(Cutsinger land use patterns as well as enhanced

(Cutsinger et al., 2005) updated the index by using twelve
conceptually distinct dimensions of land use patterns as well as enhanced the
analytical procedure by including a mixed-use
development metric – connected but distinct from proximity, and also examined
the sprawl profiles for fifty towns and cities in the United States. The
authors discovered that cities usually ranked highly in certain dimensions
score quite low on others, suggesting an intricate portrait of metropolitan
growth and morphology, and also argued that if a location may be referred to as
sprawling depends on which variables are now being considered (e.g.,
CBD-proximate development, overall density, etc.). (Laidley, 2016)

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)

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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)