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Another important initial effort was that of Ewing, Pendall, and Chen (2002). They computed sprawl in two steps: first, using principal component analysis, they developed indices for four constituents of urban form—development density, land use mix, activity centering, and street accessibility. They then combined the 4 factors into a general compactness/ sprawl index. The general index and both the single elements were then validated against transportation outcome measures. The most recent work (Hamidi & Ewing, 2014) adds employment and walkability data in constructing the sub-indices. Similar to (Cutsinger et al., 2005), Ewing and Hamidi incorporate numerous variables related to spatial morphology into their measure, among them centralized development (a measure of compact mono-centric growth), density gradients (how fast density declines with distance from the CBD), street accessibility (average city block size), and “centering” measures (the proportion of population and employment within CBDs and sub-centers). Using these measures the authors calculate sprawl indices for counties, metropolitan areas, and urbanized areas in the United States. They also demonstrate the validity of their measure by regressing a number of outcome variables (e.g., housing affordability, obesity rates, etc.) on the composite measure and its sub-indices. These approaches have many strengths, first and foremost the complex way they statistically reduce many distinct aspects of urban form. The index offered by Ewing in particular has been used on numerous research projects exploring public health and energy use outcomes, establishing a track record in the literature (e.g., (Ewing et al., 2003; Ewing & Rong, 2008; Hamidi & Ewing, 2014)

Recent work by Paulsen (2014) and Tsai focused on changes in regional sprawl patterns over time. The former describes changes in housing density using four variables: Overall change in housing unit density, marginal land consumption of each new housing unit, the density of housing in newly urbanized areas, and the percentage of net new housing construction in places already urbanized. Tsai develops a sprawl index which expresses the proportion of metro population in low- and high-density subareas (i.e., the percentage of population in the top and bottom quintiles, based on subarea density distributions computed for each metro). Tsai’s measure must not necessarily be expressed dynamically, as unlike Paulsen’s land consumption approach, it is based on discrete sprawl scores calculated at different time points. Nevertheless, it pegs thresholds to regional percentile scores rather than establishing universal cut points, making it more suitable for examining changes over time within individual urban areas as opposed to illustrating the differences between them. Although both methods offer valuable tools for analyzing the changing nature of sprawl and urban development, they are less useful for deciphering these cross-sectional interurban differences. (Laidley, 2016)

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