Environment and Planning B: Urban Analytics and City Science

This paper introduces the Multilevel Index of Dissimilarity package, which provides tools and functions to fit a Multilevel Index of Dissimilarity in the open source software, R. It extends the conventional Index of Dissimilarity to measure both the amount and geographic scale of segregation, thereby capturing the two principal dimensions of segregation, unevenness and clustering. The statistical basis for the multilevel approach is discussed, making connections to other work in the field and looking especially at the relationships between the Index of Dissimilarity, variance as a measure of segregation, and the partitioning of the variance to identify scale effects. A brief tutorial for the package is provided followed by a case study of the scales of residential segregation for various ethnic groups in England and Wales. Comparing 2001 with 2011 Census data, we find that patterns of segregation are emerging at less localised geographical scales but the Index of Dissimilarity is falling. This is consistent with a process whereby minority groups have spread out into more ethnically mixed neighbourhoods.

Neighborhoods in US metropolitan areas experienced dramatic changes in racial composition during the 1990s and again during the 2000s. We ask to what extent does the recent period of neighborhood racial change reflect an extension of the local processes operative in the 1990s, processes characteristic of large metropolitan areas or the nation more generally, or reflect new dynamics. After classifying neighborhoods in US metropolitan areas into different types based on their racial composition and having harmonized a set of tracts to consistent boundaries, we use metropolitan-scale tract transition matrices from the 1990s to predict changes in neighborhood racial mix between 2000 and 2010. To capture scale effects, we repeat this using a set of pooled metropolitan-scale tract transition matrices and again using a national tract transition matrix. We show that the main dynamic at work across the metropolitan system is the underprediction of moderately diverse white majority tracts: i.e., in the 2000s, the rate of increase in the racial diversity of white majority tracts that transitioned from being predominantly white to moderately diverse was much higher than expected based on 1990s trends. In some metropolitan areas, shares of moderately diverse white tracts in 2010 are anticipated by their 1990s neighborhood dynamics, suggesting temporal stability and a locational specificity in these processes. Others experience a temporal rupture in these dynamics, and their moderately diverse white tract share is better anticipated by pooling transition information. The study also invites us to think about the nature of residential change currently taking place that we can capture in 2020 census data.

Studies of segregation continue to explore analytic tools to engage with patterns of separation within cities. In recent work, scale has emerged as an important dimension of understanding segregation – simply put, separation is strongly affected by the scale which is used in the measurement process. Levels of segregation are also influenced by the time in which the analysis takes place. We outline an approach to separation which has four dimensions – (1) using bespoke neighborhoods – who do you meet at varying scales, (2) measuring the size of the change in separation over time, (3) estimating the rate of change in separation across space and time and (4) visualizing the change, mapping changing levels of contact. The themes are explored using data from the diverse, multi ethnic neighborhoods in Californian metropolitan areas. The result of a bespoke neighborhood approach to segregation provides a more complete demonstration of the pattern of ethnic segregation. We know that there are declining overall levels of segregation, but while levels are decreasing for Whites they are increasing for Hispanics and Asians but at different rates depending on local contexts. Viewing assimilation in a multi-scalar visual context expands our understanding of segregation and assimilation.

Multiscale segregation measures have the potential to increase understanding of residential context and ultimately a wide range of social and spatial processes. By examining segregation at multiple scales, we have the opportunity to study it as more than the outcome of a single process or a measure describing a single contextual effect. Multiscale segregation encourages us to look for sorting processes and contextual effects operating at different scales and potentially even with different meanings. However, the complexity of multiscale measures introduces significant uncertainty about the role of underlying data and assumptions in producing observed outcomes, particularly at fine geographic scales. While traditional measures of segregation have been exposed to decades of scrutiny, multiscale measures are still relatively novel and less well understood. The theoretical contribution of this paper is to consider the implications of segregation as both an outcome and signifier of sorting processes at multiple scales. The empirical contribution is to consider how zoning and the degree of spatial association shape outcomes expressed as multiscale segregation measures. I examine the effects of different allocation strategies for measuring population at small scales by comparing four delineation methods. I find that the method chosen for allocating population to small areas matters, but that by the time observation units reach about 700 m² most of the difference between methods has washed out. I also test the effect of changing the degree of assumed spatial association in generating multiscale segregation measures. I find that, as suggested by Reardon and O'Sullivan in their original exposition of their spatial segregation measure, this assumption has a relatively small effect on outcomes and is unlikely to shape substantive findings.

There has been extensive use of segregation indices for measuring residential segregation since 1950s, with continuous progress made in the field. Recent developments include the propositions of spatial global and local versions of traditionally used segregation indices, which have opened avenues for representing and analysing segregation as a multiscale and spatially varying phenomenon. Much less explored has been the issue of how important research design choices, such as the extent of geographical boundaries, grouping systems and scales of analysis, can influence the measurement of segregation. This paper contributes in this direction by investigating the impact of such decisions in the outcomes of the indices of generalized dissimilarity (D) and information theory (H) using a set of sensitivity analysis. Using a comparative study between London and São Paulo as basis, results obtained with different geographical boundaries, grouping systems and scales for the two indices are analysed visually and quantitatively. Results suggest that although D and H depict the same spatial dimension of segregation (unevenness/clustering), they present different sensitivity to geographical boundaries and grouping systems. The study also revealed how the two indices unfold different aspects of the segregation, which impact on their interpretation and applicability. The study concludes with a discussion of the considerations on research design choices concerning the interpretation of the results, which indicate the two indices should not be used interchangeably.

A well-known limitation of commonly used segregation measures is their inability to describe patterns at multiple scales. Multi-level modeling approaches can describe how different levels of geography contribute to segregation, but may be difficult to interpret for non-technical audiences and have rarely been applied in the US context. This paper provides a readily interpretable description of multi-scale Black–non-Black segregation in the United States using a multi-level modeling approach and the most recent Census data available. We fit a three-level random intercept multi-level logistic regression model predicting the proportion of the population that is Black (Hispanic and non-Hispanic) at the block group level, with block groups nested in tracts and tracts nested in Metropolitan Statistical Areas (MSAs). For the 102 largest MSAs in the United States, we then estimated the extent to which micro- versus meso-level variability drives overall racial residential patterning within the MSA. Finally, we created a typology of racial residential patterning within MSAs based on the total proportion of the MSA population that is Black and the relative contribution of block groups (micro) versus tracts (meso) in driving variation. We find that nearly 80% of the national variation in the geographic concentration of Black residents is driven by within-MSA, tract-level processes. However, the relative contribution of small versus larger scales to within-MSA segregation varies substantially across metropolitan areas. We detect five meaningfully different types of metropolitan segregation across the largest MSAs. Multi-level descriptions of segregation may help planners and policymakers understand how and why segregated residential patterns are evolving in different places and could provide important insights into interventions that could improve integration at multiple scales.

“Egocentric” segregation profiles allow researchers to avoid a reliance on a priori definitions of local neighborhoods that contribute an unknown amount of error to measures of segregation. To date, however, such profiles have used distance-decay techniques that rely on “as the crow flies” measures of space. Yet we know that major roads, railroads, and other physical attributes of space mean that such techniques may introduce error into the measurement and visualization of residential segregation. Here, I use a variation on standard smoothing techniques that allows the smoothing function to vary based on a second variable of interest, in this case, the location of major roads, railroads, and nonresidential land use. Using Philadelphia as a case study due to access to detailed land-use data, I show that barriers do not affect observed values of city-level racial and ethnic dissimilarity. Visualizing the impact of barriers on local neighborhoods, however, shows that while barriers may not affect city-wide indexes of segregation, they continue to powerfully shape local experiences of the city, including protecting new immigrant ethnic enclaves, wealthy white neighborhoods, and also isolating high-poverty, predominantly black neighborhoods in different parts of the city.

Traditional studies of residential segregation use a descriptive index approach with predefined spatial units to report the degree of neighbourhood differentiation. We develop a model-based approach which explicitly includes spatial effects at multiple scales, recognising the complexity of the urban environment while simultaneously distinguishing segregation at each scale net of all other scales. Moreover, this model distinguishes segregation as unevenness and as spatial clustering in the presence of stochastic variation. The modelling approach, unlike traditional index approaches, allows hypothesis evaluation concerning alternative scales and zonation through an accompanying badness-of-fit measure. Ultimately, this permits the identification of the scale and zonation regime where the spatial patterns come into focus thereby directly tackling the modifiable areal unit problem. The model is applied to Indian ethnicity in Leicester, UK, finding segregation as unevenness and as spatial clustering at multiple scales.

In this paper, we analyse the spatial dimension of changing ethnic diversity at the neighbourhood level. Drawing from recent work on income convergence, we characterise the evolution of population diversity in the Netherlands over space. Our analysis is structured over three dimensions, which allow us to find clear spatial patterns in how cultural diversity changes at the neighbourhood level. Globally, we use directional statistics to visualise techniques of exploratory data analysis, finding a clear trend towards ‘spatially integrated change’: a situation where the trajectory of ethnic change in a neighbourhood is closely related to that in adjacent neighbourhoods. When we zoom into the local level, a visualisation of recent measures of local concordance allows us to document a high degree of spatial heterogeneity in how the overall change is distributed over space. Finally, to further explore the nature and characteristics of neighbourhoods that experience the largest amount of change, we develop a spatial, multilevel model. Our results show that the largest cities, as well as those at the boundaries with Belgium and Germany, with the most diverse neighbourhoods, have large clusters of stable neighbourhood diversity over time, while concentrations of high dynamic areas are nearby these largest cities. The analysis shows that neighbourhood diversity spatially ‘spills over’, gradually expanding outside traditionally diverse areas.

What are the social bases of neighborhood formation in urban areas, and at what spatial scale are they most distinct from other neighborhoods? We address these questions in the case of St. Louis, Missouri, in 1930, where we can take advantage of unique geocoded census microdata on the whole population of the city that identifies who, with what background characteristics, lived where. Our analyses show that homophily by race and ethnicity was by far the strongest factor linking characteristics of persons to the composition of their neighbors. Measures of social class also were quite important, while the person’s nativity and family status were statistically significant but minor predictors. Yet while this hierarchy of social factors held for the population as a whole, their relative importance varied greatly across racial/ethnic groups. Similarity in social class to neighbors was most important for native whites, nativity counted as much or more than class for recently arriving immigrant groups including Russians, Italians, and Poles, and race/ethnicity was by far the key predictor for these groups and blacks. We also found that these patterns of homophily were clearest at the scale of individual street segment and first-order combinations of segments. They were similar but less distinct at a larger spatial scale.