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.
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.
Johnston R., Burgess S., Wilson D. and Harris R. (2006) School and residential ethnic segregation: an analysis of variations across England's Local Education Authorities, Regional Studies 40, 973-990. Schools are central to the goals of a multicultural society, but their ability to act as arenas within which meaningful intercultural interactions take place depends on the degree to which students from various cultural backgrounds meet there. Using recently released data on the ethnic composition of both schools and small residential areas, this paper explores not only the extent of ethnic segregation in England's schools, but also whether that segregation is greater than the underpinning segregation in the country's residential areas. The results show greater segregation in schools - considerably so for primary schools and more so for some ethnic groups relative to others - than in neighbourhoods, patterns which have considerable implications for educational policy. Johnston R., Burgess S., Wilson D. et Harris R. (2006) La segregation ethnique a l'ecole et au foyer: une analyse de la variation a travers les adminstrations locales d'Angleterre qui gerent les affaires scolaires, Regional Studies 40, 973-990. Les ecoles sont au coeur de la reussite d'une societe multiculturelle, mais leur capacite a se servir d'arenes au sein desquelles des interactions interculturelles significatives ont lieu depend du point auquel les ecoliers provenant de differents milieux s'y rencontrent. A partir des donnees recemment sorties sur la composition ethnique des ecoles et des petites zones residentielles, cet article cherche a examiner non seulement l'importance de la segregation ethnique dans les ecoles d'Angleterre mais aussi a etudier si, oui ou non, cette segregation-la depasse la segregation sousjacente dans les zones residentielles du pays. Les resultats laissent voir une segregation plus importante a l'ecole - notamment a l'ecole primaire et encore plus pour certains groupes ethniques par rapport aux autres - que dans les voisinages, des distributions dont il y a d'importantes lecons a tirer pour la politique de l'education. Education, Segregation, Ecoles, Voisinages, Angleterre Johnston R., Burgess S., Wilson D. und Harris R. (2006) Schulbesuch und nach Wohnsitz bestimmte ethnische 'Trennung': eine Analyse der Schwankungen im Gesamtbild der Schulbehorden Englands, Regional Studies 40, 973-990. Bei den Zielen einer von verschiedenen Kulturen gepragten Gesellschaft spielen Schulen eine wesentliche Rolle, doch ihre Fahigkeit, als Schauplatz sinnvoller, interkultureller Wechselwirkungen zu fungieren, hangt von dem Mass ab, in dem Schuler verschiedener kultureller Werdegange einander kennenlernen. Mit Hilfe kurzlich veroffentlichter Daten der ethnischen Zusammensetzung der Schulen und kleiner Wohnbezirke untersucht dieser Aufsatz nicht nur das Ausmass der ethnischen Trennung in den Schulen Englands, sondern auch, ob diese Trennung starker ist als die zugrunde liegende Trennung in den Wohnbezirken des Landes. Die Ergebnisse weisen...
Neighborhoods, ethnicity and school choice: developing a statistical framework for geodemographic analysisGeodemographics as the 'analysis of people by where they live' has origins in urban sociology and social mapping, and is experiencing a renaissance in applied spatial demography. However, some commentators have expressed reservations about the statistical limitations of common geodemographic practices, especially focusing on the potential internal heterogeneity of the geodemographic groupings, as well as the problem of clearly identifying predictor variables that might account for or explain the socio-economic patterns revealed by geodemographic analyses.In this paper we argue that geodemographic typologies are structured methods for making sense of the spatial and socio-economic patterns encoded within complex datasets such as national census data. By treating geodemographics as more a framework than a tool for analysis in its own right we are able to integrate it with the flexibility and statistical conventions offered by multilevel modeling. We demonstrate this with a case study of whether pupils from different types of neighborhood in Birmingham, England are more or less likely to attend their nearest state funded secondary school and how that likelihood varies with the ethnic composition of the neighborhood. In so-doing we build on previous research suggesting that ethnic segregation between schools is at least equal to that between neighborhoods in England and speculate in this regard on the consequences of current Government plans to extend choice to parents within a schools market.2
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.