Measuring Accessibility and Segregation

This section discusses how the concepts and techniques discussed in this chapter were translated into measures of accessibility and segregation in the literature.

Measuring Accessibility

Several approaches for quantifying accessibility in people’s activity spaces can be found in the literature. Those can be classified into four categories: geometric measures, cardinal measures, temporal measures, and utility measures.

Geometric measures are the most traditional in time geography. The volume of an individual’s space-time prism can be considered a direct proxy for that individual’s accessibility (Lenntorp 1976; Burns 1979; Miller 1991). However, due to the inherent difficulty of working with three-dimensional prisms, the area of two-dimensional potential path areas are more frequently used as measures of individual accessibility in practice, such as in Newsome, Walcott, and Smith (1998) and Kamruzzaman and Hine (2012). Such geometrical measures are not considered good measures of accessibility, though, as they may contain too many empty and unreachable spaces which provide no value to the individual (Miller 1991; Kim and Kwan 2003).

Cardinal measures are derived from the number of feasible opportu- nities in the individual’s PPA, stemming from Lenntorp’s (1976) work. These measures tend to be considered more adequate representations of an individual’s accessibility than their PPA’s geographic extent, due to the aforementioned issues with geometric measures. Following Kwan (1998) and Kim and Kwan (2003), a generic accessibility measure based on the number of reachable opportunities can be defined by equation 2.1.

As =

X

WkI(k) (2.1)

In equation 2.1, the function I(k) indicates whether the activity k is part of the individual’s feasible opportunity set (FOS), as per equation 2.2.

I(k) =    1, if k ∈ F OS, 0, otherwise; (2.2)

In equation 2.1, Wk accounts for the weight of opportunity k. This

parameter can be used to differentiate each opportunity’s contribution to the individual’s total accessibility, or else simple set to 1 to use the size of the choice set as an accessibility measure. Kwan (1998), for example, sets this parameter to the land parcel’s area multiplied by a building-height factor, as a proxy for real parcel’s properties such as retail floor space and employment. Cardinal measures can be interpreted as measures of freedom of choice (Neutens et al. 2010), since an individual is more likely to find suitable locations to carry out desired activities in larger opportunity sets.

Temporal measures of individual accessibility, according to Neutens et al. (2010), account for the amount of time available for carrying out each activity. For example, an opportunity has no practical value to an individual if its opening hours are not coincident with the individual’s free time, or if the time available is too short to carry out the desired activity. Temporal measures are defined as per equation 2.3: As= max k∈F OS[(t e k− tsk)I(k)] (2.3) In equation 2.3, te

kand tskare the earliest ending time and latest starting

time of activity k, respectively. While cardinal accessibility measures count all opportunities, temporal measures only consider the opportunity with the maxi- mum benefit in terms of the time available to participate on the activity. This is a measure of an individual’s temporal freedom (Neutens et al. 2010), or their freedom of choosing when and for how long to carry out a particular activity.

Utility measures were developed originally by Burns (1979) and extended by Miller (1999) based on concepts of random utility theory. In these measures, opportunities are differentiated by their utility to an individual, accounting for the benefits obtained from participating in that activity by weighing in factors such as attractiveness, possible activity duration and proximity (Neutens et al. 2010). A locational benefit can be defined as in equation 2.4.

Bik = akTije−λtik (2.4)

In equation 2.4, Bik is the locational benefit individual i obtains from

participating in activity k, ak is the attractiveness of activity k, Tij is the maxi-

mum duration of activity k considering individual i time-budget constraints, tik

is the combined travel time from previous activity to activity k and from activity k to the next activity, and λ is a travel time/distance decay parameter.

According to Neutens, Versichele, and Schwanen (2010), two versions of individual accessibility measures can be derived from the locational benefit concept: a) the additive, considering all opportunities in the FOS contribute to the individual’s accessibility; and b) the maximative, assuming the utility an individual obtains from the opportunities available is equal to the opportunity with the largest benefit in the FOS. The additive and maximative measures are defined below, in equations 2.5 and 2.6, respectively:

Aadd_ik = X

k∈F OS

Amax_ik = max

k∈F OSBik (2.6)

Measuring Segregation

The approach to measuring segregation on activity spaces usually follows simi- lar techniques to the place-based segregation indices discussed earlier. The main difference is that activity space segregation studies use representations of space beyond the residential location, which are derived from people’s activity and mo- bility patterns. For example, the population composition may present significant variation in different areas of the city throughout the day, even when fixed spatial units such as census tracts are considered, thus affecting the evenness/clustering dimension of segregation. People visiting different places have different probabil- ities of meeting members of other population groups, thus changing their levels of isolation and exposure. Once an activity space is defined for an individual, or even a group of individuals, applying the same place-based segregation indices to the activity spaces is usually a trivial task. A few techniques and possibilities are worth mentioning here, though.

The extent of an individual’s activity space can give insights in their mobility levels and overall experience of the city. Some travel behaviour metrics, such as number of trips (Sch¨onfelder and Axhausen 2003), number of places of activity visited (Yip, Forrest, and Xian 2016; Aksyonov 2011; Silm and Ahas 2014a), and geographical extent of activity locations (Palmer et al. 2013; Wang, Li, and Chai 2012; Wang and Li 2016) can be used to assess differences in activity spaces among groups. Some studies (Lee and Kwan 2011; Jang and Yao 2014; Huck et al. 2019) focus on techniques to visualise activity spaces, highlighting the extent of each group’s reach over the urban area and identifying patterns of occupation of each group.

The dimension of segregation most explored in activity space segrega- tion studies seems to be the exposure/isolation dimension. People living apart may interact with each other by visiting neighbourhoods mainly inhabited by other population groups (Yip, Forrest, and Xian 2016; Palmer et al. 2013) or in their trajectories on the road network when inbetween activities (Netto 2017; Netto et al. 2018). The amount of time spent on one’s own territory rather than in territories perceived as belonging to other groups can be seen as an important indicator of ethnic isolation, such as the case of ultra-ortodox Jewish and Pales- tinian Muslim women in Jerusalem, which avoid each others’ territory but share spaces inside secular Jewish areas (Greenberg Raanan and Shoval 2014).

Another method worth mentioning here was developed by Farber et al. (2015), who use origin-destination (OD) matrices from the census to calculate the Social Interaction Potential (SIP) of a region based on the concept of joint- accessibility (Farber et al. 2013). Joint-accessibility measures the amount of time

available for two individuals to participate in the same activity together. The SIP represents the average volume of the intersection between the space-time prims of all pairs of individuals in a region by aggregating their joint-accessibilities. The measure can be decomposed by social group, to estimate the exposure or isolation of each group. However, flow data contains no temporal information nor real trajectories, which need to be estimated to calculate the study region’s SIP.

Discussion

It is clear from the discussion above that accessibility and segregation are ap- proached rather differently in the literature, when it comes to actually measuring both phenomena. Individual-based measures of accessibility seem to be more mathematically well defined and applicable to more diverse situations. Segre- gation studies, however, tend to use more ad-hoc approaches to quantifying the problem, which depend on the definition of activity space used and available data. As previously mentioned, individual-based segregation studies are more re- cent than individual-based accessibility studies, which may partially explain this difference.