Duration Modeling of Spatial Point Patterns

This paper attempts to further the research by Odland and Ellis (1992) in applying event history methodology to the analysis of spatial point patterns (that is, event patterns). Its empirical focus is the event pattern derived from the adoption of an agricultural innovation, the Harvestore, in southern Ontario, Canada, from 1963 to 1986. Event history analysis involves the use of discrete-state, continuous-time stochastic models to investigate a temporal longitudinal record on discrete variables. Event history models are usually concerned with durations of time between events and the effects of intertemporal time dependencies on future event occurrences. As such, they are often referred to as duration models. Many of the methods used in event history analysis allow the use of other nonnegative interval measurements in place of standard temporal intervals to investigate a series of events. In particular, spatial intervals (or durations) of distances between events may also be accommodated by event history models. Our analysis extends the previous research of Odland and Ellis (1992) by using a wider range of parametric models to explore duration dependence, investigating the role of spatial censoring, and using a more extensive set of explanatory variables. In addition, simulation experiments and graphical tests are used to evaluate the empirical event pattern against one generated from Complete Spatial Randomness. Results indicate that the event pattern formed by the Harvestore adopter farms is clustered (that is, is described by positive duration dependency), the sales agent is a significant factor in the distribution of adopters, and that contrasting results are obtained from the analysis using censored data versus uncensored data.     

Capturing spatial patterns of rural landscapes with point cloud

Over the past few decades, rural landscapes have been the subject of increasing international cultural heritage research, and one of the most important issues under investigation at both theoretical and pragmatic levels concerns how to identify the spatial character of rural landscapes for conservation purposes. This article establishes an innovative approach adopting a cultural landscape perspective with the support of point cloud technologies to capture spatial patterns of rural landscapes. This approach was explored by reference to Tunpu villages in Guizhou, China—these being a specific kind of military fortress settlement. Cultural landscape values and landscape characters of Tunpu villages were identified using historical research and document analysis. Aerial and terrestrial photogrammetry and laser scanning systems were combined to collect and process spatial information at environmental, village, and architectural scales. Point cloud models can quantitatively represent villages' spatial patterns and inform the interpretation of their heritage significance. We conclude that the strengths of point cloud technologies could meet the requirements of rural landscape heritage documentation from a cultural landscape perspective. This mixed‐technology approach could also greatly improve the efficiency and precision of traditional rural landscape documentation, which has the potential to change methodologies applied to rural landscape research and management.     

On Geocomputational Determinants of Entropic Variations for Urban Dynamics Studies

Monitoring population characteristics and their patterns of spatial evolution are fundamental components for urban management and policy decision‐making. Societal issues such as health, transport, or crime are often explored using a range of models describing the urban dynamics of population attributes at specific scales that can be seen as complementary. Using and simulating data at different scales of aggregation asks for the need to analyze and compare spatiotemporal variations in order to better understand the model behaviors and emerging properties of the geosimulation. This article analyzes the uses of the entropy measure in the literature and constraining factors needed for its potential extension to explore the variations in geographic and time scales. In particular, the article discusses the need for a truly spatial entropy that takes into account the spatial contiguities of the observations usually aggregated within a zoning system of areal units. Two generic solutions are exposed for the various geometries and attribute structures used for census‐related analyses; they are based on existing measures for point data using (i) co‐occurrences of observations and (ii) discriminant ratios of distances between groups of observations. Their extensions to areal compositional data are articulated around their conceptual changes and geocomputational challenges. A revisited and new version of the entropy decomposition theorem, encompassing a spatiality concept semantically related to correlation, is also presented as efficiently reusing the constrained hierarchical zoning system of administrative units to enable discovery of emerging spatial pattern features from the geosimulation. A comparison of the results between the classical use of entropy and the spatial entropy framework devised shows the flexibility and added capabilities of the approach for new types of analyses, thus allowing new insight into studies of population dynamics.     

Evaluation of the Poisson Approximation To Measures of the Random Pattern in the Square

Theoretical values for spacing between points of the Poisson process are frequently used to evaluate the hypothesis that the locations within a region of pointlike objects have a random pattern. These theoretical spacing values are an approximation to spacing values for a uniform process in which the objects are uniformly and independently located in the region. The adequacy of the Poisson approximation to this uniform process for a square region is evaluated by analytic and numeric methods. The approximation is close for a small number of points when spacing between objects is measured by toroidal distance.     

A Simulation Study to Explore Inference about Global Moran's I with Random Spatial Indexes

Inference procedures for spatial autocorrelation statistics assume that the underlying configurations of spatial units are fixed. However, sometimes this assumption can be disadvantageous, for example, when analyzing social media posts or moving objects. This article examines for the case of point geometries how a change from fixed to random spatial indexes affects inferences about global Moran's I, a popular spatial autocorrelation measure. Homogeneous and inhomogeneous Matérn and Thomas cluster processes are studied and for each of these processes, 10,000 random point patterns are simulated for investigating three aspects that are key in an inferential context: the null distributions of I when the underlying geometries are varied; the effect of the latter on critical values used to reject null hypotheses; and how the presence of point processes affects the statistical power of Moran's I. The results show that point processes affect all three characteristics. Inferences about spatial structure in relevant application contexts may therefore be different from conventional inferences when this additional source of randomness is taken into account.     

旅游流空间模式基本理论:问题分析及其展望

旅游流是旅游地理学的基本问题,而旅游流空间模式的研究,自20世纪50年代以来则是旅游流研究的热点问题。通过文献分析法,本文将旅游流空间模式基本理论梳理为圈层结构理论、核心边缘理论、空间扩散理论。在此基础上,揭示其存在的若干问题,包括研究中存在的"区域视角"和"旅游者个体视角"混淆的认知问题、旅游客源地和旅游目的地在区域视角下如何界定的问题、空间模式研究中广泛存在的"二元陷阱"问题、区域间旅游职能分化及其分化程度尚无科学分析的问题等。文末对未来研究进行了展望,以期从理论意义上深化旅游流基本问题的建构。需指出的是,旅游流作为"非工作流"的一种,其"流现象"、"流空间"和"流效应"同样可适用于其它形式的"流研究"。     

Spatial Point Processes Applied to the Distribution of River Junctions

The notion of randomness has been extensively applied to topological (nondimensional) properties of drainage networks. The spatial (dimensional) organization of five fluvial hierarchies is examined herein through the application of quadrat analysis to random and clustered spatial probability models. The Poisson, Polya-Aeppli, and negative binomial models are compared with point-pattern distributions of river junction location for three basins in Indiana and two fossil systems on an erosion surface in semiarid Australia. The negative binomial model best fits all five networks, suggesting that the branching behavior of fluvial systems follows the mathematical precepts leading to clusteredness of junctions. The degree to which the Polya-Aeppli model fits the data suggests the imposition of a temporally limited set of environmental conditions optimally suited for network growth. Only for the two fossil systems does the Poisson model agree. It is speculated that the effect of prolonged subaerial erosion may be to shift a clustered distribution towards the random state as the surface approaches a pediplained state.     

Detrended fluctuation analysis of daily atmospheric surface temperature records in Atlantic Canada

The presence and properties of long‐range correlations in temperature data reflect interactions among climate components; therefore, the quantitative characterization of scaling aspects of temperature patterns is important to climate research and can serve as an effective constituent of tests for climate models. The article presents the results of a study using multiscale characterization of daily atmospheric surface temperature patterns in Atlantic Canada. Important influences in this region are exerted from the west (the Pacific Ocean), the south (the Gulf of Mexico) and the north (the Arctic), while a significant easterly impact is due to the Atlantic Ocean; the corresponding processes involve a wide range of spatial and temporal scales. The objective of the present study of long‐term temperature recordings was to evaluate the scaling properties produced in this geographical context. The data consist of homogenized daily atmospheric temperature time series recorded in stations from Atlantic Canada over a time interval of more than 100 years. Detrended fluctuation analysis (DFA) was applied both to maximum and minimum temperature records. The atmospheric temperature pattern produced by the interplay of factors of different strengths and dominating various time‐space scales was found to be characterized by consistent scaling properties, expressed over time intervals ranging from months to decades. Higher values of DFA scaling exponents were obtained for minimum temperature compared to maximum temperature records. Site‐specific properties include stronger pattern persistence—higher DFA exponents—for oceanic than for coastal locations; persistence tends to decrease with increasing distance from the coast for distances up to 10 kilometres. Scaling exponents tend to increase with decreasing difference between average minimum and maximum temperature, which may be relevant for the assessment of future changes in pattern variability if climate change involves modified contrasts between minimum and maximum temperature values.     

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.     

Exploring the Use of Computer Vision Metrics for Spatial Pattern Comparison

Detection of changes in spatial processes has long been of interest to quantitative geographers seeking to test models, validate theories, and anticipate change. Given the current “data-rich” environment of today, it may be time to reconsider the methodological approaches used for quantifying change in spatial processes. New tools emerging from computer vision research may hold particular potential to make significant advances in quantifying changes in spatial processes. In this article, two comparative indices from computer vision, the structural similarity (SSIM) index, and the complex wavelet structural similarity (CWSSIM) index were examined for their utility in the comparison of real and simulated spatial data sets. Gaussian Markov random fields were simulated and compared with both metrics. A case study into comparison of snow water equivalent spatial patterns over northern Canada was used to explore the properties of these indices on real-world data. CWSSIM was found to be less sensitive than SSIM to changing window dimension. The CWSSIM appears to have significant potential in characterizing change and/or similarity; distinguishing between map pairs that possess subtle structural differences. Further research is required to explore the utility of these approaches for empirical comparison cases of different forms of landscape change and in comparison to human judgments of spatial pattern differences.     

POISSON GRAVITY MODELS OF SPATIAL FLOWS*

ABSTRACT The purpose of this paper is to bring together a number of results on spatial flow models, and to reformulate them within a unified probability framework based on Poisson frequencies. To do so, a class of discrete stochastic processes, designated as independent flow processes, is developed which not only yields a complete characterization of Poisson flow frequencies, but also allows a wide range of gravity-type flow models to be formulated within this distributional framework. In particular, a hierarchical classification of 12 model types is developed, and each model type is shown to be characterizable directly in terms of behavioral axioms on independent flow processes.     

Constructing the Spatial Weights Matrix Using a Local Statistic

Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W , based on the principle that spatial structure should be considered in a two‐part framework, those units that evoke a distance effect, and those that do not. Our two‐variable local statistics model (LSM) is based on the G_i* local statistic. The local statistic concept depends on the designation of a critical distance, d_c, defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well‐known spatial weights matrix specifications—two different contiguity configurations, three different inverse distance formulations, and three semi‐variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran's I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.     

New insights into the neolithisation process in southwest Europe according to spatial density analysis from calibrated radiocarbon dates

The agricultural way of life spreads throughout Europe via two main routes: the Danube corridor and the Mediterranean basin. Current archaeological literature describes the arrival to the Western Mediterranean as a rapid process which involves both demic and cultural models, and in this regard, the dispersal movement has been investigated using mathematical models, where the key factors are time and space. In this work, we have created a compilation of all available radiocarbon dates for the whole of Iberia, in order to draw a chronological series of maps to illustrate temporal and spatial patterns in the neolithisation process. The maps were prepared by calculating the calibrated 14C date probability density curves, as a proxy to show the spatial dynamics of the last hunter-gatherers and first farmers. Several scholars have pointed out problems linked with the variability of samples, such as the overrepresentation of some sites, the degree of regional research, the nature of the dated samples and above all the archaeological context, but we are confident that the selected dates, after applying some filters and statistical protocols, constitute a good way to approach settlement spatial patterns in Iberia at the time of the neolithisation process.     

Determining Market Areas Captured by Competitive Facilities: A Continuous Equilibrium Modeling Approach

Many existing models concerning locations and market areas of competitive facilities assume that customers patronize a facility based on distance to that facility, or perhaps on a function of distances between the customer and the different facilities available. Customers are generally assumed to be located at certain discrete demand points in a two-dimensional space, or continuously distributed over a one-dimensional line segment. In this paper these assumptions are relaxed by employment of a continuum optimization model to characterize the equilibrium choice behavior of customers for a given set of competitive facilities over a heterogeneous two-dimensional space. Customers are assumed to be scattered continuously over the space and each customer is assumed to choose a facility based on both congested travel time to the facility and on the attributes of the facility. The model is formulated as a calculus of variations problem and its optimality conditions are shown to be equivalent to the spatial customer-choice equilibrium conditions. An efficient numerical method using finite element technique is proposed and illustrated with a numerical example.     

A Dynamic Analysis of Interaction Data: U.S. Rail Freight Flows, 1972-81

The purpose of this paper is to extend Poisson regression to the analysis of spatial interactions over time. The methodology involves derivation of models using information methods and calibration using Poisson regression. Poisson regression is then used to analyze interannual variation in U.S. rail freight flows, 1972-81. Findings indicate that import and export variability is less important than is flow variability. Import and export variability is highest for the northeastern United States, but flow variability is highest for the southern and western United States. This has implications for the specification of dynamic models of commodity flow.     

The Colocation Quotient: A New Measure of Spatial Association Between Categorical Subsets of Points. 协同区位商：点集分类子集间空间关联性的新度量标准

This article presents a new metric we label the colocation quotient (CLQ), a measurement designed to quantify (potentially asymmetrical) spatial association between categories of a population that may itself exhibit spatial autocorrelation. We begin by explaining why most metrics of categorical spatial association are inadequate for many common situations. Our focus is on where a single categorical data variable is measured at point locations that constitute a population of interest. We then develop our new metric, the CLQ, as a point‐based association metric most similar to the cross‐k‐function and join count statistic. However, it differs from the former in that it is based on distance ranks rather than on raw distances and differs from the latter in that it is asymmetric. After introducing the statistical calculation and underlying rationale, a random labeling technique is described to test for significance. The new metric is applied to economic and ecological point data to demonstrate its broad utility. The method expands upon explanatory powers present in current point‐based colocation statistics.     

BAYSIAN INFERENCE FOR ORDERED RESPONSE DATA WITH A DYNAMIC SPATIAL‐ORDERED PROBIT MODEL

ABSTRACT Many databases involve ordered discrete responses in a temporal and spatial context, including, for example, land development intensity levels, vehicle ownership, and pavement conditions. An appreciation of such behaviors requires rigorous statistical methods, recognizing spatial effects and dynamic processes. This study develops a dynamic spatial‐ordered probit (DSOP) model in order to capture patterns of spatial and temporal autocorrelation in ordered categorical response data. This model is estimated in a Bayesian framework using Gibbs sampling and data augmentation, in order to generate all autocorrelated latent variables. It incorporates spatial effects in an ordered probit model by allowing for interregional spatial interactions and heteroskedasticity, along with random effects across regions or any clusters of observational units. The model assumes an autoregressive, AR(1), process across latent response values, thereby recognizing time‐series dynamics in panel data sets. The model code and estimation approach is tested on simulated data sets, in order to reproduce known parameter values and provide insights into estimation performance, yielding much more accurate estimates than standard, nonspatial techniques. The proposed and tested DSOP model is felt to be a significant contribution to the field of spatial econometrics, where binary applications (for discrete response data) have been seen as the cutting edge. The Bayesian framework and Gibbs sampling techniques used here permit such complexity, in world of two‐dimensional autocorrelation.     

Quantifying Interpolation Errors in Urban Airborne Laser Scanning Models

Airborne laser scanning (ALS) is becoming an increasingly popular data capture technique for a variety of applications in urban surface modeling. Raw ALS data are captured and supplied as a 3D point cloud. Many applications require that these data are interpolated onto a regular grid in order that they may be processed. In this article, we identify and analyze the magnitudes and spatial patterning of residuals from ALS models of urban surfaces, at a range of different scales. Previous research has demonstrated the effects of interpolation method and scale upon the nature of error in digital surface models (DSMs), but the size and spatial patterning of such errors have not hitherto been investigated for urban surfaces. The contribution of this analysis is thus to investigate the ways in which different methods may introduce error, and to understand the uncertainty that characterizes urban surface models that are devised for a wide range of applications. The importance of the research is shown using examples of how the different methods may introduce different amounts of error and how the uncertainty information may benefit users of ALS height models. Our analysis uses a range of validation techniques, including split-sample, cross-validation, and jackknifing, to estimate the error created in DSMs of urban areas.     

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.