Semiparametric Maximum Likelihood Estimates of Spatial Dependence

We semiparametrically model spatial dependence via a combination of simpler weight matrices (termed spatial basis matrices) and fit this model via maximum likelihood. Estimation of the model relies on the intuition that bounds to the log‐determinant term in the log‐likelihood can provide penalties to overfitting both the level and pattern of spatial dependence. By relying on symmetric and doubly stochastic spatial basis matrices that reflect different weight specifications assigned to neighboring observations, we are able to derive a mathematical expression for bounds on the log‐determinant term that appears in the likelihood function. These bounds can be conveniently calculated allowing us to solve for maximum likelihood estimates at the bounds using a simple optimization over two quadratic forms that involve small matrices. An intuitively pleasing aspect of our approach is that the objective function for the bounded log‐likelihoods contains one quadratic form equal to the sum‐of‐squared errors measuring the quality of fit, and another quadratic form reflecting a penalty to overfitting spatial dependence. We apply our semiparametric estimation method to a housing model using 57,647 U.S. census tracts.     

Spatial Causality: A Systematic Review on Spatial Causal Inference

The growing interest in causal inference in recent years has led to new causal inference methodologies and their applications across disciplines and research domains. Yet, studies on spatial causal inference are still rare. Causal inference on spatial processes is faced with additional challenges, such as spatial dependency, spatial heterogeneity, and spatial effects. These challenges can lead to spurious results and subsequently, incorrect interpretations of the outcomes of causal analyses. Recognizing the growing importance of causal inference in the spatial domain, we conduct a systematic literature review on spatial causal inference based on a formal concept mapping. To identify how to assess and control for the adverse effects of spatial influences, we assess publications relevant to spatial causal inference based on criteria relating to application discipline, methods used, and techniques applied for managing issues related to spatial processes. We thus present a snapshot of state of the art in spatial causal inference and identify methodological gaps, weaknesses and challenges of current spatial inference studies, along with opportunities for future research.     

Closed‐Form Maximum Likelihood Estimates of Nearest Neighbor Spatial Dependence

Models of n² potential spatial dependencies among n observations spread irregularly over space seem unlikely to yield simple structure. However, the use of the nearest neighbor leads to a very parsimonious eigenstructure of the associated adjacency matrix which results in an extremely simple closed form for the log determinant. In turn, this leads to a closed‐form solution for the maximum likelihood estimates of the spatially autoregressive and mixed regressive spatially autoregressive models. With the closed‐form solution, one can find the neighbors and compute maximum likelihood estimates for 100,000 observations in under one minute. The model has theoretical, pedagogical, diagnostic, modeling, and methodological applications. For example, the model could serve as a more enlightened null hypothesis for geographic data than spatial independence.     

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.     

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.     

Ecological Inference and Spatial Variation of Individual Behavior: National Divide and Elections in Catalonia

When in geography one reconstructs individual behavior starting from aggregated data through ecological inference, a crucial aspect is the spatial variation of individual behavior. Basic ecological inference methods treat areas as if they were all exchangeable, which in geographical applications is questionable due to the existence of contextual effects that relate to area location and induce spatial dependence. Here that assumption is avoided by basing ecological inference on a model that simultaneously does a cluster analysis, grouping together areas with similar individual behavior, and an ecological inference analysis in each cluster, estimating the individual behavior in the areas of each group. That allows one to capture most of the spatial dependence and summarize the individual behavior at a local level through the behavior estimated for each cluster. This approach is used to investigate vote switching in Catalonia, where voters split across a national allegiance divide on top of the ideological divide. That leads to Catalans having a lot of options to choose from, and to them voting differently depending on whether the election is for the Catalan parliament or for the Spanish parliament. To investigate that, the results in the two most recent pairs of such elections are analyzed by simultaneously clustering areas based on the similarity of their vote and vote switch patterns, and estimating one vote switch pattern for each cluster. As a result, Catalonia is partitioned into four clusters that have a strong spatial structure, with all the areas in the same cluster having similar demographic composition. The estimated vote switch patterns are quite different across clusters but very similar across pairs of elections, and they help assess how the differential voter turnout and the strategic dual vote effects vary in space.     

Graphical Inference in Geographical Research

Graphical inference, a process refined by Buja et al., can be a useful tool for geographers as it provides a visual and spatial method to test null hypotheses. The core idea is to generate sample datasets from a null hypothesis to visually compare with the actual dataset. The comparison is performed from a line‐up of graphs where a single graph of the actual data is hidden among multiple graphs of sample data. If the real data is discernible, the null hypothesis can be rejected. Here, we illustrate the utility of graphical inference using examples from climatology, biogeography, and health geography. The examples include inferences about location of the mean, change across space and time, and clustering. We show that graphical inference is a useful technique to answer a broad range of common questions in geographical datasets. This approach is needed to avoid the common pitfalls of “straw man” hypotheses and “p‐hacking” as datasets become increasingly larger and more complex.     

Inference in Multiscale Geographically Weighted Regression

A recent paper expands the well-known geographically weighted regression (GWR) framework significantly by allowing the bandwidth or smoothing factor in GWR to be derived separately for each covariate in the model—a framework referred to as multiscale GWR (MGWR). However, one limitation of the MGWR framework is that, until now, no inference about the local parameter estimates was possible. Formally, the so-called “hat matrix,” which projects the observed response vector into the predicted response vector, was available in GWR but not in MGWR. This paper addresses this limitation by reframing GWR as a Generalized Additive Model, extending this framework to MGWR and then deriving standard errors for the local parameters in MGWR. In addition, we also demonstrate how the effective number of parameters can be obtained for the overall fit of an MGWR model and for each of the covariates within the model. This statistic is essential for comparing model fit between MGWR, GWR, and traditional global models, as well as for adjusting multiple hypothesis tests. We demonstrate these advances to the MGWR framework with both a simulated data set and a real-world data set and provide a link to new software for MGWR (MGWR1.0) which includes the novel inferential framework for MGWR described here.     

The Deleterious Dominance of The Times in Nineteenth-Century Scholarship

The Times was a mid-nineteenth-century newspaper phenomenon, defeating rival London newspapers through its skilful management, advanced technology, greater editorial resources and access to powerful politicians. Its authority enabled it to make and break governments. However, the uniqueness of The Times limits its usefulness as a historical source. This article begins with a brief history of The Times, before analysing how the newspaper remains centre stage in the historiography of journalism and of nineteenth-century culture more broadly, despite the digitization of provincial and other London papers. Over-dependence on The Times, it argues, has exaggerated the significance of London daily newspapers and underplayed the importance of weekly papers, particularly those published outside London. The Times was unusual because it was a metropolitan rather than provincial paper, with a focus on political news and a dearth of lighter, broader content, or news of events around the UK. Using quantitative analysis of recent scholarship, the article demonstrates that unwarranted conclusions are still drawn from over-use of this source and from a wider view that it was representative of nineteenth-century newspapers in general. The conclusion urges a more geographically and culturally nuanced approach to Victorian newspapers, beyond a metropolitan-focused political and cultural history.     

古地名蠡测二则

文章就"淹城""狗泽都"二地名进行探讨。1.在江浙地区常见用来指称洼地的"淹(渰)"作为地理通名,如古代浙江湖州的"无胥淹",江苏宜兴西北的"都山渰"等,常州武进"淹城"所在区域地势较低,故"淹城"之名也是由其处在洼地而来,和西周初年的奄族无关。2.燕国陶文"狗泽都"可读为"狗(句)泽(渎、俞)都(县)","句泽(渎、俞)"即齐国西部要地"句泽(渎、俞)",也就是"谷"(今山东菏泽),"句泽(渎、俞)都(县)"可能为燕国在公元前284—279年的燕齐战争中占领该地后所设,是先秦时期"因军设县"的表现。     

Experimental Design and Experimental Inference in Stone Artifact Archaeology

Lithic researchers rely heavily on experimentation to infer past behaviors and activities based on stone artifacts. This paper explores the analogical nature of archaeological inference and the relationship between experimental design and inference validity in stone artifact experimentation. We show that actualistic flintknapping lacks vital aspects of scientific experimentation, and thus has inherent inferential issues of analogical adequacy and confidence. It is argued that a greater emphasis on hypothesis construction and variable control is needed in order to establish sound referential linkages upon which constructive analogic inferences about the past can be built.     

Spatial Cluster Detection in Spatial Flow Data

As a typical form of geographical phenomena, spatial flow events have been widely studied in contexts like migration, daily commuting, and information exchange through telecommunication. Studying the spatial pattern of flow data serves to reveal essential information about the underlying process generating the phenomena. Most methods of global clustering pattern detection and local clusters detection analysis are focused on single‐location spatial events or fail to preserve the integrity of spatial flow events. In this research we introduce a new spatial statistical approach of detecting clustering (clusters) of flow data that extends the classical local K‐function, while maintaining the integrity of flow data. Through the appropriate measurement of spatial proximity relationships between entire flows, the new method successfully upgrades the classical hot spot detection method to the stage of “hot flow” detection. Several specific aspects of the method are discussed to provide evidence of its robustness and expandability, such as the multiscale issue and relative importance control, using a real data set of vehicle theft and recovery location pairs in Charlotte, NC.     

Spatial Entropy

A major problem in information theory concerns the derivation of a continuous measure of entropy from the discrete measure. Many analysts have shown that Shannon's treatment of this problem is incomplete, but few have gone on to rework his analysis. In this paper, it is suggested that a new measure of discrete entropy which incorporates interval size explicitly is required; such a measure is fundamental to geography and this statistic has been called spatial entropy. The use of the measure is first illustrated by application to one-and two-dimensional aggregation problems, and then the implications of this statistic for Wilson's entropy-maximizing method are traced. Theil's aggregation statistic is reinterpreted in spatial terms, and finally, some heuristics are suggested for the design of real and idealized spatial systems in which entropy is at a maximum.