No single measure such as density can capture the complexity of urban patterns, including the distribution of housing units. For my research looking at 59 large urban areas from 1950 to 2010, I wanted to develop multiple measures of urban patterns to better characterize these areas.
Since around the turn of the century a significant amount of work has been undertaken to identify many variables to quantify urban patterns, mostly to assess levels of urban sprawl. I have raised questions about these multiple dimensions of sprawl efforts before on this blog (here and here). I am not claiming now to be measuring sprawl, but these efforts provided many possible measures to consider. Too many, as some studies included literally dozens of variables with meanings and differences difficult to discern.
My objective was to identify a small set concepts that captured the most important aspects of urban patterns. I then selected a single variable for each concept that I felt was both among the best measures and, to the extent possible, was easy to understand and interpret.
The overall density of housing units in the urban area is the first, obvious measure.
The extent to which densities varied across census tracts came next. This is measured using the index of dissimilarity. This is a measure of the proportion of housing units that would have to be moved to other census tracts to produce a uniform distribution with equal densities in all tracts.
The centralization of housing units in the urban area, the extent to which more housing units were closer to the center, is an important aspect of the urban pattern. For this, I developed a measure I am calling the centralization ratio, which looks at the mean distance housing units are located from the center and is the proportional reduction of distance compared with the mean distance to the center if housing units were uniformly distributed.
Finally, while centralization is one form of clustering, multiple clusters of higher density housing units can exist at various locations in an urban area. This clustering is measured using Moran’s I, a measure of spatial autocorrelation. This is essentially a correlation coefficient between tract densities and the densities of the adjacent tracts.
More information on these measures, their rationale, and an empirical assessment can be found in my paper, “Developing Multiple Measures of Urban Patterns,” which can be downloaded here.