact the performance of MCMC model-fitting algorithms, particularly in terms of mixing and sensitivity to starting values. To address these computational issues, we demonstrate how the non-identifiable spatial variance parameter can be used to create data augmentation MCMC algorithms. We compare the performance of several non-collapsed and partially collapsed data augmentation MCMC algorithms through a simulation study and an analysis of land cover data.     

Modeling urban growth using spatially heterogeneous cellular automata models: Comparison of spatial lag,spatial error and GWR

Many methods can be used to construct geographical cellular automata (CA) models of urban land use, but most do not adequately capture spatial heterogeneity in urban dynamics. Spatial regression is particularly appropriate to address the problem to reproduce urban patterns. To examine the advantages and disadvantages of spatial regression, we compare a spatial lag CA model (SLM-CA), a spatial error CA model (SEM-CA) and a geographically-weighted regression CA model (GWR-CA) by simulating urban growth at Nanjing, China. Each CA model is calibrated from 1995 to 2005 and validated from 2005 to 2015. Among these, SLM and SEM are spatial autoregressive (SAR) models that consider spatial autocorrelation of urban growth and yield highly similar land transition probability maps. Both SAR-CA and GWR-CA accurately reproduce urban growth at Nanjing during the calibration and validation phases, yielding overall accuracies (OAs) exceeding 94% and 85%, respectively. SAR-CA is superior in simulating urban growth when measured by OA and figure-of-merit (FOM) while GWR-CA is superior regarding the ability to address spatial heterogeneity. A concentric ring buffer-based assessment shows OA valleys that correspond to FOM peaks, where the ranges of valleys and peaks indicate the areas with active urban development. By comparison, SAR-CA captures more newly-urbanized patches in highly-dense urban areas and shows better performance in terms of simulation accuracy; whereas, GWR-CA captures more in the suburbs and shows better ability to address spatial heterogeneity. Our results demonstrate that spatial regression can help produce accurate simulations of urban dynamics featured by spatial heterogeneity, either implicitly or explicitly. Our work should help select appropriate CA models of urban growth in different terrain and socioeconomic contexts.     

Spatial dependence-based fuzzy regression clustering

Fuzzy clustering based regression analysis is a novel hybrid approach to capture the linear structure while considering the classification structure of the measurement. Using the concept that weights provided via the fuzzy degree of clustering, some regression models have been proposed in literature. In these models, membership values derived from clustering or some weights obtained from geometrical functions are employed as the weights of regression system. This paper addresses a weighted fuzzy regression analysis based on spatial dependence measure of the memberships. By the methodology presented in this paper, the relative weights are used in fuzzy regression models instead of direct membership values or their geometrical transforms. The experimental studies indicate that the spatial dependence based analyses yield more reliable results to show the correlation of the independent variables into the dependent variable. In addition, it has been observed that spatial dependence based models have high estimation and generalization capacities.     

Spatial analysis in ecological risk assessment: Pollutant bioaccumulation in clams Tapes philipinarum in the Venetian lagoon (Italy)

Exposure characterization is a central step in Ecological Risk Assessment (ERA). Exposure level is a function of the spatial factors linking contaminants and receptors, yet exposure estimation models are traditionally non-spatial. Non-spatial models are prone to the adverse effects of spatial dependence: inflated variance and biased inferential procedures, which can result in unreliable and potentially misleading models. Such negative effects can be amended by spatial regression modelling: we propose an integration of geostatistics and multivariate spatial regression to compute efficient spatial regression parameters and to characterize exposure at under-sampled locations. The method is applied to estimate bioaccumulation models of organic and inorganic micropollutants in the tissues of the clam Tapes philipinarum. The models link bioaccumulation of micropollutants in clam tissue to a set of environmental variables sampled in the lagoon sediment. The Venetian lagoon case study exemplifies the problem of multiple variables sampled at different locations or spatial units: we propose and test an effective solution to this common and serious problem in environmental as well as socio-economic multivariate analysis.     

Geoadditive expectile regression

Quantile regression has emerged as one of the standard tools for regression analysis that enables a proper assessment of the complete conditional distribution of responses even in the presence of heteroscedastic errors. Quantile regression estimates are obtained by minimising an asymmetrically weighted sum of absolute deviations from the regression line, a decision theoretic formulation of the estimation problem that avoids a full specification of the error term distribution. Recent advances in mean regression have concentrated on making the regression structure more flexible by including nonlinear effects of continuous covariates, random effects or spatial effects. These extensions often rely on penalised least squares or penalised likelihood estimation with quadratic penalties and may therefore be difficult to combine with the linear programming approaches often considered in quantile regression. As a consequence, geoadditive expectile regression based on minimising an asymmetrically weighted sum of squared residuals is introduced. Different estimation procedures are presented including least asymmetrically weighted squares, boosting and restricted expectile regression. The properties of these procedures are investigated in a simulation study and an analysis on rental fees in Munich is provided where the geoadditive specification allows for an analysis of nonlinear effects of the size of flats or the year of construction and the spatial distribution of rents simultaneously.     

Linking watershed-scale stream health and socioeconomic indicators with spatial clustering and structural equation modeling

In this study, spatial clustering techniques were used in combination with Structural Equation Modeling (SEM) to characterize the relationships between in-stream health indicators and socioeconomic measures of communities. The study area is the Saginaw River Watershed in Michigan. Four measures of stream health were considered: the Index of Biological Integrity, Hilsenhoff Biotic Index, Family Index of Biological Integrity, and number of Ephemeroptera, Plecoptera, and Trichoptera taxa. The stream health indicators were predicted using nine socioeconomic variables that capture vulnerability in population. The results of spatial clustering showed that incorporating clustering configuration improves the model prediction. A total of 510 Confirmatory Factor Analysis (CFAs) and 85 multivariate regression models were developed for each spatial cluster within the watershed and compared with the model performance without spatial clustering (at the watershed level). In general, watershed level CFAs outperformed cluster level CFAs, while the reverse was true for the regression models.     

Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler?

A Gibbs sampler for a Poisson regression model including spatial effects is presented and evaluated. The approach is based on that a Poisson regression model can be transformed into an approximate normal linear model by data augmentation using the introduction of two sequences of latent variables. It is shown how this methodology can be extended to spatial Poisson regression models and details of the resulting Gibbs sampler are given. In particular, the influence of model parameterisation and different update strategies on the mixing of the MCMC chains is discussed. The developed Gibbs samplers are analysed in two simulation studies and applied to model the expected number of claims for policyholders of a German car insurance company. The mixing of the Gibbs samplers depends crucially on the model parameterisation and the update schemes. The best mixing is achieved when collapsed algorithms are used, reasonable low autocorrelations for the spatial effects are obtained in this case. For the regression effects however, autocorrelations are rather high, especially for data with very low heterogeneity. For comparison a single component Metropolis-Hastings algorithms is applied which displays very good mixing for all components. Although the Metropolis-Hastings sampler requires a higher computational effort, it outperforms the Gibbs samplers which would have to be run considerably longer in order to obtain the same precision of the parameters.     

Knowledge Discovery in Multiple Spatial Databases

In this paper, a new approach for centralised and distributed learning from spatial heterogeneous databases is proposed. The centralised algorithm consists of a spatial clustering followed by local regression aimed at learning relationships between driving attributes and the target variable inside each region identified through clustering. For distributed learning, similar regions in multiple databases are first discovered by applying a spatial clustering algorithm independently on all sites, and then identifying corresponding clusters on participating sites. Local regression models are built on identified clusters and transferred among the sites for combining the models responsible for identified regions. Extensive experiments on spatial data sets with missing and irrelevant attributes, and with different levels of noise, resulted in a higher prediction accuracy of both centralised and distributed methods, as compared to using global models. In addition, experiments performed indicate that both methods are computationally more efficient than the global approach, due to the smaller data sets used for learning. Furthermore, the accuracy of the distributed method was comparable to the centralised approach, thus providing a viable alternative to moving all data to a central location.     

Data Fusion in Radial Basis Function Networks for Spatial Regression

Conventional radial basis function (RBF) networks for spatial regression assume independent and identical distribution and ignore spatial information. In contrast to input fusion, we push spatial information further into RBF networks by fusing output from hidden and output layers. Three case studies demonstrate the advantage of hidden fusion over others and indicate the optimal value is around 1 for the coefficient used in hidden fusion, which links the output from the hidden layer for each site with their neighbors.     

Investigating spatial non-stationary and scale-dependent relationships between urban surface temperature and environmental factors using geographically weighted regression

Despite growing concerns for the variation of urban thermal environments and driving factors, relatively little attention has been paid to issues of spatial non-stationarity and scale-dependence, which are intrinsic properties of the urban ecosystem. In this paper, using Shenzhen City in China as a case study, a geographically weighted regression (GWR) model is used to explore the scale-dependent and spatial non-stationary relationships between urban land surface temperature (LST) and environmental determinants. These determinants include the distance between city and highway, patch richness density of forestland, wetland, built-up land and unused land and topographic factors such as elevation and slope aspect. For reference, the ordinary least squares (OLS) model, a global regression technique, was also employed, using the same response variable and explanatory variables as in the GWR model. The results indicate that the GWR model not only provides a better fit than the traditional OLS model, but also provides local detailed information about the spatial variation of LST, which is affected by geographical and ecological factors. With the GWR model, the strength of the regression relationships increased significantly, with a mean of 59% of the changes in the LST values explained by the predictors, compared with only 43% using the OLS model. By computing a stationarity index, one finds that different predictors have different variational trends which tend towards the stationary state with the coarsening of the spatial scale. This implies that underlying natural processes affecting the land surface temperature and its spatial pattern may operate at different spatial scales. In conclusion, the GWR model is an alternative approach to addressing spatial non-stationary and scale-dependent problems in geography and ecology.     

Block-regression based fusion of optical and SAR imagery for feature enhancement

This paper focuses on the establishment of a pixel-level fusion framework for optical and synthetic aperture radar (SAR) images to combine these two types of remotely sensed imagery for feature enhancement. We have proposed a new fusion technique, namely block-based synthetic variable ratio (Block-SVR), which is a technique based on multiple linear regression of block regions to fuse optical and SAR imagery. In order to investigate the effectiveness of the method, the fusion results of a higher resolution airborne SAR image and a lower resolution multispectral image are presented. According to the fusion results, the fused images have enhanced certain features, namely the spatial and textural content and features that are invisible in multispectral images, while preserving colour characteristics. The spectral, spatial and textural effects of the presented algorithm were also evaluated mainly by visual and quantitative methods, and compared to those of intensity-hue-saturation (IHS), principal component analysis (PCA) and wavelet-based methods. During the implementation of the block-regression based technique there are at least two advantages. One is that the block-regression based technique drastically decreases the amount of computation, whereas regression of the whole scene image is almost impossible. The other, most important, advantage is that adjustment of regressed block size can result in different emphasis between preservation of spectral characteristics and enhancement of spatial and textural content. The larger the regression block, the more the spatial and textural details are enhanced. In contrast, the smaller the regression block, the more the spectral features are preserved. The assessments indicate that the block-regression based method is more flexible than others, because it can achieve a satisfactory trade-off between preservation of spectral characteristics and enhancement of spatial and textural content by selection of optimal block size with respect to visual interpretation and mapping. This paper also proposes a scheme for the fusion of SPOT5 panchromatic, XS images with airborne SAR images using the block-regression based technique.     

The Size and Power of Bootstrap Tests for Spatial Dependence in a Linear Regression Model

In this paper, we define the spatial bootstrap test as a residual-based bootstrap method for hypothesis testing of spatial dependence in a linear regression model. Based on Moran’s I statistic, the empirical size and power of bootstrap and asymptotic tests for spatial dependence are evaluated and compared. Under classical normality assumption of the model, the performance of the spatial bootstrap test is equivalent to that of the asymptotic test in terms of size and power. For more realistic heterogeneous non-normal distributional models, the applicability of asymptotic normal tests is questionable. Instead, spatial bootstrap tests have shown superiority in smaller size distortion and higher power when compared to asymptotic counterparts, especially for cases with a small sample and dense spatial contiguity. Our Monte Carlo experiments indicate that the spatial bootstrap test is an effective alternative to the theoretical asymptotic approach when the classical distributional assumption is violated.