SUMMARYIn order to investigate the response of structures to near-fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long-period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single-degree-of-freedom (SDOF) system to near-fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near-fault ground motion characteristics that signiÿcantly a ect the elastic and inelastic structural performance. A parameter of the mathematical representation of near-fault motions, referred to as 'pulse duration' (T P ), emerges as a key parameter of the problem under investigation. Speciÿcally, T P is employed to normalize the elastic and inelastic response spectra of actual near-fault strong ground motion records. Such normalization makes feasible the speciÿcation of design spectra and reduction factors appropriate for near-fault ground motions. The 'pulse duration' (T P ) is related to an important parameter of the rupture process referred to as 'rise time' ( ) which is controlled by the dimension of the sub-events that compose the mainshock.

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.

Geographically Weighted Regression (GWR) is increasingly used in spatial analyses of social and environmental data. It allows spatial heterogeneities in processes and relationships to be investigated through a series of local regression models rather than a single global one. Standard GWR assumes that relationships between the response and predictor variables operate at the same spatial scale, which is frequently not the case. To address this, several GWR variants have been proposed. This paper describes a route map to decide whether to use a GWR model or not, and if so which of three core variants to apply: a standard GWR, a mixed GWR or a multiscale GWR (MS‐GWR). The route map comprises 3 primary steps that should always be undertaken: (1) a basic linear regression, (2) a MS‐GWR, and (3) investigations of the results of these in order to decide whether to use a GWR approach, and if so for determining the appropriate GWR variant. The paper also highlights the importance of investigating a number of secondary issues at global and local scales including collinearity, the influence of outliers, and dependent error terms. Code and data for the case study used to illustrate the route map are provided.

‘Social frontiers’ – places of sharp difference in social/ethnic characteristics between neighbouring communities – have largely been overlooked in quantitative research. Advancing this nascent field first requires a way of identifying social frontiers in a robust way. Such frontiers may be ‘open’ – an area may contrast sharply with a neighbourhood in one direction, but blend smoothly into adjacent neighbourhoods in other directions. This poses some formidable methodological challenges, particularly when computing inference for the existence of a social frontier, an important goal if one is to distinguish true frontiers from random variation. We develop a new approach using Bayesian spatial statistical methods that permit asymmetries in spatial effects and allow for spatial autocorrelation in the data. We illustrate our method using data on Sheffield and find clear evidence of ‘open’ frontiers. Permutations tests and Poisson regressions with fixed effects reveal compelling evidence that social frontiers are associated with higher rates of crime.

dents, are distributed at a fine (subdistrict) scale in urban Beijing and investigate the association between hazards, health, and geographical context. A Bayesian spatial multilevel logistic model is developed to account for spatial dependence in unobserved contextual influences (neighborhood effects) on health. The results reveal robust associations between exposure to environmental hazards and health. A unit decrease on a fivepoint Likert scale in exposure is associated with increases of 15.2 percent (air pollution), 17.5 percent (noise), and 9.3 percent (landfills) in the odds of reporting good health, with marginal groups including migrant workers reporting greater exposure. Health inequality is also evident and is associated with age, income, educational attainment, and housing characteristics. Geographical context (neighborhood features like local amenities) also plays a role in shaping the social distribution of health inequality. The results are discussed in the context of developing environmental justice policy within a Chinese social market system that experiences tension between its egalitarian roots and its pragmatic approach to tackling grand public policy challenges.

Associated with the dramatic expansion of Chinese cities are the unprecedented scale and pace of changes to urban living environment. There is an imperative to assess residents' perceptions of neighbourhood environment and the impacts on life satisfaction. Drawing on a large-scale residential satisfaction survey conducted in Beijing in 2013, we examine the finegrained spatial distribution and determinants of residents' life satisfaction. A multilevel ordinal response model is employed to investigate the roles of neighbourhood satisfaction, perceived relative income, socio-demographic characteristics, and contextual factors in predicting life satisfaction. Results show that satisfaction with key neighbourhood characteristics including safety, physical and social environments, and travel convenience is statistically significantly associated with life satisfaction. Income relative to that of peers in local areas or to that in the past is a more important predictor of life satisfaction than absolute income. Other individual-level variables, such as age, family structure, hukou status, health, commuting time, and housing-related variables including housing tenure and floor space, are significant correlates of life satisfaction.

This paper develops a methodology for extending multilevel modelling to incorporate spatial interaction effects. The motivation is that classic multilevel models are not specifically spatial. Lower level units may be nested into higher level ones based on a geographical hierarchy (or a membership structure—for example, census zones into regions) but the actual locations of the units and the distances between them are not directly considered: what matters is the groupings but not how close together any two units are within those groupings. As a consequence, spatial interaction effects are neither modelled nor measured, confounding group effects (understood as some sort of contextual effect that acts ‘top down’ upon members of a group) with proximity effects (some sort of joint dependency that emerges between neighbours). To deal with this, we incorporate spatial simultaneous autoregressive processes into both the outcome variable and the higher level residuals. To assess the performance of the proposed method and the classic multilevel model, a series of Monte Carlo simulations are conducted. The results show that the proposed method performs well in retrieving the true model parameters whereas the classic multilevel model provides biased and inefficient parameter estimation in the presence of spatial interactions. An important implication of the study is to be cautious of an apparent neighbourhood effect in terms of both its magnitude and statistical significance if spatial interaction effects at a lower level are suspected. Applying the new approach to a two-level land price data set for Beijing, China, we find significant spatial interactions at both the land parcel and district levels.

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