Examining the influences of air quality in China's cities using multi‐scale geographically weighted regression

This study evaluates the influences of air pollution in China using a recently proposed model—multi‐scale geographically weighted regression (MGWR). First, we review previous research on the determinants of air quality. Then, we explain the MGWR model, together with two global models: ordinary least squares (OLS) and OLS containing a spatial lag variable (OLSL) and a commonly used local model: geographically weighted regression (GWR). To detect and account for any variation of the spatial autocorrelation of air pollution over space, we construct two extra local models which we call GWR with lagged dependent variable (GWRL) and MGWR with lagged dependent variable (MGWRL) by including the lagged form of the dependent variable in the GWR model and the MGWR model, respectively. The performances of these six models are comprehensively examined and the MGWR and MGWRL models outperform the two global models as well as the GWR and GWRL models. MGWRL is the most accurate model in terms of replicating the observed air quality index (AQI) values and removing residual dependency. The superiority of the MGWR framework over the GWR framework is demonstrated—GWR can only produce a single optimized bandwidth, while MGWR provides covariate‐specific optimized bandwidths which indicate the different spatial scales that different processes operate.     

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.     

Spatial models with spatially lagged dependent variables and incomplete data

The purpose of this paper is to suggest estimators for the parameters of spatial models containing a spatially lagged dependent variable, as well as spatially lagged independent variables, and an incomplete data set. The specifications allow for nonstationarity, and the disturbance process of the model is specified non-parametrically. We consider various scenarios concerning the pattern of missing data points. One estimator we suggest is based on a smaller but complete subset of the sample; another is based on a larger but incomplete subset of the sample. We give large sample results for both of these cases.     

Spatial autocorrelation and the sensitivity of RESET: a simulation study

Ramsey’s regression specification error test (RESET) is thought to be robust to spatial correlation. Building on the literature on spurious spatial regression, we show that this is not so in presence of spatial correlation in both the error and the independent variable of an econometric model. Correcting the test for spatial correlation improves its performance, though in large samples this strategy is not completely successful. Once assuming that spatial autocorrelation in both the independent variable and in the error is produced by a spatial moving average model instead of a spatial autoregressive one, RESET displays more robustness.     

The hierarchical tessellation model and its use in spatial analysis

The hierarchid tessellation model belongs to a class of spatial data models based on the recursive decomposition of space. The quadtree is one such tessellation and is characterized by square cells and a 1:4 decomposition ratio. To relax these constraints in the tessellation, a generalized hierarchical tessellation data model, called Adaptive Recursive Tessellations (ART), has been proposed. ART increases flexibility in the tessellation by the use of rectangular cells and variable decomposition ratios. In ART, users can specify cell sizes which are intuitively meaningful to their applications, or which can reflect the scales of data. ART is implemented in a data structure called Adaptive Recursive Run-Encoding (ARRE), which is a variant of two-dimensional run-encoding whose running path can vary with the different tessellation structures incorporated in an ART model. Given the recognition of the benefits of implementing statistical spatial analysis in GIS, the use of hierarchical tessellation models such as ART in spatial analysis is discussed. Three examples are introduced to show how ART can: (1) be applied to solve the quadrat size problem in quadrat analysis of point patterns; (2) act as the data model in the variable resolution block kriging technique for geostatistical data to reduce variation in kriging error; and (3) facilitate the evaluation of spatial autocorrelation for area data at multiple map resolutions via the construction of a connectivity matrix for calculating spatial autocorrelation indices based on ARRE.     

Predictive fire occurrence modelling to improve burned area estimation at a regional scale: A case study in East Caprivi,Namibia

Fires threaten human lives, property and natural resources in Southern African savannas. Due to warming climate, fire occurrence may increase and fires become more intense. It is crucial, therefore, to understand the complexity of spatiotemporal and probabilistic characteristics of fires. This study scrutinizes spatiotemporal characteristics of fires and the role played by abiotic, biotic and anthropogenic factors for fire probability modelling in a semiarid Southern African savanna environment. The MODIS fire products: fire hot spots (MOD14A2 and MYD14A2) and burned area product MODIS (MCD45A1), and GIS derived data were used in analysis. Fire hot spots occurrence was first analysed, and spatial autocorrelation for fires investigated, using Moran's I correlograms. Fire probability models were created using generalized linear models (GLMs). Separate models were produced for abiotic, biotic, anthropogenic and combined factors and an autocovariate variable was tested for model improvement. The hierarchical partitioning method was used to determine independent effects of explanatory variables. The discriminating ability of models was evaluated using area under the curve (AUC) from the receiver operating characteristic (ROC) plot. The results showed that 19.2–24.4% of East Caprivi burned when detected using MODIS hot spots fire data and these fires were strongly spatially autocorrelated. Therefore, the autocovariate variable significantly improved fire probability models when added to them. For autologistic models, i.e. models accounting for spatial autocorrelation, discrimination was good to excellent (AUC 0.858–0.942). For models not counting spatial autocorrelation, prediction success was poor to moderate (AUC 0.542–0.745). The results of this study clearly showed that spatial autocorrelation has to be taken in to account in the fire probability model building process when using remotely sensed and GIS derived data. This study also showed that fire probability models accounting for spatial autocorrelation proved to be superior in regional scale burned area estimation when compared with MODIS burned area product (MCD45A1).     

Understanding the Combined Impacts of Aggregation and Spatial Non‐Stationarity: The Case of Migration‐Environment Associations in Rural South Africa

Socio‐demographic data are typically collected at various levels of aggregation, leading to the modifiable areal unit problem. Spatial non‐stationarity of statistical associations between variables further influences the demographic analyses. This study investigates the implications of these two phenomena within the context of migration‐environment associations. Global and local statistical models are fit across increasing levels of aggregation using household level survey data from rural South Africa. We raise the issue of operational scale sensitivity, which describes how the explanatory power of certain variables depends on the aggregation level. We find that as units of analysis (households) are aggregated, some variables become non‐significant in the global models, while others are less sensitive to aggregation. Local model results show that aggregation reduces spatial variation in migration‐related local associations but also affects variables differently. Spatial non‐stationarity appears to be the driving force behind this phenomenon as the results from the global model mask this relationship. Operational scale sensitivity appears related to the underlying spatial autocorrelation of the non‐aggregated variables but also to the way a variable is constructed. Understanding operational scale sensitivity can help to refine the process of selecting variables related to the scale of analysis and better understand the effects of spatial non‐stationarity on statistical relationships.     

A Spatial Filtering Specification for an Auto-negative Binomial Model of Anopheles arabiensis Aquatic Habitats

This research accounts for spatial autocorrelation by including latent map pattern components as predictor variables in a malaria mosquito aquatic habitat model specification. The data used to derive the model was from a digitized grid-based algorithm, generated in an ArcInfo database, using QuickBird visible and near-infrared (NIR) data. The Feature Extraction (FX) Module in ENVI 4.4^® was used to categorize individual pixels of field sampled aquatic habitats into separate spectral classes, convert remotely sensed raster layers to vector coverages, and classify output layers to vector format as ESRI shapefiles. These data were used to construct a geographic weights matrix for evaluation of field and remote sampled covariates of Anopheles arabiensis aquatic habitats, a major vector of malaria in East Africa. The principal finding is that synthetic map pattern variables, which are eigenvectors computed for a geographic weights matrix, furnish an alternative way of capturing spatial dependency effects in the mean response term of a regression model. The spatial autocorrelation components suggest the presence of roughly 11 to 28% redundant information in the aquatic habitat larval count samples. The presence of redundant information in the models suggest that the sampling configuration of the An. arabiensis aquatic habitats, in the study sites, may cause field and remote observations of aquatic habitats to be dependent, rather than independent, moving data analysis away from the classical statistical independence model. A Poisson regression model, with a non-constant, gamma-distributed mean, can decompose field and remote sampled An. arabiensis data into positive and negative spatial autocorrelation eigenvectors, which can assess the precision of a malaria mosquito aquatic habitat map and the significance of all factors associated with larval abundance and distribution in a riceland agroecosystem.     

Discriminant Models of Uncertainty in Nominal Fields

Despite developments in error modeling in discrete objects and continuous fields, there exist substantial and largely unsolved conceptual problems in the domain of nominal fields. This article explores a novel strategy for uncertainty characterization in spatial categorical information. The proposed strategy is based on discriminant space, which is defined with essential properties or driving processes underlying spatial class occurrences, leading to discriminant models of uncertainty in area classes. This strategy reinforces consistency in categorical mapping by imposing class-specific mean structures that can be regressed against discriminant variables, and facilitates scale-dependent error modeling that can effectively emulate the variation found between observers in terms of classes, boundary positions, numbers of polygons, and boundary network topology. Based on simulated data, comparisons with stochastic simulation based on indicator kriging confirmed the replicability of the discriminant models, which work by determining the mean area classes based on discriminant variables and projecting spatially correlated residuals in discriminant space to uncertainty in area classes.     

无缝线性回归与预测模型

建立回归模型常采用最小二乘方法并忽略自变量观测误差。尽管同时顾及自变量和因变量观测误差的总体最小二乘方法近年来得到了广泛研究,但在模型预测时,依然忽略了待预测自变量的观测误差。对此,本文提出了一种严格考虑所有变量观测误差的无缝线性回归和预测模型,该模型将回归模型的建立和因变量预测联合处理,在建立回归模型过程中对待预测自变量的观测误差进行估计并修正,从而提高了模型预测效果。理论证明,现有的几种线性回归模型都是无缝线性回归和预测模型的特例。试验结果表明,无缝线性回归和预测模型的预测效果优于现有的几种模型,尤其在变量观测误差相关性较大时,无缝模型对预测效果的改善更为显著。     

Assessment of regression kriging for spatial interpolation – comparisons of seven GIS interpolation methods

As an important GIS function, spatial interpolation is one of the most often used geographic techniques for spatial query, spatial data visualization, and spatial decision-making processes in GIS and environmental science. However, less attention has been paid on the comparisons of available spatial interpolation methods, although a number of GIS models including inverse distance weighting, spline, radial basis functions, and the typical geostatistical models (i.e. ordinary kriging, universal kriging, and cokriging) are already incorporated in GIS software packages. In this research, the conceptual and methodological aspects of regression kriging and GIS built-in interpolation models and their interpolation performance are compared and evaluated. Regression kriging is the combination of multivariate regression and kriging. It takes into consideration the spatial autocorrelation of the variable of interest, the correlation between the variable of interest and auxiliary variables (e.g., remotely sensed images are often relatively easy to obtain as auxiliary variables), and the unbiased spatial estimation with minimized variance. To assess the efficiency of regression kriging and the difference between stochastic and deterministic interpolation methods, three case studies with strong, medium, and weak correlation between the response and auxiliary variables are compared to assess interpolation performances. Results indicate that regression kriging has the potential to significantly improve spatial prediction accuracy even when using a weakly correlated auxiliary variable.     

Exploring spatiotemporal dynamics in a housing market using the spatial vector autoregressive Lasso: A case study of Seoul,Korea

House prices fluctuate spatiotemporally and when influential changes from a region happen, the effects spread out in space over time. Although many studies have introduced various models to explain the spatiotemporal dynamics in housing markets, it is always challenging to consider both dimensions in a model. Some recent studies have identified spatiotemporal interactions of house prices by combining spatial and temporal models via spatial vector autoregression. The approach, however, assumes spatial homogeneity of the variables due to insufficient degrees of freedom. Since the housing market is generally conceived as heterogeneous, we suggest an alternative model of the spatial vector autoregressive Lasso without the homogeneity assumption. As an empirical example, we examine the spatiotemporal interaction between house sales price and rent in Seoul, Korea. The results show that rent for apartments in Gangnam‐gu, a socioeconomic core of Seoul, has positive impacts on rent for apartments in surrounding suburbs rather than their sales price. Moreover, the suggested model outperforms the classical method in terms of explanation, prediction, and autocorrelation of residuals. This research is expected to provide a methodological guide to explore the interaction between house sales price and rent, and insights into the spatiotemporal dynamics of the housing market in Seoul.     

Exploring the Impact of Non-normality on Spatial Non-stationarity in Geographically Weighted Regression Analyses: Tobacco Outlet Density in New Jersey

The principal rationale for applying geographically weighted regression (GWR) techniques is to investigate the potential spatial non-stationarity of the relationship between the dependent and independent variables—i.e., that the same stimulus would provoke different responses in different locations. The calibration of GWR employs a geographically weighted local least squares regression approach. To obtain meaningful inference, it assumes that the regression residual follows a normal or asymptotically normal distribution. In many classical econometric analyses, the assumption of normality is often readily relaxed, although it has been observed that such relaxation might lead to unreliable inference of the estimated coefficients' statistical significance. No studies, however, have examined the behavior of residual non-normality and its consequences for the modeled relationships in GWR. This study attempts to address this issue for the first time by examining a set of tobacco-outlet-density and demographic variables (i.e., percent African American residents, percent Hispanic residents, and median household income) at the census tract level in New Jersey in a GWR analysis. The regression residual using the raw data is apparently non-normal. When GWR is estimated using the raw data, we find that there is no significant spatial variation of the coefficients between tobacco outlet density and percentage of African American and Hispanics. After transforming the dependent variable and making the residual asymptotically normal, all coefficients exhibit significant variation across space. This finding suggests that relaxation of the normality assumption could potentially conceal the spatial non-stationarity of the modeled relationships in GWR. The empirical evidence of the current study implies that researchers should verify the normality assumption prior to applying GWR techniques in analyses of spatial non-stationarity.     

MODIS影像植被时空变化分析——以吉林省为例

利用2000至2006年的MODIS-NDVI影像数据,通过年最大NDVI随时间的变化斜率和对变化趋势的分区统计、重心分析及空间自相关分析,探索近年来吉林省植被的时空变化规律。吉林省大多数区域NDVI呈现出稳定或增加趋势,反映出吉林省植被生态系统有所恢复。植被变化趋势具有明显的空间分异特征,东部主要为稳定型,西部主要为增长型,局部区域有衰退迹象,主要分布在吉林省东南角和西南角、长春市市辖区及沿河沿湖地区。空间自相关分析表明,植被变化过程在研究区域内具有较强的空间正相关,即变化趋势在空间上具有趋同性,集聚现象明显。     

Establishing and assessing the Integrated Surface Drought Index (ISDI) for agricultural drought monitoring in mid-eastern China

Accurately monitoring the temporal, spatial distribution and severity of agricultural drought is an effective means to reduce the farmers’ losses. Based on the concept of the new drought index called VegDRI, this paper established a new method, named the Integrated Surface Drought Index (ISDI). In this method, the Palmer Drought Severity Index (PDSI) was selected as the dependent variable; for the independent variables, 12 different combinations of 14 factors were examined, including the traditional climate-based drought indicators, satellite-derived vegetation indices, and other biophysical variables. The final model was established by fully describing drought properties with the smaller average error (relative error) and larger correlation coefficients. The ISDI can be used not only to monitor the main drought features, including precipitation anomalies and vegetation growth conditions but also to indicate the earth surface thermal and water content properties by incorporating temperature information. Then, the ISDI was used for drought monitoring from 2000 to 2009 in mid-eastern China. The results for 2006 (a typical dry year) demonstrate the effectiveness and capability of the ISDI for monitoring drought on both the large and the local scales. Additionally, the multiyear ISDI monitoring results were compared with the actual drought intensity using the agro-meteorological disaster data recorded at the agro-meteorological sites. The investigation results indicated that the ISDI confers advantages in the accuracy and spatial resolution for monitoring drought and has significant potential for drought identification in China.     

DEM误差的空间自相关特征分析

采用空间自相关分析方法,从空间角度对数字高程数据误差的空间分布特征进行了研究。实验表明,利用双线性曲面表示地形表面时,产生的数字高程数据误差的全局Moran’sI指数趋近于0,在整个区域单元上的分布不存在显著的全局空间自相关,邻近区域单元上高程数据误差之间的关系在整体上既不综合表现为趋同,也不综合表现为趋异,高程数据误差的整体空间格局为随机格局;而且数字高程数据误差在空间上的分布与地形坡度和地表粗糙度有一定的联系,一般情况下,平均坡度、地表粗糙度越大,高程数据的全局Moran’sI指数偏离0稍远一些;否则,距离0近一些,但全局空间自相关仍不显著,在整体上表现为随机格局。     

Capturing the heterogeneity of urban growth in South Korea using a latent class regression model

This study aims to analyze the spatial patterns of urban growth in South Korea between 2000 and 2010. Fourteen suspected causative independent variables were selected and latent class regression (LCR) was used to analyze the relationship between dependent (urban growth) and independent (causative) variables. The goodness‐of‐fit was assessed by comparison to logistic regression (LR) analysis. The LR analysis produced consistent coefficients for each independent variable across the study area. In contrast, an LCR analysis, with a three‐class assumption, resulted in a different magnitude and directional effects of the coefficients for each class. The LCR analysis enabled the identification of both spatially homogeneous and heterogeneous areas. In addition, the LCR analysis performed better than the LR analysis with a lower Akaike information criterion and Bayesian information criterion value, and a higher receiver operating characteristic value. We conclude that LCR analysis should be used to establish causative “driving” factors for efficient urban growth planning and urban spatial policy.     

Important considerations about space‐time data: Modeling,scrutiny, and ratification

Space‐time data are becoming more abundant as time goes by, with hands‐on interest in them becoming more prevalent. These data have a very sensitive ordering in space and time, one that the simplest of recording errors can scramble. These data are also complex, containing both spatial and temporal autocorrelation coupled with their interaction. One goal of many researchers is to disentangle and account for these autocorrelation components in a parsimonious way. This article presents three competing model specifications to achieve this end. In addition, it outlines seven best practices for vetting space‐time datasets. This article cites a publicly available corrupt (containing at least errors of omission) rabies dataset to illustrate how a large volume of potentially valuable data can be rendered meaningless. In addition, it exemplifies postulated contentions about the United States National Cancer Institute Surveillance, Epidemiology, and End Results Program’s 1969–2018 population‐by‐county dataset, a collection of population counts held in high esteem. One major empirical finding is that this particular dataset exhibits traits that may merit remedial revisions action. A key conceptual finding is a suggested set of best practices for space‐time data proofreading. These two findings contribute to an ultimate goal of a large collection of certified open access space‐time datasets supporting repeatable and replicable scientific analyses.     

Accounting for Error When Modelling with Time Series Data: Estimating the Development of Crop Pests Throughout the Year

In order to attach some statement of reliability to mesoscale maps of how pest risk may develop over time, methods were developed to enable the detection and evaluation of errors in predictions that arise from the use of input data series from remote point sources. Firstly, we investigated how predicted model results may differ as a result of the ordering of the spatial interpolation and the model procedures. Principles of logic were used to detect errors occurring in the daily sequences of predicted pest development. Analyses of spatial autocorrelation within the gridded results showed that areas where a pest was predicted to reach a certain stage of development become more fragmented as a model run progressed over time. We identified that the less intensive approach of running a model only at data points and subsequently interpolating these to a grid can, in some cases, result in errors of logic and unrealistic degrees of autocorrelation. These errors occurred particularly when mapping a non-indigenous, marginal, pest at the later stages of its development. As a strategy for error evaluation, deterministic process models were run using point-based estimates of interpolated daily temperature to give RMS data errors at the sample points. This enabled us to investigate how the component of error related to sparsely distributed point data contributed to errors in the gridded estimates of pest development over time. The error detection and evaluation methods outlined are tractable and applicable to a wide variety of cases where point based models running over multiple time steps are extended to provide spatially continuous, landscape-wide, mappable results.