How We Summarize Fine-Grained Accessibility Metrics
At Conveyal, we provide tools that allow computing multimodal accessibility at a disaggregate, granular level across an entire urban region, allowing the creation of detailed maps that show (for example) the number of jobs every resident has access to within 60 minutes. These maps are very useful, particularly for evaluating the comparative effects of different future scenarios and seeing what areas of the city see benefits from a proposed service change. However, they represent a wealth of information, and sometimes it’s useful to summarize that information down to a single number, or just a few.
In the past, we’ve used a metric known as population-weighted mean accessibility, defined in Alain Bertaud’s paper “Cities as Labor Markets.” This metric is the average number of jobs accessible to all residents in a metropolitan region.
The major critique of this measure is that it covers up the often-significant variation in accessibility across a region. For instance, residents living downtown may be able to reach a very large number of jobs within a given commuting time limit, while residents living in the suburbs may have access to few jobs (particularly via modes such as transit or bicycling). The population-weighted accessibility metric would combine the experiences of residents of these two areas, yielding an average accessibility somewhere between the two extremes.
To avoid this bias, Conveyal’s Analysis platform now provides a histogram of accessibility, rather than a simple average. This shows the number of people who can access a particular number of jobs. Others have used conceptually-similar plots of cumulative accessibility over the population (for instance Joe Grengs), or metrics related to the cumulative distribution of other transport metrics (e.g. Delbosc and Currie).
Let’s take a concrete example: New York City. The New York region has a population-weighted mean accessibility of 848,000 jobs. However, as the histogram below shows, that average covers up significant variation. The X axis indicates the number of jobs accessible via transit, while the Y axis (the height of the bars) indicates the number of workers in the region who experience that level of access.
As the histogram shows, much of the resident workforce of the New York region has access to very few jobs via transit, as indicated by the high bar on left. However, some have access to a very large number of jobs, most likely those in Manhattan and inner Brooklyn and Queens. These numbers average out to 848,000. This reflects the central tendency, but a very small number of people actually experience the mean accessibility; the population-weighted mean obscures the significant variation in the accessibility numbers.
This is true even at a smaller scale. The below histogram shows the job access for residents of Brooklyn. The population-weighted accessibility is 1.47 million, however again this covers up variation even within a single borough of New York.
In this case, the distribution is bimodal. There are a number of workers living in Brooklyn who have relatively low accessibility, and there are also a number with much higher accessibility. The population weighted average does not capture this nuance but rather falls right between the two peaks. As the map below shows, Brooklyn has a lot of residents near downtown (i.e. a high density of dots) as well as a lot of residents in outer areas away from the subway. These residents downtown experience high accessibility (dark blue, corresponding to the right peak on the above histogram), whereas those more distant experience lower accessibility.
These histograms showing the distribution of accessibility are of course interesting, but they can’t directly replace the population weighted average. There are cases where the accessibility impacts of a particular plan need to be reduced to a single number (for the purposes of setting targets for metrics, for example). While we generally caution against these situations, when they do arise it is important to carefully choose a metric that matches the goals of the city.
If we need to summarize these distributions of accessibility to a single number, we use percentiles. For example, in Brooklyn, 80 percent of the resident workforce has access to more than 537,000 jobs within a 45-minute transit commute. Setting a goal of having, say, more than 600,000 jobs accessible by at least 80 percent of the residents is more meaningful than a weighted average metric. This percentile-based metric recognizes that some percentage of residents, due to their residential location choices, cannot have a high job accessibility with a reasonable level of public investment. Additionally, it is not affected by high outliers in the way measures based on the mean are; if there is one small area that has access to a very high number of jobs (for instance, due to a well-connected train station), that will not drastically influence this metric if the number of people who live in that location and experience that access is small. These high and low outliers could greatly affect a population-weighted average accessibility number.
We recommend using the most detailed metric possible for a given task. For example, we generally recommend maps of accessibility at each point throughout a region, rather than these aggregate measures. When an aggregate measure is needed, histograms of the distribution of accessibility provide a more nuanced view than a single metric. When a single number is needed, setting a goal for a particular percentile of accessibility (e.g. 80 percent of the population has access to at least 1,000,000 jobs) is more representative and less sensitive to outliers than a population-weighted mean measure.
Conveyal provides consulting and software for undertaking accessibility analysis of public transportation systems. If you’re interesting in working with us, get in touch!
Matthew Wigginton Conway is a PhD student in the School of Geographical Sciences and Urban Planning at Arizona State University, and a former Conveyal employee.
