Spatial Autocorrelation and Spatial Interaction

This paper addresses the theme of spatial autocorrelation impacting spatial equilibria, and hence an understanding of economic network resilience and vulnerability. It exploits the notion that spatial autocorrelation in the geographic distribution of origin and destination attributes and network autocorrelation in the flows between origins and destinations constitute two spatial autocorrelation components contained in spatial interaction data. It illustrates that a spatial interaction model specification needs to incorporate both components in order to furnish sound implications about associated economic network resilience and vulnerability. Such models also need to undergo sensitivity analyses in terms of changes in geographic scale and resolution. And, it furnishes a novel 3-D visualization of geographic flows, such as journey-to-work trips, in order to achieve a better comprehension of economic network resilience and vulnerability.

This study aims at developing a data‐driven and bottom‐up spatial statistic method for identifying regions of anomalous spatial interactions (clusters of extremely high‐ or low‐value spatial flows), based on which it creates a spatial flow weights matrix. The method, dubbed flowAMOEBA, upgrades a multidirectional optimum ecotope‐based algorithm (AMOEBA) from areal data to spatial flow data through a proper spatial flow neighborhood definition. The method has the potential to dramatically change the way we study spatial interactions. First, it breaks the convention that spatial interaction data are always collected and modeled between spatial entities of the same granularity, as it delineates the OD region of anomalous spatial interactions, regardless of the size, shape, scale, or administrative level. Second, the method creates an empirical spatial flow weights matrix that can handle network autocorrelation embedded in spatial interaction modeling, thus improving related policy‐making or problem‐solving strategies. flowAMOEBA is tested and demonstrated on a synthetic data set as well as a county‐to‐county migration data set.

For many years, effective model‐based representations of the dynamics and evolution of urban spatial structure have proved elusive. While some progress has been made through the deployment of spatial interaction models, these approaches have been limited by the difficulty of representing behavioural mechanisms and processes. In this paper, it is demonstrated that evolutionary models grounded in the principles of spatial interaction are compatible with the more novel approaches of agent‐based modelling. The incorporation of agents provides a much more flexible means for the representation of behavioural mechanisms. The paper illustrates the way in which three more complicated situations can be handled through the fusion of spatial interaction and agent modelling perspectives. These situations comprise discontinuous evolution (in which structural adjustment takes place in discrete steps, and not as a continuously smooth process); nonequilibrium dynamics (in which the underlying system parameters continue to evolve through time); the incorporation of new decision variables (which we illustrate through the addition of land rents into the model). The conclusion of the paper is that the combination of spatial interaction and agent‐based modelling methods provides encouraging prospects for the social simulation of real urban systems.

Spatial heterogeneity in spatial interaction of human movements—Insights from large-scale mobile positioning data

Spatial interaction and spatial structure are foundational geographical abstractions, though there is often variation in how they are conceptualized and deployed in quantitative models. In particular, the last five decades have produced an exceptional diversity regarding the role of spatial structure within spatial interaction models. This is explored by outlining the initiation and development of the notion of spatial structure within spatial interaction modeling and critically reviewing four methodological approaches that emerged from ongoing debate about the topic. The outcome is a comprehensive coverage of the past and a sketch of one potential path forward for advancing this long-standing inquiry.

In the era of big data, large amounts of detailed spatial interaction data are readily available due to the increasing pervasiveness of location-aware devices and techniques. Such data are often applied in the research of spatial structures, land use characteristics, and human activity regularities. However, visualizing such data on maps is a great challenge. Existing approaches either encounter overlapping and intersection problems, which may cause information loss or distortion, or are unable to present interaction characteristics. Consequently, the functional and positional features of places and human mobility trends are not fully demonstrated. We propose direction-based pattern maps, a new visualization method to display the spatial interaction pattern of every place by aggregating spatial interaction data in cardinal directions. This approach can well represent local interaction characteristics and is applicable to different spatial scales. Owing to regular hexagonal tessellations, it can avoid cluttering problems and maintain a geographical context. A case study using Beijing taxi trip data is conducted to validate the usefulness of our approach.

This chapter is an introduction to the study of migration flows. It starts with a review of major definition and measurement issues. Comparative studies of migration are particularly difficult because different countries define migration differently and measurement methods are not harmonized. Insight in data collection practices is a first requirement to study flows. In the paper, several migration indicators are presented that describe the level and direction of migration. Scientists attempt to model migration flows since Ravenstein presented his migration laws at the end of the nineteenth century. Initially theories and models were borrowed from physics. The gravity model, based on Newton’s law of gravitation, has been the main model of migration flows for decades and continues to be popular today. Gradually human behaviour replaced the laws of physics and spatial interaction models the gravity model. Spatial interaction models emphasize interaction between geographically dispersed populations. Initially the gravity model had a strong influence on spatial interaction models, but the interest shifted gradually to probability theory and probability models. A parallel development was the life course perspective on migration, resulting from the increased awareness that some life events trigger migration and that during some stages of life, a person has an elevated propensity to migrate. These links produce the typical and universal age patterns of migration. Today, population projection models incorporate models of these typical age patterns (model schedules) and models of spatial interaction. Projection models may be turned into policy models to infer the migration flows required to meet demographic objectives, i.e. to offset population decline resulting from low fertility.

Spatial scale is a fundamental issue for geographical phenomena because the size of the spatial unit adopted for analysis can have a significant effect on aggregated spatial data and the corresponding analytical results. There exists much research on the scale issue of spatial distribution data while a few has paid attention to the scale effect on spatial interactions. Big geo-data with micro-level individual movements provide an unprecedented opportunity to explore spatial interactions from the bottom up and to understand the scale effect from the perspective of interaction patterns. In this paper, we introduced an empirical framework to explore spatial interaction data across scales. By incorporating two data sets of taxi trajectories in Beijing and Shanghai, we aggregated the taxi O-D trips under multiple regular grids with different cell sizes and analyzed the properties of spatial interactions in three aspects: the statistical distribution, the distance decay mechanism, and the structure pattern. Our research demonstrated the feasibility of analyzing spatial interactions from a multi-scale view and offered a basic empirical framework for future geographical research that is interested in scale and spatial interactions.

The gravity model which is based on Newton’s gravitational law, has been widely used as a spatial interaction model in the past few decades. Spatial interactions are important in epidemic modeling as different populations in the world are interconnected by them. Human dispersal behaviors are spatial interactions and they are crucial aspects of infectious disease spread. However, many existing compartmental models model epidemics in a single area. Hence, a gravity model approach to model epidemics incorporated with a multipatch compartmental model is studied here. Both human dispersal behaviors within a patch and between patches are considered. When the human dispersal behaviors within a patch are modeled, the denominator of the general gravity model becomes zero. An alternative power-based distance decay function is introduced to the gravity model to address that research gap. The parameters of the modified gravity model are estimated using a hybrid method combining ordinary least squares (OLS) and nonlinear least squares (NLS) methods (Hybrid OLS-NLS method).

ABSTRACTTraditional spatial interaction (SI) models of migration are susceptible to misspecification when the spatial structure of locations is not properly incorporated. To address this, a novel SI model for migration is introduced that integrates the theories of competing destinations (CD) and intervening opportunities (IO) to capture multiscale spatial structure using the recent generalized additive spatial smoothing (GASS) framework. This GASS CDIO model can identify the appropriate spatial scales to represent the spatial structure of origins and destinations in a data‐driven manner. Validation of the model was conducted through two simulation experiments. The first demonstrates that employing the incorrect scale to capture spatial structure in SI models biases the parameter estimates and increases uncertainty. The second demonstrates that the GASS approach reliably recovers accurate parameters by identifying optimal hyperparameters associated with multiple spatial scales. The GASS CDIO model was then applied to U.S. inter‐county migration data and compared to several other model specifications. The results reveal the unique spatial structure from the perspective of origins and destinations and illustrate the improved recoverability of anticipated migration relationships. This work suggests that the GASS CDIO model better integrates spatial theories of migration and accounts for the multiscale nature of SI processes.

A spatial impulsive interaction model is applied to the calculation of drag and lift coefficients for flat plate, sphere and circular cylinder with side-wind in “hyperthermal” free-molecule flow. Obtained results for flat plate are also compared with the corresponding coefficients calculated by Hurlbut and Sherman in1968 according to the Nocilla reemission model(1962).

This paper attempts to develop a mathematically rigid and unified framework for neural spatial interaction modeling. Families of classical neural network models, but also less classical ones such as product unit neural network ones are considered for the cases of unconstrained and singly constrained spatial interaction flows. Current practice appears to suffer from least squares and normality assumptions that ignore the true integer nature of the flows and approximate a discrete‐valued process by an almost certainly misrepresentative continuous distribution. To overcome this deficiency we suggest a more suitable estimation approach, maximum likelihood estimation under more realistic distributional assumptions of Poisson processes, and utilize a global search procedure, called Alopex, to solve the maximum likelihood estimation problem. To identify the transition from underfitting to overfitting we split the data into training, internal validation, and test sets. The bootstrapping pairs approach with replacement is adopted to combine the purity of data splitting with the power of a resampling procedure to overcome the generally neglected issue of fixed data splitting and the problem of scarce data. In addition, the approach has power to provide a better statistical picture of the prediction variability. Finally, a benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained neural network model versions in terms of generalization performance measured by Kullback and Leibler's information criterion.

This chapter aims to improve the applicability of the data created by a microsimulation model, not by increasing the complexity of the simulation framework, but by integrating the newly created data within a meso-level, spatial interaction framework. Spatial microsimulation modelling is a means of synthetically creating geographically referenced micro-data. With increases in computational power and increased access to spatially referenced micro-data, spatial microsimulation has been used extensively over the last decade to inform health policy. However, the complex dynamics which underlie health-care markets require both meso- and micro-level tools to formulate appropriate and effective health policies. In particular, there is a need to understand, estimate or predict how meso-level interactions such as access to services are going to impact on individuals and areas. To ensure that these meso-level interactions are accounted for, this chapter incorporates data from a spatial interaction model and spatial microsimulation models to account for the impact on access to GPs on individual’s health. Such an analysis provides policymakers with information on both demand for and supply of health-care services, thus allowing them to shape future service provision and target existing health resources in a more efficient and effective manner.

In this paper a highly simplified spatial search process in a linear space with a central business district and a residential periphery is examined. Measures of spatial relative concentration and polarization are introduced. These measures play a fundamental role in the analysis of a spatial search equilibrium, the main characteristics of the equilibrium being determined by them, and the realization of such an equilibrium being impossible without a minimal level of polarization. The resulting spatial interaction model clearly illustrates the main features of spatial interaction models derived from a spatial sequential search process: the interaction effect is an intervening-opportunities effect, and the attraction effects include a competing-searchers effect.

We introduce a Bayesian hierarchical regression model that extends the traditional least-squares regression model used to estimate gravity or spatial interaction relations involving origin-destination flows. Spatial interaction models attempt to explain variation in flows from n origin regions to n destination regions resulting in a sample of N=n^2 observations that reflect an n by n flow matrix converted to a vector. Explanatory variables typically include origin and destination characteristics as well as distance between each region and all other regions. Our extension introduces latent spatial effects parameters structured to follow a spatial autoregressive process. Individual effects parameters are included in the model to reflect latent or unobservable influences at work that are unique to each region treated as an origin and destination. That is, we estimate $2n$ individual effects parameters using the sample of N=n^2 observations. We illustrate the method using a sample of commodity flows between 18 Spanish regions during the 2002 period.