Personalizing the dichotomy of fixed and flexible activities in everyday life: deriving prism anchors from GPS-enabled survey data

Abstract

Space–time prism is a fundamental concept in time geography that can model an individual’s accessibility to resources under space–time constraints. A prism anchor is often defined by work, school, or home activity with a fixed location and schedule. Trips and other activities are relatively flexible and scheduled between prism anchors. This fixity-flexibility dichotomy may not capture the increasing complexity of human mobility behaviors or variations among individuals. Recent developments in location-aware technologies allow us to collect person-level mobility data with detailed space–time paths and contextual information. This article develops methods to extract prism anchors from these GPS-based survey data and examines whether home, work, and school activities can always be used to define prism anchors for everyone. To illustrate our methods, we use data collected in Minnesota and Beijing as two study cases. Results in both study cases suggest that not everyone has home, work, or school anchors, and people with the same socio-demographic background tend to have similar anchor types. By deriving home, work, and school anchors, we can better understand how a person’s everyday schedules are governed by home, work, and school and refine person-based accessibility measures.

Introduction

Space–time prism is a fundamental concept in Hägerstrand’s time geography that has been applied to model individuals’ movements in space across time and evaluate their access to resources given space–time constraints (Hägerstrand 1970; Kwan 1999; Delafontaine et al. 2011; Lee and Miller 2019). A prism anchor is defined by activity with a fixed location and time (Miller 2016). Existing studies have often used home, work, and school as prism anchors, while trips and other activities are viewed as flexible and modeled as intermediate stops scheduled between two prism anchors (Dijst and Kwan 2005; Neutens et al. 2007). This dichotomy has been widely applied to evaluate a person’s access to resources and opportunities sparsely distributed in space and time. For instance, researchers have used the home or work location of an individual as the reference place to calculate the number of reachable opportunities within a given time budget (e.g., Handy and Niemeier 1997; Talen 1997; Levinson 1998). Some studies have incorporated both the timing and location of home and work activities to measure space–time accessibility (e.g., Neutens et al. 2012).

Using home, work, and school as prism anchors are intuitive given our need to sleep at night, mostly at home, and work or attend school during regular working or school hours. However, this fixity-flexibility dichotomy has become increasingly problematic (Neutens et al. 2011). First, individuals’ activity-travel patterns have become more complex and diverse than ever before with the increasing mobility and urbanization progress. People may have multiple homes and flexible working locations and hours. Meanwhile, they may have fitness classes and social events that are fixed in space and time. So, there is a need to revisit the classic fixity-flexibility dichotomy. Second, using the same way to define prism anchors for all people ignores different scheduling and mobility constraints among individuals (and socio-economic groups). For instance, parents with young kids often have additional constraints given their childcare responsibilities besides their work schedules. Another example is that part-time employees may be less likely to have work anchors than full-time employees. The fixity-flexibility dichotomy may fail to capture these interpersonal variations and complex activity-travel behaviors. Therefore, to better measure individuals’ potential activity space and person-based accessibility, it is necessary to re-examine whether home, work or school activities can always serve as prism anchors for all individuals.

In transportation studies, traditional travel surveys and activity diaries have typically been collected and analyzed under the ‘home-work’ anchor framework. Most of these surveys often ask respondents to provide their primary home addresses and workplaces in the one-time intake survey as well as report their trip destinations or activity locations (e.g., Stecher et al. 1996; Griffiths et al. 2000; Stopher and Greaves 2007; USDOT 2017). Some surveys allow participants to list more than one home location and workplace, but most surveys only include travel and activity diaries for just one day, which makes it challenging to validate these reported locations and analyze how frequently and when the participant visits each of these locations (Aschauer et al. 2019). The newly trending GPS-enabled travel surveys can potentially address this challenge by tracking a person’s actual movements across one week or even longer periods (e.g., Wolf 2000; Shen et al. 2013; Wu et al. 2018). Such GPS-enabled surveys often contain rich thematic information about activities and trips, such as activity types and travel modes (e.g. Cottrill et al. 2013; Shen and Stopher 2014). Hence, researchers can better understand how home and work activities are conducted in space (where) and time (when). Moreover, the week-long travel data from each participant collected by GPS-enabled surveys make it possible to examine the role of ‘home’ and ‘work’ in a person’s daily schedules and the variations of such roles across multiple days (e.g. weekdays vs weekends).

Therefore, this article aims to develop a framework and methods to extract personalized prism anchors from GPS-enabled travel survey data. We develop data-driven methods to examine the space–time fixity of home, work, and school activities, which capture both global patterns and individual variations of spatial and temporal profiles of the activity. We use two sets of one-week survey data as study cases: one collected in Twin Cities metropolitan areas, Minnesota, U.S.; and one collected in the Shangdi-Qinghe area, Beijing, China. We relax the dichotomic classification of space–time fixity in time geography by looking at an individual’s actual schedule across multiple days beyond the typical ‘home-work-home’ schedule. The extracted personalized home, work, and school anchors can potentially contribute to our better understanding of individuals' activity-travel behaviors and a refined measure of person-based accessibility.

The next section provides a brief review of time geography and activity-based approaches in travel behavior studies and identifies the research gaps in the existing studies that involve prism anchors. The data section describes the two study areas and GPS-based survey data. The method section illustrates our framework to define prism anchors and the methods to determine space–time fixities of recorded activities. The result section presents findings and illustrates our contributions to travel behavior analysis and person-based accessibility measures. We conclude the article with key findings and discuss its usefulness in future studies.

Background

This section introduces the time geography theory and activity-based approach, which provide the theoretic foundation of space–time prism anchor and have been widely applied in travel behavior studies. We then focus on the previous studies which examine the important activities in one’s life and point out the usefulness of GPS-enabled surveys in the analysis. Lastly, we review the existing studies which discuss the space–time fixity and prism anchor in both analytical and data-driven frameworks of time geography, as well as highlight the motivation and objective of this article.

Time geography and activity-based analysis in travel behavior studies

Time geography provides a constraint-oriented approach to understanding human activities and trips in space across time and has been widely applied in transportation and regional planning (Hägerstrand 1970). It recognizes the space–time constraints people would face while scheduling their everyday activities and trips. Space–time prism (STP), therefore, can be defined given these constraints and used to represent an individual’s feasible and potential trips and activities (Miller 2016). Specifically, individuals’ daily activities are divided into two types: fixed activities and flexible activities. Fixed activities are those with fixed locations and time schedules and serve as anchor points in people’s daily routines. When people schedule flexible activities and trips between two fixed activities, the feasible options are confined to a certain spatial area and a time budget. Analytically, Miller (2005) developed a model that uses x, and y coordinates to represent geographic space and a vertical (z) axis to represent time. Figure 1 illustrates STPs and how prism anchors influence our ability to participate in non-anchor activities. The projection of an STP to the geographic space is called its potential path area (PPA) which delineates the potential activity space of an individual given prism constraints.

Fig. 1.

Space–Time Prisms (STPs)

Existing literature often considers home, work, and school as fixed activities and uses them to define prism anchors, whereas other activities such as leisure, recreation, and shopping are seen as flexible and scheduled between prism anchors. This is intuitive given the ‘capability constraints’ formulated from human biological construction, such as the necessity of sleeping a minimum time at one’s home base, often at night (Hägerstrand 1970). It is also necessary for people to undertake economic activities for a required amount of time to get paid for a living, mostly during regular working hours on weekdays (coupling constraints).

Defining prism anchors using home and work schedules is also consistent with the activity-based approach that studies individuals’ agendas of activity participation and views trips as derived demands to reach activities sparsely distributed in space and time (Miller 2021). The key concept ‘tour’ in the activity-based approach represents a round trip from one place back to the same place, and the occurrence of home-based tours or work-based tours has been widely used to describe or predict activity-travel patterns (Mcnally 2000; Pinjari and Bhat 2011; Jiang et al. 2017). Different representation frameworks have been developed to accommodate various social-demographic groups, such as workers and non-workers. For instance, Bhat and Singh (2000) described the daily patterns of workers by five sub-components: (1) before-work, (2) home-work commute, (3) work-based, (4) work-home commute, and (5) after-work patterns. For non-workers, Bhat and Misra (2000) represented their daily patterns as a set of home-based tours, with each as a sequence of out-of-home activities between two at-home activities. The underlying assumption of these two example frameworks is that home and work have fixed locations and everything else is organized based on them. Recent studies have started to relax such assumptions by examining the entire activity-trip sequence, but behavior patterns are still explained using similar frameworks (e.g., Kwan et al. 2014; Goulet-Langlois et al. 2017; Su et al. 2020; Song et al. 2021).

Using the ‘home-work’ framework to define individuals’ prism anchors and study activity-travel patterns, however, has become increasingly problematic. The increased mobility and, more generally, urbanization provide more choices for people and make their travel behaviors much more complex and diverse than ever before. Moreover, the nature of space–time fixity of specific activity types may change due to the development of information and communication technologies (ICTs) (Kwan 2002; Hubers et al. 2008). The space–time constraints have been relaxed since some activities no longer need to be undertaken in the presence of certain places, such as e-shopping and working from home (Schwanen and Kwan 2008). Thus, given the personal heterogeneity and increasingly complex activity-travel patterns, the classical ‘home-work’-based fixity-flexibility dichotomy in time geography may not reflect reality comprehensively.

Enhancing understanding of important activity with available data

The space–time fixity of activity was discussed earlier by Cullen and Godson (1975) that it can be determined by the degree of established commitment. Activities with high levels of commitment, such as routine activities, are considered virtually immovable points in a person’s day. In line with Cullen and Godson, some studies have started to examine the definition of routine activities. Earlier works have commonly used paper-based or computer-assisted travel surveys (or activity diaries) and considered the total number, frequency, or duration of activities across different days to identify routine activities (Kitamura and Van 1987; Huff and Hanson 1990; Kang and Scott 2010). Studies also developed specific indices to measure the day-to-day variability of activity-travel patterns, such as the concentration index and the within-person sum of squares (e.g. Schlich and Axhausen 2003; Raux et al. 2016). These attempts have mainly focused on frequencies and temporal rhythms of activities and trips, but have not addressed the spatial aspects of the patterns.

To address the spatial variations of activity locations, studies have used pure trajectory data to extract frequently visited locations as the significant places in individuals’ everyday schedules (e.g. Muthyalagari et al. 2001; Stopher and Zhang 2011; Chen et al. 2016). The rich trajectory data, however, lack thematic information provided by participants and requires further imputation, such as assigning the most frequently visited locations as home and workplace (Alexander et al. 2015; Gong et al. 2016). Recent advances in the integration of location-aware technologies (e.g. GPS) into activity-travel surveys can collect individuals’ space–time trajectories and user-entered activity information (Fan et al. 2015; Fillekes et al. 2019). These GPS-enabled surveys, therefore, allow researchers to comprehensively understand activities regarding their roles in one’s daily schedule considering the spatial, temporal, and thematic properties of each activity.

Related studies on space–time fixity and prism anchors

Discussions about the space–time fixity and prism anchor have been made in both analytical and data-driven frameworks of time geography. Some studies focused on refining the analytical representation of prism anchors to relax the restriction on using a single point to represent a prism anchor. For instance, Kuijpers et al. (2010) proposed the ‘anchor region’ with a probability distribution on the possible locations of anchor points to represent the variation of anchors’ spatial locations. For the temporal aspect, Charleux (2015) modified the temporal attribute of an anchor by using the earliest starting and latest ending times with a duration. These analytical models can perform more realistic modeling of anchored activities that allow some flexibility in their definitions. However, these studies often use hypothetical data to demonstrate the methods and need further validation using in the real world.

To examine activity space–time fixity in the real case study, some researchers have collected data with more detailed thematic information from participants. Kwan (2000) designed a survey to collect perceived fixity of activities using questions such as ‘Could you have done this elsewhere?’ and ‘Could you have done this at any other time of the day?’. Similarly, Doherty (2006) asked participants to provide the acceptable activity durations and the number of possible activity locations for each activity. The surveys also asked about individuals’ social demographics which could lead to various fixity/flexibility patterns of daily schedules (Shen et al. 2015, 2020). For instance, studies found that females have more fixed activity locations and times than males (e.g. Schwanen et al. 2008; Kwan et al. 2009). These studies proved that it is necessary and feasible to use survey data to refine the definition of fixed activities and prism anchors. However, these studies are based merely on self-report data and thus the validity of the results might be biased because people’s memories are notoriously unreliable and people’s perceptions of the degree of fixity may vary a lot. Moreover, these studies focused more on the perceived scheduling process and may ignore that a stable schema rooted in people’s everyday activity and lifestyle could also organize one’s rules of behavior and execution of activities (Ramadier et al. 2005).

To address these gaps, this article examines whether home or work activity can serve as the prism anchor in a person’s everyday life according to its space–time fixity from a data-driven perspective. We use newly available GPS-enabled survey data that contain automatically recorded GPS trajectories and user-entered thematic (activity) information. Instead of relying on people’s perceived fixity, we adopt data-driven approaches to evaluate fixity by considering both spatial locations and temporal profiles of home and work activity across a person’s multi-day schedules.

Data and study area

In this article, we use two data sets collected in Twin Cities, Minnesota, U.S., in 2016–2017, and Shangdi-Qinghe areas, Beijing, China, in 2012. The Minnesota survey recruited 372 residents from six neighborhoods in the region, and the Beijing survey contains 677 participants recruited from 23 communities and 19 companies in the area (see Fig. 2).

Fig. 2.

a Study area in Twin Cities, Minnesota; b Study area in Shangdi-Qinghe, Beijing

The two datasets were collected using GPS-enabled activity-travel survey techniques but under different mechanisms. The Minnesota survey was collected using a smartphone application called Daynamica. Given the tracked GPS locations, the Daynamica app can automatically detect activity and trip episodes, impute travel modes in near real-time, and list them in the user interface. Participants are asked to confirm or modify these auto-detected activities and trips in the app at their earliest convenience. The detailed app structure and computation algorithms can be found in Fan et al. (2015). The Beijing survey used passive GPS trackers to collect movement trajectories, and a separate online survey was given at the end of each survey day to collect activity-trip diaries. The online survey visualizes the recorded GPS trajectories, and participants will use these maps to recall their activities and trips and enter basic information for each activity and trip episode (Chai et al., 2014). The GPS trajectories and activity-travel diary were integrated and reconciled as one dataset after all data have been collected. In sum, the major difference between the two datasets is how GPS trajectories are utilized in the data collection process. For the Minnesota data set, GPS trajectories are imputed into activity and trip episodes within the smartphone app; whereas for the Beijing data set, GPS trajectories are only used as a visualization tool for recall purposes. Another difference is that participants in Minnesota can confirm or edit the imputed activities and trips at their earliest convenience, but participants in Beijing need to fill out the activity-travel diary at the end of each day. In this paper, we format these two datasets in the same way:

$$E{p}_i:\left\{{\left({\left\{{\left(x,y\right)}_k\right\}}_{\mathit{ij}},T_{\mathit{ij}},A_{\mathit{ij}}\right)}_{j=1}^J\right\}$$ 1

where a person $i$’s daily log is structured as a sequence of activity-travel episodes $E{p}_i$ including spatial, temporal, and thematic information. Spatial information ${\left\{{\left(x,y\right)}_k\right\}}_{\mathit{ij}}$ is stored as the trajectory of the $j$th episode of the person $i$ as a series of longitudes and latitudes. Temporal information $T_{\mathit{ij}}$ is stored as the start and ending time of the episode $E{p}_{\mathit{ij}}$ with a precision level of 1-min. Thematic information $A_{\mathit{ij}}$ is stored as activity types and travel modes, such as home, work, school, and recreation for activity types, and car, bus, bike, and walk for travel modes.

Methodology

Framework

To better describe activity-travel behaviors and identify potential prism anchors for each individual, we propose a framework to conceptualize spatial fixity and temporal fixity and characterize each activity in terms of its space–time fixity (Table 1). The spatial fixity requires an activity to be stationary and performed at one single location or a few locations. As for the temporal aspect, the activity should be repetitive, that is, performed frequently enough across days. Furthermore, to be fixed in both space and time, the activity also needs to occur during similar times at each stationary location. Table 1 lists various classes of activities regarding fixity in space and time and uses ‘work’ activity and its space–time path as examples to illustrate these classes.

Table 1.

Conceptual framework of space–time anchor (taking Work as an example)

Degree of Fixity	Spatial Fixity
	Stationary location		Non-stationary location
	Single location	Set of locations
Temporal Fixity
Repetitive			Non-stationary “I work as an Uber driver/delivery man”
Similar period(s)	Single Anchor	Multiple Anchors
	“I work at my office from 9 am until 5 pm on workday”	“I work at my office on Mon-Wed, and work from home on Thu–Fri, 9 am–5 pm”
Different periods	Favorite Location	Preferred Locations
	“I work at my office with a flexible working time”	“I often work at my office or home with a flexible working time”
Non-repetitive	Occasional Event	Random Event
	“I sometimes go to my office to print materials”	“I sometimes work as a temporary babysitter for different families”

In this article, we focus on whether home and work activity serve as a single anchor or multiple anchors (or not serve any) in one’s schedule, and propose data-driven methods to identify them from GPS-based survey data. According to our framework, home or work activity serves as a single anchor, meaning that it happens at a single location and repetitively in similar periods. A person may have multiple home/work/school anchors if they happen in a set of locations (spatial fixity) repetitively during similar periods (temporal fixity).

Spatial fixity

In the GPS-based survey, users can confirm or modify the detected activity or trip episode, and thus, the survey can capture non-stationary activities that might be mistakenly imputed as a trip from a raw trajectory, such as working as an Uber driver and jogging for leisure along the river. To examine the spatial fixity of activities, we first distinguish stationary activities from those nonstationary activities and then identify their representative locations based on selected spatial indices and statistical methods.

Stationary/non-stationary activity

As illustrated in the Data and Study Area section, the spatial information of activity is stored as an ordered series of longitude and latitude (${\{{\left(x,,,y\right)}_k\}}_{\mathit{ij}}$ in Eq. 1). To identify stationary activities, we look at the shapes of trajectories for the same type of activities (e.g., home activity) for all people. We characterize the shapes of trajectories via the three indices below (Manaugh and El-Geneidy 2012).

1. Square Root of Area (SRA) is the minimum convex polygon (MCP) including the trajectory of an activity. The SRA can measure the covered geographical area, and thus, the spatial dispersion of activity.

2. Maximum Distance to Mean center (MDM) is the maximum distance between any trajectory points and the mean center of the trajectory. The MDM can be used to further identify a round-trip with a small SRA, such as strolling along one street back and forth (see example in Fig. 3B).

3. Distance from start to end location (Dist) uses the spatial displacement between the first and last trajectory points to describe the change in status of the movement.

Fig. 3.

Comparison between different trajectory shapes of home activities

Figure 3 shows a comparison between various shapes of ‘home’ activities in our real data set to illustrate the rationale of the chosen indices. A is within a limited space with small SRA, MDM, and Dist. B represents a movement along the road, typically with small SRA, but larger MDM and Dist; C is dispersed in the space with large SRA, MDM, and Dist; and D shows a round-trip with the same start and end location, and thus has a large MDM but small Dist. So these three indices can effectively capture the shape of activity and identify stationary activities.

We then use the gaussian mixture model (GMM) to classify activity into stationary and non-stationary given the indices SRA, MDM, and Dist for the same type of activities for all people. The GMM considers each observation as a mixture of $K$ multivariate-normal distributions where $K$ is the number of clusters (Banfield and Raftery 1993; Scrucca et al. 2016). Analytically, let $X=\left\{x_1,,,.,.,.,,,{x_i,..,x}_n\right\}$ be all activities of a given type (e.g., home activity), where$x_i=\left\{{\mathit{SRA}}_i,,,{\mathit{MDM}}_i,,,{\mathit{Dist}}_i\right\}$. The probability of $x_i$ is modeled as the weighted sum of $K$ multivariate-normal distributions at $x_i$

$$P(x_i|\mathrm{\Pi },\mathrm{\Theta })=\sum _{k=1}^K{\pi }_{k}f\left(x_i,{\mathrm{\Theta }}_k\right)$$ 2

where, $\mathrm{\Pi }=\left\{{\pi }_1,{\pi }_2,...,{\pi }_K\right\}$ are weights for $K$ multivariate-normal distributions; $f\left(·\right)\sim N\left(\mu ,\mathrm{\Sigma }\right)$ follows a gaussian distribution; $\mathrm{\Theta }=\left\{{\theta }_1,{\theta }_2,...,{\theta }_K\right\}$ are parameters of $K$ multivariate-normal distributions. Since we have three indices, ${\theta }_k$ contains a 3 by 1 mean $\mu$ and 3 by 3 covariance $\mathrm{\Sigma }$. Each activity episode is assigned to a group given its dominant Gaussian component, that is, the component with the highest weight ${\pi }_k$. The distribution parameter $\mathrm{\Theta }$ and weight $\mathrm{\Pi }$ are estimated using the expectation–maximization (EM) algorithm (Do and Batzoglou 2008). To determine the number of Gaussian components $K$, the Bayesian Information Criterion (BIC) is used to evaluate model fitness. We choose GMM because the K components can capture various shapes of activity trajectories, such as the linear shape in Fig. 3B and the round-trip in Fig. 3C. In addition, different components can also address different spatial scales (dispersions) of activities, such as staying at home, wandering within the neighborhood, or long-distance trips.

Stationary activity location(s)

For each person, we further examine whether all their stationary activities of a given type (e.g. home activity) are performed at a single location or a few locations apart from each other. We use the mean center of each activity trajectory to represent its location and then apply the agglomerative hierarchical clustering (AHC) method to group these locations into spatial clusters. The AHC is a bottom-up approach where each input is considered as a separate cluster at the beginning. Each iteration merges the two most similar clusters to a new cluster. The iteration would end until all inputs are merged as one single root cluster, and the whole process result is in a tree-like structure. In our case, the inputs are locations and the dissimilarity between two clusters is measured by the maximum Euclidean distance between any two locations in these two clusters. Lastly, we choose a break value to cut the hierarchical tree into ‘sub-trees’ so that the root clusters always have a distance larger than the break value. To determine the break value for AHC, we use the cutoff values that define stationary activities in the previous step. This is because the cutoff value for defining stationary activities of a given type (e.g. 319 m for home activities) reflects the spatial scale of stationariness, and activities within this spatial scale can therefore be considered as occurring at the same place. In this article, we apply the loose restriction, and we consider the two times the maximum value as the break value for AHC because it can account for spatial shifts (e.g., GPS offsets) in two opposite directions (Yelamarthi et al. 2010). Analytically, the break value of a given specific activity type (e.g. home activities) can be defined as:

$$2\times \text{max}{\left\{max{\left\{SR{A}_{\mathit{ij}},MD{M}_{\mathit{ij}},Dis{t}_{\mathit{ij}}\right\}}_{j=1}^J\right\}}_{i=1}^I$$ 3

where $SR{A}_{\mathit{ij}}$, $MD{M}_{\mathit{ij}}$, and $Dis{t}_{\mathit{ij}}$ are the shape indices of a stationary activity $E{p}_{\mathit{ij}}$ of person $i$. The AHC result indicates the representative activity location for each person. In specific, we define it as the mean center of all locations in each cluster. The number of clusters indicates the number of representative locations.

Temporal fixity and space–time fixity

In terms of temporal fixity, we consider an activity as a prism anchor if it repetitively occurs during a similar time across multiple days. When multiple-week data are available, an activity that occurs weekly on the same day at similar time is also considered a prism anchor. Hence, we first calculate the Repetitive Ratio(RR) to measure the repetitiveness of activity and classify the activity into repetitive or non-repetitive. For a repetitive activity, we further derive the Repetitive Interval(RI), that is, the period(s) that the activity repetitively occurs at a given location (i.e., space–time fixity).

Repetitive Ratio (RR) For each person, the RR of an activity is calculated as

$$RR=\sum _i^{N}R\left(i\right)/N$$ 4

$$R\left(i\right)=\left\{\begin{array}{c}1\text{if}\text{the}\text{activity}\text{occurs}\text{on}\text{the}i\text{th}\text{day}\\ 0\text{else}\\ \end{array}\right)$$ 5

where $N$ is the total number of survey days, and the sum of $R(i)$ is the number of days with the performed activity. The $\mathit{RR}$ falls within the range [0,1], and a larger RR value indicates that the person tends to conduct the activity almost every day. In line with the spatial fixity analysis, the GMM is applied again to classify the activity into repetitive and non-repetitive based on the RR for each person. The components in the mixture model would represent different levels of the repetitiveness of the activity.

Repetitive Intervals(RI) To derive RI, we represent one day as a sequence of 1440 1-min intervals given that the temporal resolution of our data is 1 min. Future research can modify the time interval based on the data resolution or special research needs. Figure 4 shows an example activity sequence between 6 and 7 pm. Each number in the sequence represents the total occurrence of an activity type across days. The RI can be identified as the time interval with the occurrence equal to or larger than the threshold. However, defining thresholds that can characterize the repetitive intervals is challenging due to the uncertainty or inherent flexibility of activities in a person’s everyday schedule (Schwanen et al. 2008; Charleux 2015). Hence, we define threshold from a data-driven perspective. Firstly, we consider that activities need to be repetitive across days and thus use the cutoff values of the repetitive ratio obtained from the previous step. Secondly, we consider the maximum occurrence as the baseline and allow some flexibility for activities (e.g., different schedules during weekdays and weekends). Similar to previous steps, we apply the loose restriction and set the threshold as the smaller value of the two parameters:

$$\text{min}\left\{N\times {\varphi }_{\mathit{RR}},\text{max}\left(\alpha \right)\times \lambda \right\}$$ 6

where $N$ is the total number of survey days; ${\varphi }_{\mathit{RR}}$ is the cutoff value of repetitive ratios obtained in the previous step; $\text{max}\left(\alpha \right)$ is the maximum occurrence of the activity (e.g., 7 in Fig. 4); $\lambda$ is set as 80% in this article. Note that $\lambda$ can be modified according to how rigid the activity is expected to be. In Fig. 4, the RI can be 6:16–6:47 pm, fixed in 7 days, or 6:08–7:00 pm, fixed in 6 days.

Fig. 4.

An example sequence of sampling activity episodes at a 1-min interval

Finally, a personalized prism anchor can be defined based on the RIs at a representative activity location. Specifically, the start time of a RI defines the latest arrival time from its previous trip/activity (destination anchor), and the end time of that RI defines the earliest departure time to start the next trip or activity (origin anchor).

Results

This section first uses ‘home’ activity in the Minnesota data set to demonstrate our methods and procedure. Next, we compare the results for ‘home’, ‘work’, and ‘school’ activities in two study areas and discuss potential reasons for the different activity-travel patterns. Lastly, we illustrate our contributions to travel behavior analysis and person-based accessibility measures.

We use programming language R and its supporting packages to group an individual’s daily activities by type, analyze their space–time fixity, and visualize analysis results. We use package ‘adehabitatHR’ to calculate the SRA of trajectories, package ‘mclust’ and ‘stats’ for GMM and AHC, and package ‘TraMineR’ to visualize activity sequences.

Home activity analysis

We exclude 9 out of 372 participants who had only one survey day. We also filter out activities with spatial indices within the range of the GPS precision and consider them as stationary. Since the GPS precision is typically 2–3 m for mobile devices nowadays (Yelamarthi et al. 2010), we use 5 m as the threshold so that the two GPS points within 5 m are potentially the two measures of the same location. Therefore, an activity is considered stationary (as group 0) if it satisfies $SRA\le 5\times \sqrt{\pi }$, $\text{MDM}\le 5/2$, and $\text{Dist}\le 5$. The rest of activities are used for the next classification steps.

Then, we apply the GMM to classify activities into stationary and non-stationary based on indices SRA, MDM, Dist. Figure 5 shows the GMM model selection and clustering results. According to Fig. 5a, we choose 3 as the optimal number of clusters (i.e. the number of Gaussian components) because the BIC value1 increases slowly for more than 3 clusters. Figure 5b presents the visualization results of the three indices for each cluster with different colors. Based on our knowledge, we view home activities in groups 1 and 2 (which are at the block levels) as stationary. The embedded table in Fig. 5 shows the exact cutoff values for each component. For home activities in groups 0 to 2, SRA is smaller than 216 m, MDM is smaller than 293 m, and Dist is smaller than 319 m. Hence, we view activities in these groups as stationary. And we use the maximum cutoff value among SRA, MDM, and Dist, that is 319 m, as the threshold for the AHC in the following steps to keep the parameter settings consistent.

Fig. 5.

a Model selection for the optimal number of GMM clusters; b GMM clustering results for home Activity

We then apply AHC to identify the representative home location(s) for each person. The results show that 24 out of 363 valid participants have no home location; 270 persons have 1 home location; 40 persons have 2 home locations; 29 persons have 3 or more home locations. In Fig. 6, the blue dots represent the locations of all home activities of a person during different times that are stationary, and the red stars show the representative locations for these home locations. The stationary activities at the same representative location may deviate a little due to GPS accuracy and/or stationary activities near the house (e.g. shoveling snow). Figure 6a shows an example where a person’s representative home location is fixed in a single location, and the person in Fig. 6b has two representative home locations. If we only use one home location to define prism anchors, the behaviors of people living at multiple locations may be misunderstood and not well-predicted.

Fig. 6.

a Person with a single home location; b Person with two home locations

Given representative locations, we calculate the repetitive ratio and identify the repetitive intervals for each person. For persons who have at least one home location (first two columns in Table 1), the median and mean values of the repetitive ratios are 1 and 0.961. This indicates that people perform home activities almost every day, and thus home can potentially serve as prism anchors for most people. To quantitively determine whether home activities repetitively occur in one’s schedule, we group people based on their repetitive ratios. The GMM result suggests five groups with value ranges [0.091, 0.429], [0.500, 0.667], [0.700, 0.800], [0.833, 0.929], and [1.000, 1.000]. We consider people in the last four groups as potentially having at least one home anchor.

Lastly, for each person who potentially has home anchors, we identify repetitive intervals at each representative home location. The repetitive intervals at all representative home locations together define a person’s home anchors. Figure 7 presents two examples. Figure 7a shows a person with one home location and two repetitive intervals, one from midnight to 8:19 am and the other from 7:37 pm until midnight. This pattern is consistent with the setting in most existing studies, where the home anchor is defined by the earliest departure time (8:19 am) and the latest arrival time (7:37 pm) from one single home location. Figure 7b shows an example of two home locations and Fig. 7c shows the corresponding home anchors. Across 9 survey days, this person stayed at home location 1 in 6 out of 9 survey days and stayed at home location 2 in 2 out of 9 survey days. In this case, home activities may serve as anchors at multiple locations in this person’s schedule. For instance, a person may routinely stay at a rented apartment near work or school on weekdays and go to their own or parents’ house on weekends. Commonly, participants only reported their primary residential location in the travel survey. Therefore, the second home anchor is often ignored and may cause biases in their travel demand and behaviors estimations.

Fig. 7.

a Person with single home anchor; b Person with two home anchors; c Home space–time trajectory with two home anchors

Comparative analysis

We also examine the space–time fixity of work and school activities. Table 2 shows the summary of indicators, clustering results, and final results. For spatial fixity, the break value to define stationary activity for work and school are 406 m and 435 m, which are larger than 319 m for home activity (see bolded numbers in Table 2). This may be because the spatial region of work and school are relatively larger than residential houses. Thus, our data-driven method can derive metrics for each activity type rather than set rigid thresholds for all activity types.

Table 2.

Space–Time fixity of Home, Work, School activity in Minnesota and Beijing

	Minnesota (363 persons)			Beijing (675 persons)
	Home	Work	School	Home	Work	School
Spatial fixity
Stationary activity
Percentage	98.1%	97.3%	97.5%	75.7%	70.9%	59.3%
Max(SRA)	216 m	259 m	230 m	298 m	299 m	276 m
Max(MDM)	293 m	406 m	366 m	377 m	404 m	326 m
Max(Dist)	319 m	347 m	435 m	399 m	347 m	359 m
Number of activity locations
0	24 (6.6%)	123 (33.9%)	254 (70.0%)	24 (3.56%)	123 (14.8%)	615 (91.1%)
1	270 (74.4%)	110 (30.3%)	77 (21.2%)	547 (81.0%)	457 (67.7%)	42 (6.2%)
2	40 (11.0%)	48 (13.2%)	17 (4.7%)	91 (13.5%)	76 (11.3%)	14 (2.1%)
3 +	29 (8.0%)	82 (22.6%)	15 (4.1%)	13 (1.93%)	19 (2.8%)	4 (0.6%)
Temporal fixity
Repetitive Ratio
Mean	0.961	0.536	0.309	0.742	0.471	0.272
Median	1.000	0.556	0.250	0.800	0.500	0.200
Space–time fixity
Anchor number (at different locations)
0	27 (7.4%)	174 (47.9%)	324 (89.3%)	85 (12.6%)	295 (43.7%)	659 (97.6%)
1	316 (87.1%)	149 (41.1%)	37 (10.2%)	544 (80.6%)	360 (53.3%)	14 (2.1%)
2	16 (4.4%)	35 (9.6%)	2 (0.6%)	46 (6.8%)	20 (3.0%)	2 (0.3%)
3	4 (1.1%)	5 (1.4%)	0 (0%)	0 (0%)	0 (0%)	0 (0%)

We apply our methods to data collected in Minnesota and Beijing. These two datasets use the two most typical forms of GPS-enabled travel surveys (as described in the Data section). The results suggest that our methods can apply to GPS-enabled travel surveys collected using different mechanisms. Furthermore, the metrics and parameters in our methods can be calibrated to capture distinct travel behaviors in different geographical regions. The different patterns can be explained from the perspectives of cultural differences and survey designs, and we highlight the lessons that we took from the comparison of these two study areas. For example, the percentage of classified stationary home activities is lower in Beijing (75.7%) than in Minnesota (98.1%). This may be because people in China perform some activities in their residential communities that are usually within walking distance (a.k.a. Xiao Qu), such as dining and shopping grocery. And these activities may be viewed as home activities by respondents and reported as home activities, which results in more non-stationary home activities. In contrast, people in the U.S. typically need to travel a longer distance to shopping grocery and dining, so people commonly separate these activities from home activities. This suggests that researchers need to clarify the definition of home activity when they design the survey and include languages in survey instructions provided to the participants.

For the temporal fixity, the mean values of the repetitive ratios for home, work, and school activity are 0.961, 0.536, and 0.309 in Minnesota and 0.742, 0.471, and 0.272 in Beijing. And the median values are 1.00, 0.556, and 0.250 in Minnesota and 0.800, 0.500, and 0.200 in Beijing. The results reveal that home activity occurs most frequently across days in both study areas, and work activity occurs less frequently given the presence of weekends and part-time employees. A repetitive interval at a distinct activity location can be used to define one prism anchor. Among 363 participants in Minnesota, 27 persons (7.4%) have no home anchor, 316 persons (87.1%) have a single home anchor, and 20 persons (5.5%) have multiple home anchors. For the work activity, 174 persons (47.9%) have no anchors, 149 persons (41.1%) have a single anchor, and 40 persons (11.0%) have multiple anchors. For the school activity, 324 persons (89.3%) have no anchor, 37 persons (10.2%) have a single anchor, and 2 persons (0.6%) have multiple anchors. Among 675 participants in Beijing, for the home activity, 85 persons (12.6%) have no anchor, 544 persons (80.6%) have a single anchor, and 46 persons (6.8%) have multiple anchors. For the work activity, 295 persons (43.7%) have no anchor, 360 persons (53.3%) have a single anchor, and 20 persons (3.0%) have multiple anchors. For the school activity, 659 persons (97.6%) have no anchor, 14 persons (2.1%) have a single anchor, and 2 persons (0.3%) have multiple anchors. In sum, participants in the two study areas share similar patterns: most people have one potential home anchor; over half of participants have one or more work anchors; and most people have no school anchor. This suggests that using home and work to define prism anchors can reflect reality most of the time, but not everyone follows this dichotomy. The different anchor patterns may be because different demographic compositions in the two data set. Thus, we conduct demographic analysis to further explain these patterns.

For demographic analysis, we group participants based on their demographic and social-economic profiles and summarize the percentage of people with at least one home, work, and school anchor for each group (Table 3). In general, the home activity shows a higher level of space–time fixity compared to work and school activities across all groups. For home activities, people with lower education levels, no driver's licenses, or no private automobiles are less likely to have home anchors. This suggests that these people may have to sacrifice regular stay-at-home times and prioritize other activities due to limited mobility levels. Unemployed people are less likely to have home anchors (80.56%), whereas full-time employees have the largest percentage (95.27%). This may be because unemployed people are less constrained by working schedules and conduct out-of-home activities more freely throughout the day. For work activities, full-time workers are most likely to have work anchors (83.78%), and senior people and people with no vehicle access tend to have no work anchors. This is intuitive considering that many senior people no longer work full-time, and people with no automobile access tend to have less access to job opportunities. For school activities, 54.45% of full-time students have school anchors, but people with other student statuses all have relatively small percentages below 30%.

Table 3.

Percentages of persons who have anchors across socio-demographic groups

	Minnesota (%)				Beijing (%)
	Pct	Home	Work	School	Pct	Home	Work	School
Sex
Male	32.78	89.92	55.46	7.56	46.07	87.46	55.63	2.25
Female	66.67	93.80	50.41	12.40	53.93	87.36	56.87	2.47
Age
Below 25	6.61	95.83	70.83	45.83	16.59	89.29	55.36	1.79
26–40	27.00	94.90	63.27	13.27	59.26	88.25	61.75	3.00
41–60	33.06	90.83	58.33	7.50	23.56	84.28	44.65	1.26
Above 60	33.33	91.74	33.06	4.96	0.59	75.00	0	0
Employment
Full-time Employed	40.77	95.27	83.78	8.78	89.78	87.95	60.89	1.98
Part-time Employed	30.58	93.69	60.36	15.32	3.85	69.23	23.08	0
Full-time Student	9.09	93.94	69.70	54.45	0.44	66.67	0	33.33
Part-time Student	5.23	84.21	47.37	26.32	0.15	100	0	0
Homeworker	12.95	91.49	23.40	6.38	0.59	100	25.00	0
Retired	20.66	89.33	10.67	5.33	2.22	86.67	6.67	0
Unemployed	9.92	80.56	13.89	8.33	1.19	87.50	0	25.00
Education
Less than High School	1.65	83.33	16.67	16.67	2.52	82.35	41.18	0
High School	7.16	88.46	53.85	11.54	12.15	79.27	41.46	2.44
Technical School	7.16	88.46	42.31	15.38	28.30	87.96	52.36	2.62
College, no degree yet	14.05	88.24	29.41	7.84	–	–	–	–
Bachelor	32.51	94.92	60.17	11.86	42.52	90.59	64.11	1.05
Graduate	37.19	94.07	57.04	9.63	14.52	84.69	56.12	6.12
Driver License
Yes	88.43	94.39	54.83	10.90	40.89	86.96	55.07	2.90
No	11.02	80.00	32.50	10.00	59.11	87.72	57.14	2.01
Automobile Ownership
Yes	88.43	95.02	54.52	10.90	56.59	86.39	53.40	3.66
No	10.47	76.32	36.84	10.53	43.41	88.74	60.07	0.68

Similar to Minnesota, full-time workers and full-time students in Beijing have higher percentages of work (60.89%) and school (33.33%) anchors than other employment and student status. This suggests that people’s behavior patterns are greatly influenced by their employment and student status in general. However, people with the same employment/student status may not always share the same patterns. For instance, we also observe some different patterns in the two study areas that might be caused by their distinct urban and cultural contexts. For instance, the difference between males and females regarding home and work anchors is larger in Minnesota than in Beijing. This may suggest more significant gender gaps in everyday life in Minnesota. Besides employment and student status, people with driver’s licenses and automobile access in Minnesota tend to have home and work anchors, but such patterns are not found in Beijing. This may be because transit systems in Beijing have great coverage and service frequencies, and may even require less travel time than driving, and many people still cannot afford private vehicles. So people can commonly rely on public transit for commuting, and not being able to drive has no significant influence on activity scheduling. In sum, these findings suggest that the demographic and socio-economic characteristics of individuals have great impacts on the activity space–time fixity patterns, and our methods can derive personalized prism anchors that seem to be consistent with the characters of people and their living environment.

Result discussion

Home and work anchors derived from the two data sets indicate that people travel and perform everyday activities with various and complex patterns. The assumption that people’s schedules are anchored at home (or home and work) applies to the majority of people. However, it may fail to account for those non-typical behaviors and then lead to biases in behavior description, travel demand estimation, and potential activity space and accessibility measurement. In this section, we present how our personalized prism anchor could refine person-based accessibility measures.

In the Minnesota dataset, the respondents reported their residential neighborhood besides their recorded activities and trips, which would be considered their home locations by default. We compare home anchors derived from the data with self-reported residential neighborhoods to see whether they are spatially consistent. The six neighborhoods in the Minnesota database are Phillips, Near North, Prospect Park, St. Anthony Park, Blaine, and Brooklyn Center (see Fig. 2). Table 4 shows the number and percentage of people who have at least one anchor of a given type outside their residential neighborhoods. We find that about 10% of people have at least one home anchor outside their residential neighborhoods in all six neighborhoods. Moreover, the distance between the identified home anchor and the centroid of the neighborhood may exceed 20 km. So, it may be biased if we simply use the self-reported neighborhood to describe the home location.

Table 4.

Anchored home activity and residential neighborhood (Minnesota)

Neighborhood	Phillips (70)	Near North (53)	Prospect Park (65)	St. Anthony Park (70)	Blaine (53)	Brooklyn Center (52)
Whether the identified anchor is within the reported neighborhood
No anchor was identified
	10 (14.3%)	6 (11.3%)	1 (1.5%)	4 (5.7%)	2 (3.8%)	4 (7.7%)
All identified anchors are within the reported neighborhood
	48 (68.6%)	37 (69.8%)	59 (90.8%)	63 (90%)	46 (86.8%)	45 (86.5%)
At least one anchor is out of the reported neighborhood
	12 (17.1%)	10 (18.9%)	5 (7.7%)	3 (4.3%)	5 (9.4%)	3 (5.8%)
Summary of distances between identified anchors and the centroid of reported neighborhood
Mean (dist)	1407 m	1823 m	708 m	1457 m	4144 m	1835 m
Median (dist)	107 m	897 m	700 m	1227 m	3087 m	1893 m
Max (dist)	10727 m	12260 m	2735 m	19590 m	22345 m	3838 m

We further study how the complexity of activity-travel patterns may impact the potential activity space and accessibility. Figure 8 shows the activity space of a person in the Minnesota data set considering different ‘peg’ in the person’s daily schedule. This person has one home anchor at one location and two work anchors at two locations. Figure 8a shows the person’s activity space that is centered on the residential neighborhood near home, which has been widely used in health studies. Figure 8b accounts for the primary work anchor beside the home anchor and includes space around work that is accessible. However, it neglects the second work anchor. Figure 8c illustrates the multi-day accessibility given all three anchors and provides a more comprehensive view and refined representation of the person’s space–time accessibility.

Fig. 8.

Illustrations of person-based accessibility: a residential neighborhood-based; b single Home-Work anchored; c multiple Home-Work anchored

Conclusion

The space–time prism is a fundamental concept in time geography to understand individuals’ potential activities and trips in space across time under various constraints. This concept has been widely applied in travel behavior analysis and regional planning. Most existing methods use home and work activity to define prism anchors and only consider one home and work location. However, this fixity-flexibility dichotomy cannot capture the increasing complexity of human mobility or inter-person variations. To address these gaps, this article proposes a framework and methods to re-examine home and work prism anchors using GPS-enabled activity-travel survey data. We define space–time fixity and adopt data-driven approaches to derive prism anchors from two sets of survey data collected in Minnesota and Beijing. The results suggest that not every person has a home, work, and school anchor, and people belonging to the same socio-demographic groups tend to have similar space–time fixity patterns. The example space–time accessibility measures prove that our methods can capture the complexity of urban mobility patterns and provide more accurate estimations of person-based accessibility across multiple days.

The study can be extended in six major directions. First, our methods can be applied to identify potential prism anchors besides home, work, and school activities. For example, a person may have recreation classes every morning, which are not often rescheduled. Other activities are organized to accommodate this. Thus, the recreation activity may also serve as prism anchors to define this person’s everyday prisms. Second, further analysis, such as statistical analysis, can be done to associate the detected anchors with a person’s socio-economic and demographic profiles and identify potential disparities among social groups. Third, future surveys can add questions for participants' perceptions of the fixity of their activities (e.g. using similar ways as in Kwan 2000). This subjective measurement of fixity can be compared with our identified prism anchors to further validate our proposed methods and identify the pros and cons of using subjective and objective extraction of fixed activities for use in defining anchors of our everyday prisms. Forth, given prism anchors for all activity types for a person, we can generate prisms for their entire day. This can be done by first ordering all the prism anchors chronologically and then using every two consecutive anchors to define a prism. We can then examine how other activities and trips are scheduled within these prisms and evaluate the flexibility of one’s daily schedule. We can also overlay such prism with land-use and other build environment data to evaluate the potential space–time accessibility for that person, which is learned from historical behaviors and could capture inter-person variations. Fifth, rather than using 7-day survey data, future studies can collect multi-week data (at least 14 days as suggested in Zenk et al. 2018) so that activities that occur weekly at the same location during similar periods can also be detected and used to define prism anchors. Use the recreation activity as an example again, recreation classes are commonly scheduled every week instead of every day such as skating classes every Saturday afternoons during a season. Such recreation classes can be detected using similar methods in this article if multi-week data become available. Sixth, the proposed methods can be used to analyze data collected during or after the COVID-19 pandemic and examine the changes in behaviors due to the pandemic. For instance, surveys can include additional questions regarding the work-from-home (WFH) status of the participants and the working hours while they are at home. Then, the methods in our paper can be modified and applied to detect WFH anchors. Specifically, the home location can define the location of a work anchor if the participant has regular working hours while at that home location. The extraction of these WFH anchors would significantly influence the measure of job accessibility and potentially identify disparities in job accessibility among various occupations.

Biographies

Yaxuan Zhang

is a Ph.D. candidate in the Department of Geography, Environment, and Society at the University of Minnesota. Her research interests focus on studying human space-time travel behaviors in the context of daily schedules and urban transportation. Her work also includes applying geospatial techniques to address spatial-social disparities and promote equity in health and transportation planning.

Chunjiang Li

is a Ph.D. candidate of human geography at the College of Urban and Environmental Sciences, Peking University. He is currently a visiting scholar at the University of Gothenburg. His major research focus is digital transformation of daily life from the perspective of time geography. He also contributes in practical field of 15-min city and life circle planning.

Ying Song

is an associate professor at the Department of Geography, Environment, and Society at the University of Minnesota. Her research focuses on developing and applying spatial methods to visualize, explore, analyze, and model movement and change in geographic space with respect to time. Her major empirical focus is human mobility and accessibility within transportation networks, especially at the urban and regional level. Her research aims to promote equitable, green, and healthy transportation planning with cutting-edge geospatial data and methods.

Yanwei Chai

is a professor of human geography at the College of Urban and Environmental Sciences, Peking University. He obtained his PhD degree from Hiroshima University. His research interests are in spatiotemporal behavior, life circle planning and smart cities, mainly focusing on how human behavior is influenced by built environment and how human behavior reshapes the spatial and temporal resources of the city. He has published over 300 papers in behavioral geography, time-geography and urban social geography from home and abroad and has released more than 20 monographs. Taking Beijing as his main research area, he has conducted approximately a hundred of academic surveys and projects in the past decades.

Yingling Fan

is Professor of Urban and Regional Planning at the Humphrey School of Public Affairs at the University of Minnesota. Her research focuses on human emotions in urban environments. By promoting shared happiness in urban environments, her research has transformed the way people experience the city, creating innovative urban solutions that can synergistically foster climate resilience, public health, and social equity. She is the lead inventor of the Daynamica app—a smartphone app that integrates mobile GPS sensing with subjective data entered by users to digitally capture human activities, trips, and emotions throughout the day. The app enables social and health researchers to make new discoveries in understanding people’s everyday life activities and experiences.

Author's contribution

YZ methodology, formal analysis, software, writing, visualization. CL formal analysis, software, methodology, writing. YS conceptualization, methodology, writing, visualization, supervision. YC conceptualization, data curation, supervision. YF conceptualization, data curation, writing.