Geographically Weighted Discriminant Analysis

In this article, we propose a novel analysis technique for geographical data, Geographically Weighted Discriminant Analysis. This approach adapts the method of Geographically Weighted Regression (GWR), allowing the modeling and prediction of categorical response variables. As with GWR, the relationship between predictor and response variables may alter over space, and calibration is achieved using a moving kernel window approach. The methodology is outlined and is illustrated with an example analysis of voting patterns in the 2005 UK general election. The example shows that similar social conditions can lead to different voting outcomes in different parts of England and Wales. Also discussed are techniques for visualizing the results of the analysis and methods for choosing the extent of the moving kernel window.     

Guns and Homicides: A Multiscale Geographically Weighted Instrumental Variables Approach

This article assesses the locally varying effects of gun ownership levels on total and gun homicide rates in the contiguous United States using cross-sectional county data for the period 2009–2015. Employing a multiscale geographically weighted instrumental variables regression that takes into account spatial nonstationarity in the processes and the endogenous nature of gun ownership levels, estimates show that gun ownership exerts spatially monotonically negative effects on total and gun homicide rates, indicating that there are no counties supporting the “more guns, more crime” hypothesis for these two highly important crime categories. The number of counties in the contiguous United States where the “more guns, less crime” hypothesis is confirmed is limited to at least 1258 counties (44.8% of the sample) with the strongest total homicide-decreasing effects concentrated in southeastern Texas and the deep south. On the other hand, stricter state gun control laws exert spatially monotonically negative effects on gun homicide rates with the strongest effects concentrated in the southern tip of Texas extending toward the deep south.     

Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity

Spatial nonstationarity is a condition in which a simple “global” model cannot explain the relationships between some sets of variables. The nature of the model must alter over space to reflect the structure within the data. In this paper, a technique is developed, termed geographically weighted regression, which attempts to capture this variation by calibrating a multiple regression model which allows different relationships to exist at different points in space. This technique is loosely based on kernel regression. The method itself is introduced and related issues such as the choice of a spatial weighting function are discussed. Following this, a series of related statistical tests are considered which can be described generally as tests for spatial nonstationarity. Using Monte Carlo methods, techniques are proposed for investigating the null hypothesis that the data may be described by a global model rather than a non-stationary one and also for testing whether individual regression coefficients are stable over geographic space. These techniques are demonstrated on a data set from the 1991 U.K. census relating car ownership rates to social class and male unemployment. The paper concludes by discussing ways in which the technique can be extended.     

Multiple Contexts as Cross-classified Models: The Labor Vote in the British General Election of 1992

Voters make their decisions in social and geographical contexts that can be seen as different levels in an overall data structure. Increasingly these structures are being analyzed by multilevel models, but this approach has so far been limited to structures that are strictly hierarchical. This paper outlines the approach of cross-classified multilevel models in which units at lower levels in the structure can be nested in more than one higher-level unit simultaneously. An appropriate modeling framework is outlined, models are specified, and particular attention is paid to efficient computation. The approach is illustrated through a cross-classified logit analysis of Labor versus Conservative support for a nationally representative sample of voting behavior for the 1992 British General Election. The data is structured so that individual voters at level 1 are nested within constituencies at level 2 which are cross-classified by geographical and functional regionalizations at level 3. A conclusion discusses the general utility of a cross-classified approach to geographically based contextual research, while two technical appendices provide details on model estimation.     

A Note on the Mixed Geographically Weighted Regression Model*

Abstract. A mixed, geographically weighted regression (GWR) model is useful in the situation where certain explanatory variables influencing the response are global while others are local. Undoubtedly, how to identify these two types of the explanatory variables is essential for building such a model. Nevertheless, It seems that there has not been a formal way to achieve this task. Based on some work on the GWR technique and the distribution theory of quadratic forms in normal variables, a statistical test approach is suggested here to identify a mixed GWR model. Then, this note mainly focuses on simulation studies to examine the performance of the test and to provide some guidelines for performing the test in practice. The simulation studies demonstrate that the test works quite well and provides a feasible way to choose an appropriate mixed GWR model for a given data set.     

Exploring Heterogeneities with Geographically Weighted Quantile Regression: An Enhancement Based on the Bootstrap Approach

Geographically weighted quantile regression (GWQR) has been proposed as a spatial analytical technique to simultaneously explore two heterogeneities, one of spatial heterogeneity with respect to data relationships over space and one of response heterogeneity across different locations of the outcome distribution. However, one limitation of GWQR framework is that the existing inference procedures are established based on asymptotic approximation, which may suffer computation difficulties or yield incorrect estimates with finite samples. In this article, we suggest a bootstrap approach to address this limitation. Our bootstrap enhancement is first validated by a simulation experiment and then illustrated with an empirical U.S. mortality data. The results show that the bootstrap approach provides a practical alternative for inference in GWQR and enhances the utilization of GWQR.     

Exploring the Relations Between Riverbank Erosion and Geomorphological Controls Using Geographically Weighted Logistic Regression

The relations between riverbank erosion and geomorphological variables that are thought to control or influence erosion are commonly modelled using regression. For a given river, a single regression model might befitted to data on erosion and its geomorphological controls obtained along the river's length. However, it is likely that the influence of some variables may vary with geographical location (i.e., distance upstream). For this reason, the spatially stationary regression model should be replaced with a non‐stationary equivalent. Geographically weighted regression (GWR) is a suitable choice. In this paper, GWR is extended to predict the binary presence or absence of erosion via the logistic model. This extended model was applied to data obtained from historical archives and a spatially intensive field survey of a length of 42 km of the Afon Dyfi in West Wales. The model parameters and the residual deviance of the model varied greatly with distance upstream. The practical implication of the result is that different management practices should be implemented at different locations along the river. Thus, the approach presented allowed inference of spatially varying management practice as a consequence of spatially varying geomorphological process.     

Geographically Weighted Extreme Learning Machine: A Method for Space–Time Prediction

Spatial heterogeneity has been regarded as an important issue in space–time prediction. Although some statistical methods of space–time predictions have been proposed to address spatial heterogeneity, the linear assumption makes it difficult for these methods to predict geographical processes accurately because geographical processes always involve complicated nonlinear characteristics. An extreme learning machine (ELM) has the advantage of approximating nonlinear relationships with a rapid learning speed and excellent generalization performance. However, determining how to incorporate spatial heterogeneity into an ELM to predict space–time data is an urgent problem. For this purpose, a new method called geographically weighted ELM (GWELM) is proposed to address spatial heterogeneity based on an ELM in this article. GWELM is essentially a locally varying ELM in which the parameters are regarded as functions of spatial locations, and geographically weighted least squares is applied to estimate the parameters in a local model. The proposed method is used to analyze two groups of different data sets, and the results demonstrate that the GWELM method is superior to the comparative method, which is also developed to address spatial heterogeneity.     

艾德礼政府和1951年英国大选

1951年艾德礼领导的英国工党政府在大选中失利。当时工党政府处于极其不利的经济困顿时期,且在内外政策上有诸多失误不当之处．而保守党则趁此时机进行改革和政策调整。此外．工党失去执政党地位也与时机不好．运气欠佳有关。     

The 1892 General Election and the Eclipse of the Liberal Unionists

This article seeks to establish that the 1892 general election marked a major change in the relative positions of the parties in the Unionist alliance. Not only did it reveal the limitations of the Liberal Unionist Party's strategy and appeal in an age of increasingly organised, mass politics, but it also acted as a brake on the ambitions of the new leader of the Liberal Unionists in the house of commons, Joseph Chamberlain. It argues that the Liberal Unionist Party suffered a more severe setback in 1892 than has been recognized hitherto and that Chamberlain's attempts to revive his party both before and after the general election were now prescribed by the reality of the political position in which the party now found itself. Rather than regarding the fluid political circumstances of the 1890s as the outcome of an emerging struggle between increasingly polarised ideologies, it seeks to reinforce the significance of local political circumstances and the efficacy of party management in the growing dominance of Lord Salisbury and Arthur Balfour and the Conservative central organisers.     

A Call to Action: New Party Candidates and the 1931 General Election*

Sir Oswald Mosley established his New Party in early 1931. It proposed to cut across the party and class divides, with the objective of providing a ‘national’ solution to the economic crisis of the time. According to Mosley, the ‘old parties’– meaning the Labour, Conservative and Liberal Parties – had revealed themselves unable to adapt to the post‐war age. In their place, he argued, a modern organisation, based on youth, vitality and a scientifically reasoned economic plan, was needed to save Britain from terminal decline. Few heeded his call, and the party ultimately paved the way for the British Union of Fascists to emerge in 1932. Nevertheless, the New Party fought the general election of 1931, offering an unsuccessful but suitably intriguing challenge to the National coalition and Labour Party. This article will assess the New Party's election campaign, concentrating on those who briefly rallied to Mosley's appeal only to fall foul of the ballot box. In other words, it provides a case study of those who contributed to a dramatic electoral failure, and traces a significant stage along Mosley's journey to fascism.     

Change and Continuity in Irish Politics: The General Election of 2007

Bertie Ahern, the incumbent Taoiseach or Prime Minister of Ireland, was elected to a third term in the general election of 24 May 2007. While Ahern's party, Fianna Fáil, was able to retain its governing coalition, the level of support of some of the other parties changed dramatically. Fine Gael, the principal opposition party, saw its number of seats in the parliament, Dáil Éireann, increase by nineteen. Some of the minor parties did less well than expected or compared to previous elections. Only the Greens maintained their six representatives. As a result, they were rewarded with a share in the new government. This election suggests that, while Irish society is changing rapidly, the political system is changing more slowly and subtly. This article examines the election results in terms of the fate of the political parties and focuses on one constituency, Tipperary South, to illustrate trends in Irish electoral politics.