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.     

Knowledge Spillovers and Total Factor Productivity: Evidence Using a Spatial Panel Data Model

This article investigates the impact of knowledge capital stocks on total factor productivity (TFP) through the lens of the knowledge capital model proposed by Griliches (1979) , augmented with a spatially discounted cross-region knowledge spillover pool variable. The objective is to shift attention from firms and industries to regions and to estimate the impact of cross-region knowledge spillovers on TFP in Europe. The dependent variable is the region-level TFP, measured in terms of the superlative TFP index suggested by Caves, Christensen, and Diewert (1982) . This index describes how efficiently each region transforms physical capital and labor into output. The explanatory variables are internal and out-of-region stocks of knowledge, the latter capturing the contribution of cross-region knowledge spillovers. We construct patent stocks to proxy annual regional knowledge capital stocks for N =203 regions during 1997–2002. In estimating the effects, we implement a spatial panel data model that controls for spatial autocorrelation as well as individual heterogeneity across regions. The findings provide a fairly remarkable confirmation of the role of knowledge capital contributing to productivity differences among regions and add an important spatial dimension to discussions in the literature by showing that productivity effects of knowledge spillovers increase with geographic proximity.     

Exploring Spatial Process Dynamics Using Irregular Cellular Automaton Models

Cellular automaton models have enjoyed popularity in recent years as easily constructed models of many complex spatial processes, particularly in the natural sciences, and more recently in geography also. Most such models adopt a regular lattice (often a grid) as the basis for the spatial relations of adjacency that govern evolution of the model. A number of variations on the cellular automaton formalism have been introduced in geography but the impact of such variations on the likely behavior of the models has not been explored. This paper proposes a method for beginning to explore these issues and suggests that this is a new approach to the investigation of the relationships between spatial structure and dynamics of spatial processes. A framework for this exploration is suggested, and details of the required methods and measures are provided. In particular, a measure of spatial pattern—spatial information—based on entropy concepts is introduced. Initial results from investigation along the proposed lines are reported, which suggest that a distinction can he made between spatially robust and fragile processes. Some implications of this result and the methodology presented are briefly discussed.     

Lagrange Multiplier Test Diagnostics for Spatial Dependence and Spatial Heterogeneity

Several diagnostics for the assessment of model misspecification due to spatial dependence and spatial heterogeneity are developed as an application of the Lagrange Multiplier principle. The starting point is a general model which incorporates spatially lagged dependent variables, spatial residual autocorrelation and heteroskedasticity. Particular attention is given to tests for spatial residual autocorrelation in the presence of spatially lagged dependent variables and in the presence of heteroskedasticity. The tests are formally derived and illustrated in a number of simple empirical examples.     

A NEW SPATIAL MULTIPLE DISCRETE‐CONTINUOUS MODELING APPROACH TO LAND USE CHANGE ANALYSIS

This paper formulates a multiple discrete‐continuous probit (MDCP) land use model within a spatially explicit economic structural framework for land use change decisions. The spatial MDCP model is capable of predicting both the type and intensity of urban development patterns over large geographic areas, while also explicitly acknowledging geographic proximity‐based spatial dependencies in these patterns. At a methodological level, the paper focuses on specifying and estimating a spatial MDCP model that allows the dependent variable to exist in multiple discrete states with an intensity associated with each discrete state. The formulation also accommodates spatial dependencies, as well as spatial heterogeneity and heteroskedasticity, in the dependent variable, and should be applicable in a wide variety of fields where social and spatial dependencies between decision agents (or observation units) lead to spillover effects in multiple discrete‐continuous choices (or states). A simulation exercise is undertaken to evaluate the ability of the proposed maximum approximate composite marginal likelihood (MACML) approach to recover parameters from a cross‐sectional spatial MDCP model. The results show that the MACML approach does well in recovering parameters. An empirical demonstration of the approach is undertaken using the city of Austin parcel level land use data.     

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.     

A Multipopulation Comparison of the Diffusion of Public Organizations and Policies across Space and Time

This study examined the longitudinal spatial diffusion of state government policies and their related implementation organizations in the American states. The impact of coercive, institutional, and competitive processes on policy and state agency adoption were considered, as well as how aspects of the underlying policy can impact the degree of spatial diffusion. The rises of 27 different policy populations were analyzed over time, each representing not only a different policy form but a distinct implementation organization.
The policy adoption/spatial diffusion relationship across all populations was examined and results showed that the degree of spatial diffusion varied greatly. Analysis of potential relationship moderators indicated that federal impetus (coercive processes) led to an absence of spatial diffusion. Policies with an institutional basis also showed an absence of spatial diffusion while competition-based policies diffused spatially.     

Analyzing the Relationship Between Smoking and Coronary Heart Disease at the Small Area Level: A Bayesian Approach to Spatial Modeling

We model the relationship between coronary heart disease and smoking prevalence and deprivation at the small area level using the Poisson log-linear model with and without random effects. Extra-Poisson variability (overdispersion) is handled through the addition of spatially structured and unstructured random effects in a Bayesian framework. In addition, four different measures of smoking prevalence are assessed because the smoking data are obtained from a survey that resulted in quite large differences in the size of the sample across the census tracts. Two of the methods use Bayes adjustments of standardized smoking ratios (local and global adjustments), and one uses a nonparametric spatial averaging technique. A preferred model is identified based on the deviance information criterion. Both smoking and deprivation are found to be statistically significant risk factors, but the effect of the smoking variable is reduced once the confounding effects of deprivation are taken into account. Maps of the spatial variability in relative risk, and the importance of the underlying covariates and random effects terms, are produced. We also identify areas with excess relative risk.     

WHERE IS THE ECONOMICS IN SPATIAL ECONOMETRICS?*

ABSTRACT Spatial econometrics has been criticized by some economists because some model specifications have been driven by data‐analytic considerations rather than having a firm foundation in economic theory. In particular, this applies to the so‐called W matrix, which is integral to the structure of endogenous and exogenous spatial lags, and to spatial error processes, and which are almost the sine qua non of spatial econometrics. Moreover, it has been suggested that the significance of a spatially lagged dependent variable involving W may be misleading, since it may be simply picking up the effects of omitted spatially dependent variables, incorrectly suggesting the existence of a spillover mechanism. In this paper, we review the theoretical and empirical rationale for network dependence and spatial externalities as embodied in spatially lagged variables, arguing that failing to acknowledge their presence at least leads to biased inference, can be a cause of inconsistent estimation, and leads to an incorrect understanding of true causal processes.     

Unconditional Maximum Likelihood Estimation of Linear and Log-Linear Dynamic Models for Spatial Panels

This article hammers out the estimation of a fixed effects dynamic panel data model extended to include either spatial error autocorrelation or a spatially lagged dependent variable. To overcome the inconsistencies associated with the traditional least-squares dummy estimator, the models are first-differenced to eliminate the fixed effects and then the unconditional likelihood function is derived taking into account the density function of the first-differenced observations on each spatial unit. When exogenous variables are omitted, the exact likelihood function is found to exist. When exogenous variables are included, the pre-sample values of these variables and thus the likelihood function must be approximated. Two leading cases are considered: the Bhargava and Sargan approximation and the Nerlove and Balestra approximation. As an application, a dynamic demand model for cigarettes is estimated based on panel data from 46 U.S. states over the period from 1963 to 1992.     

Balancing Spatial and Non-Spatial Variation in Varying Coefficient Modeling: A Remedy for Spurious Correlation

This study discusses the importance of balancing spatial and non-spatial variation in spatial regression modeling. Unlike spatially varying coefficients (SVC) modeling, which is popular in spatial statistics, non-spatially varying coefficients (NVC) modeling has largely been unexplored in spatial fields. Nevertheless, as we will explain, consideration of non-spatial variation is needed not only to improve model accuracy but also to reduce spurious correlation among varying coefficients, which is a major problem in SVC modeling. We consider a Moran eigenvector approach modeling spatially and non-spatially varying coefficients (S&NVC). A Monte Carlo simulation experiment comparing our S&NVC model with existing SVC models suggests both modeling accuracy and computational efficiency for our approach. Beyond that, somewhat surprisingly, our approach identifies true and spurious correlations among coefficients nearly perfectly, even when usual SVC models suffer from severe spurious correlations. It implies that S&NVC model should be used even when the analysis purpose is modeling SVCs. Finally, our S&NVC model is employed to analyze a residential land price data set. Its results suggest existence of both spatial and non-spatial variation in regression coefficients in practice. The S&NVC model is now implemented in the R package spmoran.     

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.     

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 TRANSLOG APPROACH TO CONSUMER SPATIAL BEHAVIOR*

With the view that travel behavior stems from the principle of utility maximization, in this paper I present a spatial translog demand model that accounts for interdependence among travel alternatives and that handles varying elasticities of substitution for various destination pairs. Using simulation as the mode of inquiry, this model describes the effect of spatial size, spatial configuration, and spatial substitution on spatial interaction. In addition to indicating how varying spatial sizes and configurations affect the average trip length and the trip making pattern, the simulation results also point out the possible effect of having spatially dependent locations in the system. Competing destinations increase the attractiveness of nearby locations, and complementary destinations reduce the impeding effect of space. The model is primarily relevant to the demand for shopping trips.     

Local indicators for categorical data: impacts of scaling decisions

When the geographic distribution of landscape pattern varies, global indices fail to capture the spatial nonstationarity within the dataset. Methods that measure landscape pattern at a spatially local scale are advantageous, as an index is computed at each point in the dataset. The geographic distribution of local indices is used to discover spatial trends. Local indicators for categorical data (LICD) can be used to statistically quantify local spatial patterns in binary geographic datasets. LICD, like other spatially local methods, are impacted by decisions relating to the spatial scale of the data, such as the data grain (p), and analysis parameters such as the size of the local neighbourhood (m). The goal of this article is to demonstrate how the choice of the m and p parameters impacts LICD analysis. We also briefly discuss the impacts spatial extent can have on analysis; specifically the local composition measure. An example using 2006 forest cover data for a region in British Columbia, Canada where mountain pine beetle mitigation and salvage harvesting has occurred is used to show the impacts of changing m and p. Selection of local window size (m = 3,5,7) impacts the prevalence and interpretation of significant results. Increasing data grain (p) had varying effects on significant LICD results. When implementing LICD the choice of m and p impacts results. Exploring multiple combinations of m and p will provide insight into selection of ideal parameters for analysis.     

相关多样化、非相关多样化与区域创新产出——以长三角地区为例

创新是当今区域经济增长的关键驱动力之一,区域多样化与区域发展之关联是经济地理学研究的重要议题。目前国内的创新来源逐渐从外部知识引进为主向依靠区域自身创新能力为主转变,即重视本地知识结构对创新产出的重要影响。然而,现有研究主要关注多样化对区域经济发展的影响,较少分析多样化对区域创新产出的影响,也很少涉及多样化对邻近地区创新产出的空间效应。为此,本文构建了分析相关多样化和非相关多样化对区域创新产出影响的理论框架,并基于2011—2016年长三角地区26个地级市IPC分类专利的面板数据,运用空间杜宾模型,分析了本地知识结构的多样化对区域创新产出的影响。研究发现：①长三角城市群内部相关多样化与非相关多样化格局相似,省际间呈现沿海高内部低、省内呈现中心城市高周围城市低的空间格局。②知识相关多样化能够促进地方创新产出,而非相关多样化与地方创新产出之间呈现倒U型关系,即区域过度的非相关多样化对其创新产出有负向影响。③本地创新受相邻地区相关多样化的负向影响。本文对长三角区域创新机理的研究对于丰富我国创新地理学的理论与应用具有重要意义。     

Local Spatial Autocorrelation in a Biological Model

We review the recently developed local spatial autocorrelation statistics I_i, c_i, G_i, and G_i*. We discuss two alternative randomization assumptions, total and conditional, and then newly derive expectations and variances under conditional randomization for I_i and c_i, as well as under total randomization for c_i. The four statistics are tested by a biological simulation model from population genetics in which a population lives on a 21 × 21 lattice of stepping stones (sixty-four individuals per stone) and reproduces and disperses over a number of generations. Some designs model global spatial autocorrelation, others spatially random surfaces. We find that spatially random designs give reliable test results by permutational methods of testing significance. Globally autocorrelated designs do not fit expectations by any of the three tests we employed. Asymptotic methods of testing significance failed consistently, regardless of design. Because most biological data sets are autocorrelated, significance testing for local spatial autocorrelation is problematic. However, the statistics are informative when employed in an exploratory manner. We found that hotspots (positive local autocorrelation) and coldspots (negative local autocorrelation) are successfully distinguished in spatially autocorrelated, biologically plausible data sets.     

Does Econometric Methodology Matter? An Analysis of Public Policy Using Spatial Econometric Techniques

A popular approach to examining the effects of public policy has been to rely on a spatial data sample of border counties as in Holmes (1998)—border counties from a sample of states that are used in conjunction with least‐squares estimation techniques in an attempt to isolate the policy impact while controlling for spatial dependence that often arises from latent or unobserved variables. This technique is in the spirit of control‐group methodologies from the laboratory sciences. This paper contrasts border‐county estimation results from Holmes' (1998) approach and those from a related methodology set forth in Holcombe and Lacombe (2003), with estimates from a spatial autoregressive model explicitly accounting for within‐state and between‐state public policy effects. As an illustration, the paper examines the effects of Aid to Families with Dependent Children (AFDC) and Food Stamp payments on female‐headed households and female labor force participation using the three different methods.     

基于GWR模型的合肥居住地价影响因素研究

以合肥市主城区为例,基于2010-2014年居住用地的出让数据,运用地统计法、GWR模型等方法,对合肥市居住地价的空间异质性及其影响因素进行研究。研究表明：①合肥市居住地价的空间分布呈现出显著的多中心的空间结构,地价的峰值区分别以老城区、政务区天鹅湖及滨湖新区塘西河公园为中心呈现圈层式分布;②不同的地价影响因素表现出不同的空间分布特征,其中容积率对居住地价的贡献度空间差异最大,其次是宗地面积,主干路次之,交通站点对居住地价的贡献度最小;③厘清各影响因素对地价的作用机制,建立动态的数字地价模型,不仅能促进土地资源的集约利用,重塑城市的空间结构,而且能为城市整体价值的发挥提供重要的理论支撑。     

Properties of Tests for Spatial Dependence in Linear Regression Models

Based on a large number of Monte Carlo simulation experiments on a regular lattice, we compare the properties of Moran's I and Lagrange multiplier tests for spatial dependence, that is, for both spatial error autocorrelation and for a spatially lagged dependent variable. We consider both bias and power of the tests for six sample sizes, ranging from twenty-five to 225 observations, for different structures of the spatial weights matrix, for several underlying error distributions, for misspecified weights matrices, and for the situation where boundary effects are present. The results provide an indication of the sample sizes for which the asymptotic properties of the tests can be considered to hold. They also illustrate the power of the Lagrange multiplier tests to distinguish between substantive spatial dependence (spatial lag) and spatial dependence as a nuisance (error autocorrelation).