Using Spatial Filters and Exploratory Data Analysis to Enhance Regression Models of Spatial Data

Residual spatial autocorrelation is a situation frequently encountered in regression analysis of spatial data. The statistical problems arising due to this phenomenon are well‐understood. Original developments in the field of statistical analysis of spatial data were meant to detect spatial pattern, in order to assess whether corrective measures were required. An early development was the use of residual autocorrelation as an exploratory tool to improve regression analysis of spatial data. In this note, we propose the use of spatial filtering and exploratory data analysis as a way to identify omitted but potentially relevant independent variables. We use an example of blood donation patterns in Toronto, Canada, to demonstrate the proposed approach. In particular, we show how an initial filter used to rectify autocorrelation problems can be progressively replaced by substantive variables. In the present case, the variables so retrieved reveal the impact of urban form, travel habits, and demographic and socio‐economic attributes on donation rates. The approach is particularly appealing for model formulations that do not easily accommodate positive spatial autocorrelation, but should be of interest as well for the case of continuous variables in linear regression.     

Building Spatial Choice Models from Aggregate Data

Abstract Choice model construction is usually based on information about a number of separate choice situations, for which all relevant quantities are known. This paper concerns the case where only higher level, aggregate information is available about the choice results and the prevailing conditions. We demonstrate the applicability of a generic inverse parameter estimation method in estimating a model for grocery store choice. We also propose some enhancements to standard spatial choice models and demonstrate their applicability.     

Spatial Autoregressive Models for Geographically Hierarchical Data Structures

This article discusses how standard spatial autoregressive models and their estimation can be extended to accommodate geographically hierarchical data structures. Whereas standard spatial econometric models normally operate at a single geographical scale, many geographical data sets are hierarchical in nature—for example, information about houses nested into data about the census tracts in which those houses are found. Here we outline four model specifications by combining different formulations of the spatial weight matrix W and of ways of modeling regional effects. These are (1) groupwise W and fixed regional effects; (2) groupwise W and random regional effects; (3) proximity‐based W and fixed regional effects; and (4) proximity‐based W and random regional effects. We discuss each of these model specifications and their associated estimation methods, giving particular attention to the fourth. We describe this as a hierarchical spatial autoregressive model. We view it as having the most potential to extend spatial econometrics to accommodate geographically hierarchical data structures and as offering the greatest coming together of spatial econometric and multilevel modeling approaches. Subsequently, we provide Bayesian Markov Chain Monte Carlo algorithms for implementing the model. We demonstrate its application using a two‐level land price data set where land parcels nest into districts in Beijing, China, finding significant spatial dependence at both the land parcel level and the district level.     

Combining Geostatistical Methods and Hierarchical Scene Models for Analysis of Multiscale Variation in Spatial Data

Concepts from Hierarchical Analysis of Variance (ANOVA) can be combined with ideas from geostatistics to describe the multiscale structure of spatial data. Hierarchical ANOVA involves modeling spatial data as the sum of effects associated with processes acting at different spatial scales. These effects can be modeled as stationary regionalized variables, whose spatial structure can be described using the variogram. According to this model, the variogram of the spatial data is the sum of variograms and cross‐variograms of the effects. Whereas hierarchical ANOVA reveals the relationship between scale and variability, the hierarchical decomposition of the variogram relates scale with spatial structure. This analysis method can reveal otherwise undetected features of spatial data, and can guide further analysis.     

中国旅游创新与旅游经济增长关系研究——基于空间面板数据模型

本文运用空间面板数据模型,选用1998～2009年数据研究了中国省域旅游创新与旅游经济增长的关系,发现：中国省域旅游创新与旅游经济增长呈现显著空间集聚性;旅游创新不仅推动当地旅游经济的增长,还通过空间传导机制对邻近区域的旅游经济产生正向的溢出效应。说明应充分重视创新在旅游经济增长中的积极作用,通过旅游创新成果的溢出效应扩大旅游创新对旅游经济增长的作用程度和范围。     

GeoDa : An Introduction to Spatial Data Analysis

This article presents an overview of GeoDa™, a free software program intended to serve as a user-friendly and graphical introduction to spatial analysis for non-geographic information systems (GIS) specialists. It includes functionality ranging from simple mapping to exploratory data analysis, the visualization of global and local spatial autocorrelation, and spatial regression. A key feature of GeoDa is an interactive environment that combines maps with statistical graphics, using the technology of dynamically linked windows. A brief review of the software design is given, as well as some illustrative examples that highlight distinctive features of the program in applications dealing with public health, economic development, real estate analysis, and criminology.     

The Spatial Distribution of French Agricultural Cooperatives: An Exploratory Spatial Data Analysis

Abstract

This paper studies the spatial dynamics of French agricultural cooperatives using the recently developed exploratory spatial data analysis tool. Analysis at the level of French districts in 1995 and 2005 shows strong evidence for global and local spatial autocorrelations in the geographical distribution of agricultural cooperatives. The presence of spatial disparities between French districts is confirmed by the detection of such specific spatial patterns as district clusters, a group of neighbouring districts with the same high or low level of agricultural cooperative activities. A typology of all the different Regions is developed to examine the specific spatial patterns of the agricultural cooperative activities. The results indicate that major organizational changes in cooperatives do not significantly modify the initial dynamics concerning the location of activities.     

Destination Choice of Athenians: An Application of Geographically Weighted Versions of Standard and Zero Inflated Poisson Spatial Interaction Models

The main aim of this article is to combine recent developments in spatial interaction modeling to better model and explain spatial decisions. The empirical study refers to migration decisions made by internal migrants from Athens, Greece. To achieve this, geographically weighted versions of standard and zero inflated Poisson (ZIP) spatial interaction models are defined and fit. In the absence of empirical studies for the effect of potential determinants on internal migration decisions in Greece and the presence of an excessive number of zero migration flows among municipalities in Greece, this article provides empirical evidence for the power of the proposed Geographically Weighted ZIP regression method to better explain destination choices of Athenian internal migrants. We also discuss statistical inference issues in relation to the application of the proposed regression techniques.     

Beyond Moran's I: Testing for Spatial Dependence Based on the Spatial Autoregressive Model

The statistic known as Moran's I is widely used to test for the presence of spatial dependence in observations taken on a lattice. Under the null hypothesis that the data are independent and identically distributed normal random variates, the distribution of Moran's I is known, and hypothesis tests based on this statistic have been shown in the literature to have various optimality properties. Given its simplicity, Moran's I is also frequently used outside of the formal hypothesis-testing setting in exploratory analyses of spatially referenced data; however, its limitations are not very well understood. To illustrate these limitations, we show that, for data generated according to the spatial autoregressive (SAR) model, Moran's I is only a good estimator of the SAR model's spatial-dependence parameter when the parameter is close to 0. In this research, we develop an alternative closed-form measure of spatial autocorrelation, which we call APLE , because it is an approximate profile-likelihood estimator (APLE) of the SAR model's spatial-dependence parameter. We show that APLE can be used as a test statistic for, and an estimator of, the strength of spatial autocorrelation. We include both theoretical and simulation-based motivations (including comparison with the maximum-likelihood estimator), for using APLE as an estimator. In conjunction, we propose the APLE scatterplot, an exploratory graphical tool that is analogous to the Moran scatterplot, and we demonstrate that the APLE scatterplot is a better visual tool for assessing the strength of spatial autocorrelation in the data than the Moran scatterplot. In addition, Monte Carlo tests based on both APLE and Moran's I are introduced and compared. Finally, we include an analysis of the well-known Mercer and Hall wheat-yield data to illustrate the difference between APLE and Moran's I when they are used in exploratory spatial data analysis.     

Implementing Spatial Data Analysis Software Tools in R

This article reports on work in progress on the implementation of functions for spatial statistical analysis, in particular of lattice/area data in the R language environment. The underlying spatial weights matrix classes, as well as methods for deriving them from data from commonly used geographical information systems are presented, handled using other contributed R packages. Since the initial release of some functions in 2001, and the release of the spdep package in 2002, experience has been gained in the use of various functions. The topics covered are the ingestion of positional data, exploratory data analysis of positional, attribute, and neighborhood data, and hypothesis testing of autocorrelation for univariate data. It also provides information about community building in using R for analyzing spatial data.     

Beyond Replication: the Quantification of Route Models in the North Jazira,Iraq

The primary aim of this paper is to present a solution to the issue of the statistical validation of route models. In addition, it introduces a body of theory taken from the broader field of route studies, isolates individual physical variables commonly used to predict route locations and quantifies them against the preserved hollow ways in the North Jazira Survey area, ending with a discussion of the complexity of human travel and the paramount importance of cultural variables.     

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.     

Exploring a Relationship Between Aggregate and Individual Levels Spatial Data Through Semivariogram Models

Analysis of social data is frequently done using aggregate-level data. There may not be a direct interest in spatial relationships in the data, but the presence of spatial interdependence may still need to be taken into account. This article explores the aggregation effect from a spatial perspective by assuming nonzero covariance for individual data from two different groups. We investigate the bias associated with aggregate-level data for semivariogram analysis. We show that the bias mainly arises from the average of the semivariogram within the groups. It is also shown how aggregated-level data may be used to estimate parameters of an individual-level semivariogram model. A nonlinear regression method is proposed to carry out this estimation procedure and a simulation is done to clarify the results.     

Crime Risk Maps: A Multivariate Spatial Analysis of Crime Data

In crime analyses, maps showing the degree of risk help police departments to make decisions on operational matters, such as where to patrol or how to deploy police officers. This study statistically models spatial crime data for multiple crime types in order to produce joint crime risk maps. To effectively model and map the spatial crime data, we consider two important characteristics of crime occurrences: the spatial dependence between sites, and the dependence between multiple crime types. We reflect both characteristics in the model simultaneously using a generalized multivariate conditional autoregressive model. As a real‐data application, we examine the number of incidents of vehicle theft, larceny, and burglary in 83 census tracts of San Francisco in 2010. Then, we employ a Bayesian approach using a Markov chain Monte Carlo method to estimate the model parameters. Based on the results, we detect the crime hotspots, thus demonstrating the advantage of using a multivariate spatial analysis for crime data.     

Geography, Spatial Data Analysis, and Geostatistics: An Overview

Geostatistics is a distinctive methodology within the field of spatial statistics. In the past, it has been linked to particular problems (e.g., spatial interpolation by kriging) and types of spatial data (attributes defined on continuous space). It has been used more by physical than human geographers because of the nature of their types of data. The approach taken by geostatisticians has several features that distinguish it from the methods typically used by human geographers for analyzing spatial variation associated with regional data, and we discuss these. Geostatisticians attach much importance to estimating and modeling the variogram to explore and analyze spatial variation because of the insight it provides. This article identifies the benefits of geostatistics, reviews its uses, and examines some of the recent developments that make it valuable for the analysis of data on areal supports across a wide range of problems.     

Models for Spatial Weights: A Systematic Look

General properties of spatial weights models, in particular Markovian properties, are systematically investigated. The role of stationary spatial distribution, interpretable as an importance-centrality or prominence index, is emphasized. Spatial interaction models, and among them the gravity model, are classified with respect to the time reversal and aggregation invariance properties obeyed by the associated spatial weights. Nine examples, involving connectivity, flows and distance decay analysis, integral geometry, and Dirichlet-Voronoi tessellations illustrate the main concepts, with a particular geometrical emphasis, and show how traditional, heuristic ingredients aimed at defining spatial weights can be recovered from general models.