# Supplementary Information for
Behavior-based dependency networks between places
shape economic resilience of cities

Takahiro Yabe1,∗, Bernardo García Bulle Bueno1, Morgan R. Frank2,3,4,
Alex Pentland1,4, Esteban Moro1,4,5,∗

( 1Institute for Data, Systems, and Society, Massachusetts Institute of
Technology, USA
2Department of Informatics and Networked Systems, University of Pittsburgh,
USA
3Digital Economy Lab, Institute for Human-Centered AI, Stanford University,
Stanford, CA, USA
4Media Lab, Massachusetts Institute of Technology, USA
5Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de
Matemáticas, Universidad Carlos III de Madrid, Spain
∗Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS>)

###### Supplementary Notes

  1. 1 Mobility data analytics and representativeness
    1. 1.1 Home estimation and stop detection
    2. 1.2 Safegraph POI data and visit attribution
    3. 1.3 Data representativeness
    4. 1.4 Post-stratification of mobility data
  2. 2 Behavior-based dependency networks
    1. 2.1 Measuring behavior-based dependency between places
    2. 2.2 Qualitative characteristics of networks
    3. 2.3 Comparison of networks under different co-visit detection parameters
  3. 3 Statistical robustness of behavior-based dependency networks
    1. 3.1 Robustness against choice of time period
    2. 3.2 Computing quartiles of $w_{ij}$ via bootstrap method
    3. 3.3 Robustness against post-stratification processing
  4. 4 Modeling dependency network weights
    1. 4.1 Gravity-based null networks
    2. 4.2 Regression model of $w_{ij}$
    3. 4.3 Robustness against different network instances
    4. 4.4 Robustness against co-visit detection parameters
    5. 4.5 Robustness against different time periods
  5. 5 Impacts of behavior-based dependency during the COVID-19 pandemic
    1. 5.1 Analysis of visitation losses in cities
    2. 5.2 Model specification and estimation results
    3. 5.3 Robustness against co-visit detection parameters
    4. 5.4 Results using changes in visits during different time periods
    5. 5.5 Robustness of regression results when using different time periods to generate dependency networks
    6. 5.6 Robustness of regression results when using only short non-work stays
    7. 5.7 Case study on school closure period
  6. 6 Cascading impacts of hypothetical shocks
    1. 6.1 Leontief open model
    2. 6.2 Cascading effects of individual place closures
  7. 7 Software

###### List of Figures

  1. S1 Estimates of number of visits to POIs under different maximum spatial threshold parameters
  2. S2 Sample rates of mobile phone location data across the five metropolitan areas.
  3. S3 Comparison of census population and smartphone users for census block groups in the five metropolitan areas
  4. S4 Comparison of census block group median income and the sample rate of mobile phone smartphone users in the five metropolitan areas
  5. S5 Distribution of time and step differences between two POIs visited by the same individual on the same day
  6. S6 POI subcategories with the largest average in- and out-weights
  7. S7 Proportion of edge weights among POI category pairs
  8. S8 POI subcategories with the largest average in- and out-weights, when $T_{c}=1$ hour
  9. S9 POI subcategories with the largest average in- and out-weights, when $T_{c}=3$ hour
  10. S10 Dependency network in New York under different co-visit detection parameters
  11. S11 Dependency network in Boston under different co-visit detection parameters
  12. S12 Dependency network in Seattle under different co-visit detection parameters
  13. S13 Dependency network in Los Angeles under different co-visit detection parameters
  14. S14 Dependency network in Dallas under different co-visit detection parameters
  15. S15 Network diagram showing the average dependencies between POI subcategories in New York and Boston
  16. S16 Network diagram showing the average dependencies between POI subcategories in Seattle and Los Angeles
  17. S17 Network diagram showing the average dependencies between POI subcategories in Dallas
  18. S18 Comparison of in- and out-weights of each POI across different data collection periods
  19. S19 Comparison of in- and out-weights of each POI across different data collection periods, contd.
  20. S20 Comparison of category pairwise weight proportion across different data collection periods
  21. S21 Comparison of category pairwise weight proportion across different data collection periods
  22. S22 Out- and in-weights of POIs when applying bootstrap method to remove smaller weights
  23. S23 Out- and in-weights of categories when applying bootstrap method to remove insignificant weights
  24. S24 Out- and in-weights of POIs when applying post-stratification to correct for biases in mobile phone data
  25. S25 Correlation between the observed $n_{ij}$ values and the gravity component $g_{ij}$ under different model parameters
  26. S26 Comparison of actual and null networks in New York and Boston
  27. S27 Comparison of actual and null networks in Seattle and Los Angeles
  28. S28 Comparison of actual and null networks in Dallas
  29. S29 Comparison between real and null network on the proportion of edge weights among POI category pairs
  30. S30 Histograms of edge distances between actual and null networks.
  31. S31 Regression results for dependency weights when using different co-visit detection parameters, contd.
  32. S32 Change in visits to POIs in New York, Boston, Seattle, Los Angeles, and Dallas during the pandemic period.
  33. S33 Correlation between change in visits of ego and the weighted change in visits of alters by category pairs
  34. S34 Regression results for dependency weights when using different co-visit detection parameters, contd.
  35. S35 Change in visits to POIs in New York, Boston, Seattle, Los Angeles, and Dallas during the fall semester period.
  36. S36 Cascading impacts of a 50% visit reduction to colleges.
  37. S37 Cascading impacts of a 100% visit reduction to colleges.
  38. S38 Cascading impacts of a 25% visit reduction to colleges.
  39. S39 Total cascading impact of closing places on other locations in New York and Boston
  40. S40 Total cascading impact of closing places on other locations in Seattle and Los Angeles
  41. S41 Total cascading impact of closing places on other locations in Dallas

###### List of Tables

  1. S1 Number of places in the Safegraph dataset in the five core-based statistical areas (CBSAs) analyzed in this study.
  2. S2 Description of the four core-based statistical areas (CBSAs) analyzed in this study.
  3. S3 Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) using physical factors
  4. S4 Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) selected using the bootstrap method with physical factors
  5. S5 Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) selected using only short stays ($<$ 4 hrs) with physical factors
  6. S6 Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) using network from 2019 January - April data
  7. S7 Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) selected using network from 2019 May - August data
  8. S8 Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in New York
  9. S9 Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in Boston
  10. S10 Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in Seattle
  11. S11 Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in Los Angeles
  12. S12 Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in Dallas
  13. S13 Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in New York
  14. S14 Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in Boston
  15. S15 Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in Seattle
  16. S16 Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in Los Angeles
  17. S17 Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in Dallas
  18. S18 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in New York
  19. S19 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Boston
  20. S20 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Seattle
  21. S21 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Los Angeles
  22. S22 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Dallas
  23. S23 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in New York when using dependency network generated from data between 2019 January to April
  24. S24 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Boston when using dependency network generated from data between 2019 January to April
  25. S25 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Seattle when using dependency network generated from data between 2019 January to April
  26. S26 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Los Angeles when using dependency network generated from data between 2019 January to April
  27. S27 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Dallas when using dependency network generated from data between 2019 January to April
  28. S28 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in New York when using dependency network generated from data between 2019 May to August
  29. S29 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Boston when using dependency network generated from data between 2019 May to August
  30. S30 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Seattle when using dependency network generated from data between 2019 May to August
  31. S31 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Los Angeles when using dependency network generated from data between 2019 May to August
  32. S32 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Dallas when using dependency network generated from data between 2019 May to August
  33. S33 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in New York when using dependency network generated from stays shorter than 4 hours
  34. S34 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Boston when using dependency network generated from stays shorter than 4 hours
  35. S35 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Seattle when using dependency network generated from stays shorter than 4 hours
  36. S36 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Los Angeles when using dependency network generated from stays shorter than 4 hours
  37. S37 Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Dallas when using dependency network generated from stays shorter than 4 hours
  38. S38 Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in New York
  39. S39 Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in Boston
  40. S40 Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in Seattle
  41. S41 Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in Los Angeles
  42. S42 Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in Dallas

##  1 Mobility data analytics and representativeness

###  1.1 Home estimation and stop detection

In this study, we utilize an anonymized location dataset of mobile phones and
smartphone devices provided by Spectus Inc., a location data intelligence
company which collects anonymous, privacy-compliant location data of mobile
devices using their software development kit (SDK) technology in mobile
applications and ironclad privacy framework. Spectus processes data collected
from mobile devices whose owners have actively opted in to share their
location and requires all application partners to disclose their relationship
with Spectus, directly or by category, in the privacy policy. With this
commitment to privacy, the data set contains location data for roughly 15
million daily active users in the United States. Through Spectus’ Data for
Good program, Spectus provides mobility insights for academic research and
humanitarian initiatives. All data analyzed in this study are aggregated to
preserve privacy111https://spectus.ai/privacy/privacy-policy/. Each entry in
the data table comprises anonymized device ID, location coordinates, start
time, and dwell time of the stop for the device.

To define the type of location (Home or Work), different variables are used,
including the number of days spent in a given location in the last month, the
daily average number of hours spent in that location, and the time of the day
spent in the location (nighttime/daytime). To estimate the home position of a
user, the algorithm combines the three variables and creates a score that
represents the probability that the position points to the home. The more days
and the average number of hours spent in the position, the higher the score
is. Higher scores will also be assigned to the most common places during the
night. The location that maximizes this score is defined as the home of the
device.

Once the location of the home location is identified, the algorithm looks for
the work position. Note that the algorithm requires the work location to be
located at least 100 meters apart from the home location. The same variables
used for the detection of the home location are used, but a higher score is
given to daytime locations for the work location rather than nighttime
locations. Spectus runs the algorithm every week in order to confirm or update
the inferred home and work locations as we observe new data. We will only
consider devices that have been present in Spectus’ dataset for at least 15
days. Spectus tightly restricts access to the inferred precise home and work
locations of devices. Furthermore, it is used as input into various downstream
processes to create more privacy-protected versions of Spectus datasets. For
example, we only expose home and work datasets in Spectus Workbench associated
with standard Census Block Groups, created by the U.S. Census Bureau, rather
than the precise locations. This offers a good balance between utility and
privacy: according to the U.S. Census Bureau, there are between 600 and 3000
people living in each block group. Each block group is an aggregate of
contiguous U.S. blocks sharing similar socio-demographic characteristics. The
representativeness of this data has been tested and corrected in Section 1.3
in the Supplementary Material. The stops, which are location clusters where
individual users stay for a given duration, are estimated using the Sequence
Oriented Clustering approach [17].

In this study, we selected New York, Boston, Seattle, Los Angeles, and Dallas
as the five CBSAs given constraints on data collection. The five cities were
selected with respect to the diversity of characteristics in terms of
geographical locations (2 Northeast, 1 Northwest, 1 Southwest, and 1
Southern), sociodemographic details (population ranges from 3.5M in Seattle to
19.8M in New York), political inclinations, and weather characteristics.

###  1.2 Safegraph POI data and visit attribution

To measure the visitation patterns of individuals in urban environments, we
attribute the stops of individual users to specific places in the city. To
study the stops at different places, we use stops that are longer than 10
minutes but shorter than ten hours. In our study, we use location data of
places collected by Safegraph 222https://www.safegraph.com/. To protect the
users’ privacy, we have removed various privacy-sensitive places from our
places database. Sensitive places include health-related places, places where
the vulnerable population are located, military-related, religious facilities,
places that are related to sexual-orientation, and adult-oriented places
333https://spectus.ai/privacy/spoi-policy/. As a result, we have a total of
403,669 places in New York, 107,081 places in Boston, 81,140 places in
Seattle, 326,332 places in Los Angeles, and 136,686 places in Dallas. The
breakdown of the number of places by the place category is shown in Table S1.
To attribute a stop to a place, we simply attribute each stop the closest
place in our dataset. To avoid attributing a stop to place far away, we
attribute the stop to a place within $d_{max}=100$ meters from the observed
location of the stop. If the stop is further away than 100 meters from any
place in the dataset, the stop is discarded from our dataset and not used for
computing the diversity of encounters.

Table S1: Number of places in the Safegraph dataset in the five core-based statistical areas (CBSAs) analyzed in this study. | CBSAs
---|---
Place category | New York | Boston | Seattle | Los Angeles | Dallas
Arts and Museums | 4,580 | 1,183 | 799 | 3,697 | 1,073
City and Outdoors | 7,201 | 5,311 | 2,792 | 4,817 | 2,174
Coffee and Tea | 14,799 | 3,481 | 3,392 | 11,395 | 4,360
College | 3,737 | 1,266 | 766 | 2,661 | 942
Entertainment | 2,296 | 657 | 584 | 2,101 | 745
Food | 66,348 | 12,687 | 9,924 | 39,907 | 16,795
Grocery | 14,763 | 2,942 | 1,964 | 7,636 | 3,792
Health | 20,654 | 4,799 | 3,913 | 14,212 | 5,806
Office | 7,840 | 3,256 | 2,628 | 10,936 | 6,128
Service | 114,581 | 33,525 | 23,920 | 104,253 | 45,520
Shopping | 92,211 | 20,302 | 14,089 | 79,024 | 29,069
Sports | 12,383 | 5,892 | 2,464 | 10,509 | 3,782
Transportation | 41,729 | 11,114 | 13,245 | 32,141 | 14,056
All places | 403,669 | 107,081 | 81,140 | 326,332 | 136,686

The robustness of our estimation of the number of visits to different
locations has been tested using different spatial thresholds of $d_{max}$.
Different levels of $d_{max}$ could change how individuals’ stays are
attributed to the places and thus could affect our estimates of the income
diversity of physical encounters. Figure S1 compares the estimated number of
visits to places over a 1 month period in the five cities when we use
different levels of $d_{max}$ (y-axis) with our default parameter
$d_{max}=100m$ (x-axis). For all values $d_{max}=\\{50,150,200\\}$, the
Pearson correlation of the number of visits are extremely high, in most cases
above $\rho>0.95$. This robustness check shows that the estimated visitation
patterns do not depend on the choice of the spatial threshold parameter for
visit attribution.

Figure S1: Estimates of number of visits to POIs under different maximum
spatial threshold parameters. Pearson correlation of estimated number of
visits to different POIs between different spatial threshold parameters are
extremely high across all cities.

###  1.3 Data representativeness

The location data used in our study is collected from smartphones via various
apps and services. Although a significant portion (85% according to 2021
data444https://www.statista.com/topics/2711/us-smartphone-
market/#topicHeader__wrapper) of the US population owns a smartphone, one
could question the representativeness of the 1.16 million user samples across
geographical regions and income quantiles. Studies have reported the digital
divide and smartphone usage gaps across sociodemographic groups in the US
[14]. In this section, we test whether our group of users in the mobility data
is representative of the total population, and further employ post-
stratification techniques to correct for any potential biases in the sampling
rates across places and socioeconomic status and to test whether the results
on income diversity dynamics are robust to such uncertainties concerning data
representativeness.

The sampling percentage of the mobility data (100% $\times$ number of observed
mobile phone users divided by the total population from the census data) is
around 5% to 10% across all census block groups (CBGs) in the metropolitan
regions, as shown in Figure S2. Sample rates are calculated by dividing the
total number of users who were observed across a three-month period in the
dataset by the census block group population obtained from the American
Community Survey [2]. There is a large variation in the sample rates, within
and across metropolitan areas. To test whether the users in the location data
are representative of the entire population, first, we compare the population
detection in our mobility data and the 2019 ACS data for each of the CBGs in
the cities. The panels in Figure S3 show the comparison between the census
population (x-axis) and the number of observed smartphone users (y-axis) on
the CBG scale in the months of September 2019 to January 2020 in the five
metropolitan areas. The correlation is moderately high, between around
$\rho=0.55$ and $\rho=0.78$, showing that despite the use of such small census
areas and potential bias in the smartphone usage patterns, we are able to
obtain a good representation of the population. To overcome this bias, in
Section 1.4, we use post-stratification techniques to correct for such
differences in the sample percentages across CBGs. Later, in Section 3.3, we
assess whether our estimates of visitation patterns are affected by the
representativeness of the data.

(a) New York

(b) Boston

(c) Seattle

(d) Los Angeles

(e) Dallas

Figure S2: Sample rates of mobile phone location data across the five
metropolitan areas. Sample rates are calculated by dividing the total number
of users who were observed across a three month period in the dataset by the
census block group population obtained from the American Community Survey [2].
Maps were produced in Python using the TIGER shapefiles from the U.S. Census
Bureau [15]

In addition to the differences in sampling rates across CBGs, differences in
representativeness across income groups are important to ensure the findings
of the study are not biased toward specific sociodemographic groups. To
measure the representativeness across income quantiles, we plot the
correlation between the median income of the census block group and the sample
rate (shown in Figure S2) for the five metropolitan areas, as shown in Figure
S4. A balanced dataset would have a nonsignificant correlation between the two
metrics. However, we observe a small (below $\rho=0.2$) but significant
positive correlation between income and sample rates for New York, Los
Angeles, and Dallas. This indicates that in these metropolitan areas, higher
income groups are over-represented in the dataset. In Section 1.4, we use
post-stratification techniques to correct for such differences in the sample
percentages across CBGs and income groups.

Figure S3: Comparison of census population and smartphone users for census
block groups in the five metropolitan areas. The correlation is moderately
high, between around $\rho=0.55$ and $\rho=0.78$, showing that despite the use
of such small census areas and potential bias in the smartphone usage
patterns, we are able to obtain a good representation of the population. This
bias is corrected using post-stratification techniques. Figure S4: Comparison
of census block group median income and the sample rate of mobile phone
smartphone users in the five metropolitan areas. The correlation is small
(below $\rho=0.2$) but significantly positive in New York, Los Angeles, and
Dallas. This indicates that in these metropolitan areas, higher income groups
are over-represented in the dataset. This bias is corrected using post-
stratification techniques.

###  1.4 Post-stratification of mobility data

To correct for, and to understand the effects of the varying sampling rates
across CBGs and income groups on our estimation of visitation patterns to
places, we apply a post-stratification technique, which is used in previous
studies [10, 18]. Post-stratification is a well know sampling tool [11] and is
typically used to study the impact of sampling biases in mobile phone location
data [6] or (geolocated) social media data [16] on various downstream tasks
and analyses. Following the methods employed in Moro et al. [10], we denote
$w_{g}$ the expansion factor, which is the ratio of the population of census
block group $g$ to the population detected in our mobility data. We then
weight the visits completed by people from census block group $g$ spends at
place $\alpha$ by

$\hat{n}_{gi}=w_{g}n_{gi}$

where the assumption is that $n_{g\alpha}$ is proportional to the number of
people visiting the place. Using this method, we could increase (decrease) the
visits to places by people coming from census block groups that are under-
estimated (over-estimated).

Table S2: Description of the four core-based statistical areas (CBSAs)
analyzed in this study.

CBSA | Population | # users (monthly) | # stays (monthly) | # places
---|---|---|---|---
New York-Newark-Jersey City | 19.95M | 1,456K | 36.67M | 403,669
Boston-Cambridge-Newton | 4.64M | 144K | 2.34M | 107,081
Seattle-Tacoma-Bellevue | 3.55M | 141K | 2.23M | 81,140
Los Angeles-Long Beach-Anaheim | 13.05M | 452K | 10.00M | 326,332
Dallas-Fort Worth-Arlington | 6.70M | 425K | 8.83M | 136,686
Total | 47.89M | 2.62M | 60.07M | 1,054,908

##  2 Behavior-based dependency networks

###  2.1 Measuring behavior-based dependency between places

Using the large and longitudinal dataset of GPS location records in five major
US metropolitan areas introduced in Supplementary Note 1, we construct the
behavior-based dependency network at the level of points-of-interest (POIs;
e.g., businesses and amenities) in cities. Within the mobility dataset, we
identified stays at places that were detected to be between 10 minutes and 10
hours and we spatially matched those stays with the closest place locations
within 100 meters to infer visits to specific POIs, as described in
Supplementary Note 1. The representativeness of the data across regions and
income levels was ensured via post-stratification techniques.

In this study, the dependence of a POI $i$ on another POI $j$ is defined as

$w_{ij}=\frac{n_{ij}}{n_{i}}$ (1)

where $n_{i}$ denotes the number of visits to POI $i$ and $n_{ij}$ denotes the
number of ‘co-visits’ between POIs $i$ and $j$. A co-visit is defined as an
instance in which POIs $i$ and $j$ were visited by the same individual:

  * •

on the same day,

  * •

within $T_{c}$ hours from exiting POI $i$ ($j$) to entering POI $j$ ($i$), and

  * •

within $T_{s}$ intermediate POIs

Because the denominator is based on the number of visits to the target POI,
$w_{ij}\neq w_{ji}$. This simple but intuitive measure considers the
asymmetric nature of dependencies between POIs. As shown in Figure S5, the
distributions of the time difference or number of intermediate steps between
any given two POIs within a movement trajectory follow a long-tailed
distribution, where the majority of the pairs of POIs can be included within 6
hours and 1 step difference. Therefore, as a baseline parameter setting, we
use $T_{c}=6$ hours and $T_{s}=1$ POIs (which indicates direct visitation from
POI $i$ to POI $j$, or vice-versa). The characteristics of the dependency
network when using different co-visit detection threshold parameters $T_{c}$
and $T_{s}$ are tested and discussed in the following sections such as
Supplementary Note 2.3 and 4.2. By computing the dependency weights
$w_{ij}\leavevmode\nobreak\ \forall i,j$, we obtain the behavior-based
dependency matrix $W\in\mathbb{R}^{N\times N}$ where $N$ is the total number
of POIs present in the CBSA.

Figure S5: Distribution of time and step differences between two POIs visited
by the same individual on the same day. The majority of the co-visits can be
captured by using a threshold of 6 hours time difference and 1 step
difference. The dependency networks were computed using co-visits that
occurred within 6 hours and 1 step.

###  2.2 Qualitative characteristics of networks

To obtain a better understanding of the generated behavior-based dependency
network, the POI subcategories with the largest average in- and out- weights
were plotted in Figure S6. Supercenters, malls, department malls, and airports
had the largest in-weights, indicating that these places were depended by many
other POIs. On the other hand, places such as art dealers and various types of
retail stores had the largest average out-weight, indicating that such places
had high dependency on other places. The subcategories that appeared in both
rankings were consistent across the five metropolitan areas. As shown in
Figures S8 and S9, the POI subcategories that appeared in each ranking were
similar when we changed the co-visit detection parameter to $T_{c}=1$ and
$T_{c}=3$, respectively.

To further observe the dependency relationships between categories, we
computed the proportion of edge weights among POI category pairs, shown in
Figure S7. The proportion of edge weights was computed by taking the sum of
weights that connect the vertical and horizontal categories and dividing that
by the total weights that exist in the network, more formally, by $\sum_{i\in
A,j\in B}w_{ij}/\sum_{i,j}w_{ij}$. As the matrices in Figure S7 show, the
patterns of dependency are consistent across cities, with Food, Service,
Shopping, and Transport playing a big role in both depending on and being
depended by others.

Figure S6: POI subcategories with the largest average in- and out-weights
Supercenters, malls, department malls, and airports had the largest in-
weights, while places such as art dealers and various types of retail stores
had the largest average out-weight.

(a) New York

(b) Boston

(c) Seattle

(d) Los Angeles

(e) Dallas

Figure S7: Proportion of edge weights among POI category pairs. The proportion
of edge weights was computed by taking the sum of weights that connect the
vertical and horizontal categories and dividing that by the total weights that
exist in the network. The patterns of dependency are consistent across cities,
with Food, Service, Shopping, and Transport playing a big role in both
depending on and being depended by others.

###  2.3 Comparison of networks under different co-visit detection parameters

How much do the co-visit detection parameters ($T_{s}$,$T_{c}$) affect the
structural properties of the dependency networks? To investigate this, we
generated the dependency network using 25 pairs of parameters
($T_{s}=[1,2,3,5,unlimited]$ and $T_{c}=[1,3,6,12,24]$ hours). The following
analysis compares the following characteristics of the dependency networks
across different co-vist detection parameters:

  * •

POI subcategories with largest in- and out-weights (Figures S8 and S9)

  * •

Distributions of in-weights and out-weights per POI (panels (a) and (b) in
Figures S10 to S14)

  * •

Relationship between average weight and physical distance between the POIs
(panels (a) and (b) in Figures S10 to S14)

  * •

Difference in the proportion of weights for each category pair (positive means
baseline network has more weights between the category pairs) (panel (c) in
Figures S10 to S14)

As shown in Figures S8 and S9, the POI subcategories that appeared in each
ranking were similar when we changed the co-visit detection parameter to
$T_{c}=1$ and $T_{c}=3$, respectively. Under all parameters, supercenters,
malls, department malls, and airports had the largest in-weights, while places
such as art dealers and various types of retail stores had the largest average
out-weight.

Panels (a) in Figures S10 to S14) show that although the distribution
obviously shifts to the right (more steps would include more links, thus more
in- and out- weights) the maximum step difference parameter does not make a
big difference on the distributions of the in-weights, out-weights, or the
decay of average weights with the physical distance.

On the other hand, Panels (b) in Figures S10 to S14) show that the
distributions are significantly affected by the choice of time difference
parameter. Obviously, the longer the temporal threshold we use, the
distributions shift to the right (more time difference would include more
links, thus more in- and out- weights). Especially, the dependency networks
with the 1 hour threshold present a significantly sparser network with lower
in-weights, out-weights, and faster decay of distance with respect to physical
distance. The $T_{c}=6$ threshold that we chose as the baseline parameter
generates network characteristics that are closely in between $T_{c}=3$, and
$T_{c}=12$ and $T_{c}=24$.

Panels (c) in Figures S10 to S14) show that despite the changes in co-visit
detection parameters, the proportion of weights among category pairs are not
affected significantly. Note that positive differences (blue color) mean that
the baseline network ($T_{s}=1$,$T_{c}=6$) contains more weight in the
specific category pair. The only exception is $T_{c}=1$ (similar to the in-
weights, out-weights, and distance decay curves), where we observe much fewer
weights among shopping POIs in the baseline network. This indicates that when
we limit the time difference to 1 hour, we capture significantly more of the
shopping-to-shopping weights compared to other category pairs.

Network diagrams in Figures S15 to S17 show the average dependencies between
POI subcategories in the five cities. Each node represents a POI subcategory
(there are 96 of them in the dataset) and the three largest outgoing
dependency edges are shown for each node. Node sizes show the in-degree of the
constructed network (i.e., how many other POI categories depend on that node).
Many shopping subcategories including supercenters, department stores, malls,
and clothing stores, and colleges, cafes, restaurants are depended by many
other subcategories.

Figure S8: POI subcategories with the largest average in- and out-weights,
when $T_{c}=1$ hour Supercenters, malls, department malls, and airports had
the largest in-weights, while places such as art dealers and various types of
retail stores had the largest average out-weight. Results were similar to the
baseline parameter when $T_{c}=6$ hours. Figure S9: POI subcategories with the
largest average in- and out-weights, when $T_{c}=3$ hour Supercenters, malls,
department malls, and airports had the largest in-weights, while places such
as art dealers and various types of retail stores had the largest average out-
weight. Results were similar to the baseline parameter when $T_{c}=6$ hours.

(a) Network characteristics under different maximum step difference $T_{s}$

(b) Network characteristics under different maximum time difference $T_{c}$

(c) Difference in category pairwise dependency weights compared to baseline
network

Figure S10: Dependency network in New York under different co-visit detection
parameters.

(a) Network characteristics under different maximum step difference $T_{s}$

(b) Network characteristics under different maximum time difference $T_{c}$

(c) Difference in category pairwise dependency weights compared to baseline
network

Figure S11: Dependency network in Boston under different co-visit detection
parameters.

(a) Network characteristics under different maximum step difference $T_{s}$

(b) Network characteristics under different maximum time difference $T_{c}$

(c) Difference in category pairwise dependency weights compared to baseline
network

Figure S12: Dependency network in Seattle under different co-visit detection
parameters.

(a) Network characteristics under different maximum step difference $T_{s}$

(b) Network characteristics under different maximum time difference $T_{c}$

(c) Difference in category pairwise dependency weights compared to baseline
network

Figure S13: Dependency network in Los Angeles under different co-visit
detection parameters.

(a) Network characteristics under different maximum step difference $T_{s}$

(b) Network characteristics under different maximum time difference $T_{c}$

(c) Difference in category pairwise dependency weights compared to baseline
network

Figure S14: Dependency network in Dallas under different co-visit detection
parameters.

(a) New York

(b) Boston

Figure S15: Network diagram showing the average dependencies between POI
subcategories in New York and Boston. Each node is a POI subcategory and the
three largest outgoing dependency edges are shown for each node. Node sizes
show the in-degree of the constructed network.

(a) Seattle

(b) Los Angeles

Figure S16: Network diagram showing the average dependencies between POI
subcategories in Seattle and Los Angeles. Each node is a POI subcategory and
the three largest outgoing dependency edges are shown for each node. Node
sizes show the in-degree of the constructed network. (a) Dallas Figure S17:
Network diagram showing the average dependencies between POI subcategories in
Dallas. Each node is a POI subcategory and the three largest outgoing
dependency edges are shown for each node. Node sizes show the in-degree of the
constructed network.

##  3 Statistical robustness of behavior-based dependency networks

Apart from co-visit detection parameters $T_{c}$ and $T_{s}$, many factors and
decision parameters could affect the characteristics of the dependency network
and its weights. In this section, we test the statistical robustness of the
edge weights and network characteristics by comparing the dependency network
with several variants. More specifically, we will make comparisons with the
following networks:

  * •

Dependency network computed using data from a different time period, for
example, January – April 2019, instead of September – December 2019.

  * •

Dependency network where edges with small weights are removed. This is done by
computing the 25th percentile of the weights $w_{ij}$ using bootstrap method.

  * •

Dependency network calculated without the post-stratification procedure.

The following subsections show the details of how each type of network is
calculated and comparisons of network statistics with the empirical dependency
network. In this section, comparisons of edge-based and category-aggregated
edge weights are compared between the empirical and alternative dependency
networks. Further robustness checks on the modeling of network weights, the
predictability of shocks during COVID-19, and resilience to future
hypothetical shocks are performed in Supplementary Notes 4, 5, and 6,
respectively.

###  3.1 Robustness against choice of time period

The baseline dependency network was generated using data collected during the
period of September to December, 2019. To assess whether the dependency
networks are dynamic across time, we compared the in- and out-weights of each
POI across different data collection periods. Figures S18 and S19 shows that
the in- and out-weights across different time periods (2019 May – August and
2019 January – April) are highly correlated ($\rho>0.7$) with the baseline
time period (2019 September – December). Moreover, the category pairwise
weight proportions were compared across different data collection periods, as
shown in Figures S20 and S21. The category pairs that are highly dependent on
eachother are consistent across different time periods (2019 May – August and
2019 January – April) with the baseline time period (2019 September –
December).

(a) New York, in-weight

(b) New York, out-weight

(c) Boston, in-weight

(d) Boston, out-weight

(e) Seattle, in-weight

(f) Seattle, out-weight

Figure S18: Comparison of in- and out-weights of each POI across different
data collection periods for New York, Boston, and Seattle. In- and out-weights
across different time periods (2019 May – August and 2019 January – April) are
highly correlated ($\rho>0.7$) with the baseline time period (2019 September –
December).

(a) Los Angeles, in-weight

(b) Los Angeles, out-weight

(c) Dallas, in-weight

(d) Dallas, out-weight

Figure S19: Comparison of in- and out-weights of each POI across different
data collection periods for Los Angeles and Dallas. In- and out-weights across
different time periods (2019 May – August and 2019 January – April) are highly
correlated ($\rho>0.7$) with the baseline time period (2019 September –
December).

(a) New York

(b) Boston

(c) Seattle

Figure S20: Comparison of category pairwise weight proportion across different
data collection periods, for New York, Boston, and Seattle. The category pairs
that are highly dependent on eachother are consistent across different time
periods (2019 May – August and 2019 January – April) with the baseline time
period (2019 September – December).

(a) Boston

(b) Boston

Figure S21: Comparison of category pairwise weight proportion across different
data collection periods, for Los Angeles and Dallas. The category pairs that
are highly dependent on eachother are consistent across different time periods
(2019 May – August and 2019 January – April) with the baseline time period
(2019 September – December).

###  3.2 Computing quartiles of $w_{ij}$ via bootstrap method

As shown in Figure 1 of the main manuscript and other figures in the
Supplementary Material (e.g., Figures S10 \- S14), edge weights $w_{ij}$ are
distributed across 4 orders of magnitude, and there exist edges with very
small weights (i.e., $w_{ij}<0.001$). To test the robustness of the results
presented in this paper to such extremely small edge weights, we estimate the
confidence interval of each edge weight $w_{ij}$ using bootstrap resampling.

To obtain bootstrapped samples of the dependency weights $w_{ij}$, the co-
visits were sampled randomly with replacement from the original co-visit
dataset. For each bootstrap sample the bootstrap replication of the dependency
weights $w^{b}_{ij}$ where $b=1,2,3,...,30$ were computed. The 25th percentile
of the distribution of the weights, denoted by $w^{p25}_{ij}$ were computed
from the sample distribution, and only edges with $w^{p25}_{ij}>0$ were used
in the ’bootstrap network’.

Figure S22 shows the in- and out- weights of POIs before and after applying
the bootstrap method to select statistically significant edges. The
correlation is generally moderate ($\rho=0.6$) for out-weight and high
($\rho=0.9$) for in-weights. The variance becomes larger especially for the
nodes with out-weights below 1. Figure S23 shows the out- and in-weights of
categories when applying bootstrap method to remove insignificant weights. The
correlation is extremely high ($\rho>0.99$) for both out- and in-weights when
aggregated to POI categories, indicating that bootstrapping does not have a
significant effect when the analysis is aggregated to the category level.

(a) Out-weights of POIs

(b) In-weights of POIs

Figure S22: Out- and in-weights of POIs when applying bootstrap method to
remove smaller weights. The correlation is generally moderate ($\rho=0.6$) for
out-weight and high ($\rho=0.9$) for in-weights.

(a) Out-weights of categories

(b) In-weights of categories

Figure S23: Out- and in-weights of categories when applying bootstrap method
to remove insignificant weights. The correlation is extremely high
($\rho>0.99$) for both out- and in-weights when aggregated to POI categories.

###  3.3 Robustness against post-stratification processing

In Supplementary Note 1, analyses showed significant biases in sampling rates
of mobile phone users across census block groups and income ranges. To correct
for such bias, we conducted post stratification method (Supplementary Note
1.4) and used the corrected data to estimate and analyze the dependency
networks. Here, we measure how different the estimates of out- and in-weights
of POIs would be if we did not apply the post-stratification technique to
correct for biases in mobile phone data. In Figure S24, we observe that the
correlation is high ($\rho>0.8$) for both out- and in-weights even though
there was significant bias in sample rates across CBGs and income groups.

(a) Out-weights of POIs

(b) In-weights of POIs

Figure S24: Out- and in-weights of POIs when applying post-stratification to
correct for biases in mobile phone data. The correlation is high ($\rho>0.8$)
for both out- and in-weights even though there was significant bias in sample
rates across CBGs and income groups.

##  4 Modeling dependency network weights

###  4.1 Gravity-based null networks

To further understand the structural properties of the dependency networks, we
generated null networks that satisfy the following properties:

  * •

the weight $w_{ij}$ decays with physical distance

  * •

the in-weight $w_{ij}$ is larger for nodes with larger visitation $n_{i}$

To generate such null networks that preserve such qualities, we utilized the
generalized gravity law as the theoretical starting point, where we can model
the number of common visitors as the gravity component $g_{ij}$, which is the
product of the total number of visitors to places $i$ and $j$, $n_{i}$ and
$n_{j}$, divided by a function of the distance between $i$ and $j$, $d_{ij}$,
which takes the form $f(d_{ij})=(d_{0}+d_{ij})^{\gamma}$:

$g_{ij}=n_{i}n_{j}/(d_{0}+d_{ij})^{\gamma}$ (2)

where $n_{i}$ and $n_{j}$ are the total number of visits to POIs $i$ and $j$,
$d_{ij}$ is the physical distance between POIs $i$ and $j$, $d_{0}$ is the
distance cutoff parameter, and $\gamma$ is the exponent parameter of the
gravity model. Parameters $d_{0}$ and $\gamma$ were fitted empirically to
maximize the correlation between $g_{ij}$ and $n_{ij}$, which is the total
number of common visitors between POIs $i$ and $j$, and as shown in Figure
S25, $d_{0}=0.2$ and $\gamma=1.5$ showed the highest correlation when the
values were logged and not logged.

Figure S25: Correlation between the observed $n_{ij}$ values and the gravity
component $g_{ij}$ under different model parameters

Using the fitted gravity model $w_{ij}=n_{ij}/n_{i}\sim
n_{j}/(d_{0}+d_{ij})^{\gamma}$, we now construct null networks that mimic the
physical properties of the actual dependency networks. To enable a fair
comparison between the actual dependency network and the null network, we
constructed the null networks while fulfilling the following two properties:

  1. 1.

the in-degree of each node are kept consistent in the null network

  2. 2.

the in-weight of each node are kept consistent in the null network

To achieve this, first we construct a linear relationship between the gravity
component $g_{ij}=n_{j}/(d_{0}+d_{ij})^{\gamma}$ and $w_{ij}$,
$g_{ij}=\phi(w_{ij})$. Then, for each edge in the actual dependency network
connecting $i$ and $j$ with a dependency weight $w_{ij}$, we compute its
theoretical gravity component using the linear relationship $\phi$ and select
an alternative node with the same level of corresponding gravity component
from its 10,000 closest nodes, and is assigned the same weight $w_{ij}$. This
algorithm enables us to construct a null network where we 1) maintain the
linear relationship between $w_{ij}$ and $g_{ij}$, 2) the same number of in-
edges are selected for each node, and 3) the total in-weight for each node is
kept consistent.

Figures S26 to S28 show the map visualizations of the actual (left) and null
(right) networks for the five cities. In all cities, we can observe the null
network being more locally clustered around large POIs, while the actual
network is more dispersed and contains more long-distance connections. Note
that the in-degrees and in-weights of all nodes are equivalent across the two
networks. Figure S29 shows the histogram of physical distances of all edges in
the actual and null networks. Figure S30 compares the proportion of edge
weights among POI category pairs across the actual and null networks. The
proportion of edge weights was computed by taking the sum of weights that
connect the vertical and horizontal categories and dividing that by the total
weights that exist in the network. The patterns of dependency are consistent
across cities, with Service and Transport node depending more on other nodes
in the real network compared to the null network.

(a) New York

(b) Boston

Figure S26: Comparison of actual and null networks in New York and Boston. For
visual purposes, around 1 million links are shown for both the actual and null
networks.

(a) New York

(b) Boston

Figure S27: Comparison of actual and null networks in Seattle and Los Angeles.
For visual purposes, around 1 million links are shown for both the actual and
null networks. (a) Dallas Figure S28: Comparison of actual and null networks
in Dallas. For visual purposes, around 1 million links are shown for both the
actual and null networks.

(a) New York

(b) Boston

(c) Seattle

(d) Los Angeles

(e) Dallas

Figure S29: Comparison between real and null network on the proportion of edge
weights among POI category pairs. The proportion of edge weights was computed
by taking the sum of weights that connect the vertical and horizontal
categories and dividing that by the total weights that exist in the network.
The patterns of dependency are consistent across cities, with Service and
Transport node depending more on other nodes in the real network compared to
the null network.

(a) New York

(b) Boston

(c) Seattle

(d) Los Angeles

(e) Dallas

Figure S30: Histograms of edge distances between actual and null networks. The
actual networks contain more long distance edges than the null networks.

###  4.2 Regression model of $w_{ij}$

Results comparing the relationship between dependency weights and physical
distance suggest that the dependency weights could be dictated by physical
factors. Here, we model dependency weights $w_{ij}$ with various physical
factors to investigate how much of the variance we observe in dependency
weights can be explained by such factors. We build simple linear regression
models of the form:

$\log_{10}w_{ij}\sim\log_{10}d_{ij}+n_{j}+\eta_{i}+\eta_{j}+\theta_{i}+\theta_{j}$
(3)

where $\log_{10}w_{ij}$ denotes the logged dependency weight of POI $i$ on POI
$j$, and:

  * •

$\log_{10}d_{ij}$ is the logged Haversine distance between POIs $i$ and $j$.

  * •

$n_{j}$ is the number of visitors that POI $j$ receives. The premise is that
popular POIs are depended more by other POIs. This variable was standardized
($(x-\mu)/\sigma$) prior to the analysis for comparison across cities.

  * •

$\eta_{i}$ is the fixed effect (FE) for POI $i$’s subcategory. There are 97
subcategories in the POI dataset, and examples are shown in Figure S6.

  * •

$\theta_{i}$ is the fixed effect for POI $i$’s located Public Use Microdata
Area (PUMA).

The regression results are shown in Table S3. To save computation time, 1
million edges were randomly sampled to include in the regression. The
resulting $R^{2}$ or the coefficients were robust against different sampling
runs. Overall, the adjusted $R^{2}$ was relatively low (between $0.10$ and
$0.16$ for all cities), suggesting that physical factors determine a small %
of the variance of dependency weights. The coefficients are similar across
cities, with the logged Haversine distance showing a slower decay compared to
the decay observed in Figure S10, which is due to the samples in the
regression being limited to ones that have non-zero weights.

Table S3: Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) in US cities using the logged Haversine distance ($\log_{10}d_{ij}$), the popularity in visits to place $j$ ($v_{j}$), and the subcategory fixed effects and PUMA fixed effects of POIs $i$ and $j$. Variables were centered and standardized prior to analysis. | Dependent Variable: $\log_{10}w_{ij}$
---|---
Variable | New York | Boston | Seattle | Los Angeles | Dallas
Constant | -2.268 ∗∗∗ | -2.291 ∗∗∗ | -2.315 ∗∗∗ | -2.312 ∗∗∗ | -2.408 ∗∗∗
$\log_{10}d_{ij}$ | -0.129 ∗∗∗ | -0.147 ∗∗∗ | -0.134 ∗∗∗ | -0.125 ∗∗∗ | -0.143 ∗∗∗
$v_{j}$ (standardized) | 0.022 ∗∗∗ | 0.026 ∗∗∗ | 0.027 ∗∗∗ | 0.020 ∗∗∗ | 0.022 ∗∗∗
Subcategory FE for $i$ and $j$ | Y | Y | Y | Y | Y
PUMA FE for $i$ and $j$ | Y | Y | Y | Y | Y
Observations (sampled) | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000
Adj. $R^{2}$ | 0.089 | 0.117 | 0.122 | 0.108 | 0.115

###  4.3 Robustness against different network instances

Table S4 shows the same regression results using the selected network edges
using the bootstrap method introduced in Supplementary Note 3.2. The bootstrap
method removed edges with weights that were almost zero (if the 25th
percentile of the bootstrap sample distribution was below zero), and as a
result, as shown in Figure S22(a), the POIs with smaller weights (especially
out-weights) experienced a significant decrease in edge weights. The
regression results show a much higher $R^{2}$ compared to the original results
using all of the edges, explaining around 20% to 30% of the variance in the
dependency weights. The results are once again consistent across cities, with
regression coefficients in the same range.

Table S5 shows the same regression results using the dependency network
computed using only short stays ($<$ 4 hours). The results of the regression
(adjusted R squared and the model coefficients) are consistent with the
results from the full network shown in Table S3.

Table S4: Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) in US cities which were selected using the bootstrap method, using the logged Haversine distance ($\log_{10}d_{ij}$), the popularity in visits to place $j$ ($v_{j}$), and the subcategory fixed effects and PUMA fixed effects of POIs $i$ and $j$. Variables were centered and standardized prior to analysis. | Dependent Variable: $\log_{10}w_{ij}$
---|---
Variable | New York | Boston | Seattle | Los Angeles | Dallas
Constant | -2.067 ∗∗∗ | -1.978 ∗∗∗ | -2.100 ∗∗∗ | -2.249 ∗∗∗ | -2.005 ∗∗∗
$\log_{10}d_{ij}$ | -0.163 ∗∗∗ | -0.199 ∗∗∗ | -0.186 ∗∗∗ | -0.188 ∗∗∗ | -0.232 ∗∗∗
$v_{j}$ (standardized) | 0.025 ∗∗∗ | 0.033 ∗∗∗ | 0.032 ∗∗∗ | 0.030 ∗∗∗ | 0.032 ∗∗∗
Subcategory FE for $i$ and $j$ | Y | Y | Y | Y | Y
PUMA FE for $i$ and $j$ | Y | Y | Y | Y | Y
Observations (sampled) | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000
Adj. $R^{2}$ | 0.136 | 0.192 | 0.172 | 0.215 | 0.244
Table S5: Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) in US cities which were selected using only short stays (¡ 4 hrs), using the logged Haversine distance ($\log_{10}d_{ij}$), the popularity in visits to place $j$ ($v_{j}$), and the subcategory fixed effects and PUMA fixed effects of POIs $i$ and $j$. Variables were centered and standardized prior to analysis. | Dependent Variable: $\log_{10}w_{ij}$
---|---
Variable | New York | Boston | Seattle | Los Angeles | Dallas
Constant | -2.182 ∗∗∗ | -2.220 ∗∗∗ | -2.202 ∗∗∗ | -2.280 ∗∗∗ | -2.259 ∗∗∗
$\log_{10}d_{ij}$ | -0.131 ∗∗∗ | -0.149 ∗∗∗ | -0.134 ∗∗∗ | -0.126 ∗∗∗ | -0.145 ∗∗∗
$v_{j}$ (standardized) | 0.022 ∗∗∗ | 0.029 ∗∗∗ | 0.028 ∗∗∗ | 0.021 ∗∗∗ | 0.024 ∗∗∗
Subcategory FE for $i$ and $j$ | Y | Y | Y | Y | Y
PUMA FE for $i$ and $j$ | Y | Y | Y | Y | Y
Observations (sampled) | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000
Adj. $R^{2}$ | 0.096 | 0.125 | 0.131 | 0.117 | 0.121

###  4.4 Robustness against co-visit detection parameters

The regression analysis showed two main findings: 1) the physical factors can
only explain a fraction of the variance in dependency weights, and 2) the
coefficient of the logged Haversine distance is moderate compared to distance
exponents used in traditional models such as the Gravity Model (i.e., $-2$).
To assess the robustness of these findings of the regression model, the
regression was performed using dependency networks generated using different
co-visit detection parameters (also used in Supplementary Note 2.3). The 10
pairs of parameters ($T_{s}=[1,2,3,5,unlimited]$ and $T_{c}=[1,3,6,12,24]$
hours) were used to generate the dependency networks for each city, and the
regression results (adjusted $R^{2}$ and coefficient for Haversine distance)
are shown in Figure S31. The matrix plots across the five metropolitan areas
show similar patterns, both the adjusted $R^{2}$ and coefficient for Haversine
distance are relatively different when the maximum time difference is 1 hour.
In the rest of the parameter pairs, we obtain a similar result compared to
Table S3.

(a) Step difference parameter

(b) Time difference parameter

Figure S31: Regression results for dependency weights when using different co-
visit detection parameters, continued for Los Angeles and Dallas. Except for
the networks generated using maximum time difference of 1 hour, the results
(adjusted $R^{2}$ and coefficient for Haversine distance) are relatively
similar as the results in Table S3.

###  4.5 Robustness against different time periods

To check the robustness of the results with respect to the time periods used
to generate the dependency network, the same regression experiments were
performed using 2019 January – April data and 2019 May – August data, as shown
in Tables S6 and S7. We can observe that the $R^{2}$ values and the regression
coefficients are similar with those obtained in Table S3.

Table S6: Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) in US cities using network from 2019 January - April data. | Dependent Variable: $\log_{10}w_{ij}$ (2019 January - April data)
---|---
Variable | New York | Boston | Seattle | Los Angeles | Dallas
Constant | -2.157 ∗∗∗ | -2.242 ∗∗∗ | -2.273 ∗∗∗ | -2.264 ∗∗∗ | -2.268 ∗∗∗
$\log_{10}d_{ij}$ | -0.128 ∗∗∗ | -0.146 ∗∗∗ | -0.132 ∗∗∗ | -0.127 ∗∗∗ | -0.144 ∗∗∗
$v_{j}$ (standardized) | 0.019 ∗∗∗ | 0.029 ∗∗∗ | 0.026 ∗∗∗ | 0.019 ∗∗∗ | 0.021 ∗∗∗
Subcategory FE for $i$ and $j$ | Y | Y | Y | Y | Y
PUMA FE for $i$ and $j$ | Y | Y | Y | Y | Y
Observations (sampled) | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000
Adj. $R^{2}$ | 0.092 | 0.120 | 0.121 | 0.112 | 0.117
Table S7: Linear regression models predicting the logged dependency weights between POIs $i$ and $j$ ($log_{10}w_{ij}$) in US cities using network from 2019 May - August data. | Dependent Variable: $\log_{10}w_{ij}$ (2019 May - August data)
---|---
Variable | New York | Boston | Seattle | Los Angeles | Dallas
Constant | -2.312 ∗∗∗ | -2.292 ∗∗∗ | -2.320 ∗∗∗ | -2.333 ∗∗∗ | -2.421 ∗∗∗
$\log_{10}d_{ij}$ | -0.130 ∗∗∗ | -0.146 ∗∗∗ | -0.134 ∗∗∗ | -0.127 ∗∗∗ | -0.143 ∗∗∗
$v_{j}$ (standardized) | 0.020 ∗∗∗ | 0.023 ∗∗∗ | 0.024 ∗∗∗ | 0.019 ∗∗∗ | 0.021 ∗∗∗
Subcategory FE for $i$ and $j$ | Y | Y | Y | Y | Y
PUMA FE for $i$ and $j$ | Y | Y | Y | Y | Y
Observations (sampled) | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000
Adj. $R^{2}$ | 0.090 | 0.114 | 0.118 | 0.108 | 0.114

##  5 Impacts of behavior-based dependency during the COVID-19 pandemic

###  5.1 Analysis of visitation losses in cities

To investigate the usefulness of the dependency network for understanding the
resilience of businesses, we construct a regression modeling framework that
predicts the change in visitation patterns to a POI using information about
the change in visitation patterns to its alters and the dependency network.
The observed change in visits to different places is computed by:

$\tilde{v}_{i}=\big{(}\frac{v_{i}^{after}}{v_{i}^{before}}-1\big{)}*100(\%)$
(4)

where $v_{i}^{before}$ and $v_{i}^{after}$ denote the number of visits to
place $i$ before the pandemic (September - December 2019) and during the
pandemic period (March - June 2020), respectively. The left side panels in
Figure S32 plots the distribution of the change in visits $\tilde{v}_{i}$ in
the five metropolitan areas. Overall, as expected, we observe a peak at around
$\tilde{v}_{i}=-75$ for all cities, suggesting the overall substantial
decrease in visits during the initial stages of the pandemic. The right side
panels in Figure S32 plots the average change in visits across different POI
categories. We observe heterogeneity across POI categories, where Arts,
Colleges, Food, and Sports POIs experienced the largest losses during the
initial stages of the pandemic. On the other hand, Outdoor and Grocery places
had a minor impact compared to the other POI types. Moreover, prior studies
have found that POIs located in urban areas were affected more compared to
rural areas (e.g., [18]). Therefore, we take into consideration the effects of
the category of the places and the area in which the POIs are located to
predict the visitation losses to POIs.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Figure S32: Change in visits to POIs in New York, Boston, Seattle, Los
Angeles, and Dallas during the pandemic period. The left panels show the
distribution of the change in visits, and the right panels show the average
effects per POI category.

To test the hypothesis that the change in visitation patterns to a POI can be
modeled using information about the change in visitation patterns to its
alters and the dependency network, we first investigate the simple correlation
between the two metrics. Figure S33 shows the partial correlation
$\rho(\tilde{v}_{i},\sum_{j}w_{ij}\tilde{v}_{i})$, where POI $i$ and $j$s’
categories are $A$ (vertical) and $B$ (horizontal), respectively. Overall,
several category pairs exhibit significant and strong correlation. For
example, coffee POIs’ changes in visits are strongly correlated with the
weighted changes in visits to connected food, service, and shopping POIs
across the five metropolitan areas. This significant and strong correlation
suggests that the changes in the visitation of the ego may be predicted using
the information of the alter POIs connected via the dependency network.

(a) New York

(b) Boston

(c) Seattle

(d) Los Angeles

(e) Dallas

Figure S33: Correlation between change in visits of ego and the weighted
change in visits of alters by category pairs. Significant correlation between
several category pairs suggest predictability of $\tilde{v}_{i}$ using
information of alters.

###  5.2 Model specification and estimation results

Using the correlations revealed in the previous section, we build a simple
linear regression model of the form:

$\tilde{v}_{i}\sim\sum_{j}w_{ij}\tilde{v}_{j}+\sum_{j}\delta_{ij}\tilde{v}_{j}+\eta_{i}+\theta_{i}$
(5)

where $\tilde{v}_{i}$ denotes the change in visitations to POI $i$ during the
initial stages of the pandemic (March 1st - May 21st, 2020), and:

  * •

$\sum_{j}w_{ij}\tilde{v}_{j}$ is the sum of the neighbors’ (POIs $j$) change
in visitations ($\tilde{v}_{j}$) weighted by the dependency network weights
$w_{ij}$.

  * •

$\sum_{j}\delta_{ij}\tilde{v}_{j}$ is the sum of the neighbors’ (POIs $j$)
change in visitations ($\tilde{v}_{j}$) weighted by the distance based network
weights $\delta_{ij}$. The distance based network weights mimic the patterns
observed between physical distance and dependency weights, which are constant
until 100 meters, but decays as the inverse squared of the actual distance
beyond 100 meters.

  * •

$\eta_{i}$ is the fixed effect (FE) for POI $i$’s subcategory. There are 97
subcategories in the POI dataset, and examples are shown in Figure S6.

  * •

$\theta_{i}$ is the fixed effect for POI $i$’s located Public Use Microdata
Area (PUMA).

Tables S9 to S12 show the regression results for New York, Boston, Seattle,
Los Angeles, and Dallas, under the following four models:

  1. (1)

using only the subcategory and PUMA fixed effects,

  2. (2)

using the distance-based network effects $\sum_{j}\delta_{ij}\tilde{v}_{j}$ in
addition to the subcategory and PUMA fixed effects,

  3. (3)

using the behavior-based dependency network effects
$\sum_{j}w_{ij}\tilde{v}_{j}$ in addition to the subcategory and PUMA fixed
effects, and

  4. (4)

using all of the factors introduced in the full model.

Both the distance-based network effects and behavior-based dependency network
effects were standardized (by subtracting the mean and dividing by the
standard deviation) before analysis, therefore the magnitude of the
coefficients can be compared.

In all cities, the model performance significantly increases when we use the
behavior-based dependency network effects in model (3), compared to the
baseline model (1) and distance-based network effects model (2). Including
both distance-based network effects and the behavior-based network effects
slightly increases the $R^{2}$, however, the estimated coefficients for
$\sum_{j}w_{ij}\tilde{v}_{j}$ are substantially larger (5 to 15 fold) than the
coefficients of $\sum_{j}\delta_{ij}\tilde{v}_{j}$, indicating the
significance of the dependency network effects.

Table S8: Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in New York. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -40.9∗∗∗ | -41.6∗∗∗ | -41.7∗∗∗ | -42.2∗∗∗
| (5.345) | (5.110) | (5.110) | (5.089)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.278∗∗∗ |  | 3.410∗∗∗
|  | (0.085) |  | (0.082)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.59∗∗∗ | 14.26∗∗∗
|  |  | (0.103) | (0.103)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 213,140 | 213,140 | 213,140 | 213,140
$R^{2}$ | 0.158 | 0.168 | 0.230 | 0.237
Adjusted $R^{2}$ | 0.157 | 0.167 | 0.230 | 0.236
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S9: Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in Boston. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -20.1∗∗∗ | -22.1∗∗∗ | -33.7∗∗∗ | -34.9∗∗∗
| (6.512) | (6.253) | (6.253) | (6.221)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.919∗∗∗ |  | 3.946∗∗∗
|  | (0.182) |  | (0.176)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 13.00∗∗∗ | 12.60∗∗∗
|  |  | (0.201) | (0.200)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 48,848 | 48,848 | 48,848 | 48,848
$R^{2}$ | 0.145 | 0.158 | 0.213 | 0.221
Adjusted $R^{2}$ | 0.143 | 0.155 | 0.210 | 0.218
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S10: Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in Seattle. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -21.5∗∗ | -22.2∗∗ | -26.3∗∗∗ | -26.6∗∗∗
| (10.58) | (10.06) | (10.06) | (10.00)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 5.021∗∗∗ |  | 3.993∗∗∗
|  | (0.187) |  | (0.179)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 13.72∗∗∗ | 13.32∗∗∗
|  |  | (0.205) | (0.205)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 41,451 | 41,451 | 41,451 | 41,451
$R^{2}$ | 0.168 | 0.182 | 0.249 | 0.258
Adjusted $R^{2}$ | 0.166 | 0.180 | 0.247 | 0.256
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S11: Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in Los Angeles. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -17.3∗∗∗ | -17.8∗∗∗ | -21.2∗∗∗ | -21.4∗∗∗
| (4.820) | (4.554) | (4.554) | (4.534)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.860∗∗∗ |  | 3.531∗∗∗
|  | (0.095) |  | (0.091)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.30∗∗∗ | 13.89∗∗∗
|  |  | (0.100) | (0.100)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 168,385 | 168,385 | 168,385 | 168,385
$R^{2}$ | 0.137 | 0.150 | 0.229 | 0.236
Adjusted $R^{2}$ | 0.136 | 0.149 | 0.228 | 0.235
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S12: Linear regression models predicting the change in visits to POIs during the pandemic (2019 March - May) in Dallas. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 3.944 | 1.362 | -11.3 | -12.6
| (10.25) | (9.730) | (9.730) | (9.671)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 5.985∗∗∗ |  | 4.427∗∗∗
|  | (0.146) |  | (0.140)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 15.28∗∗∗ | 14.66∗∗∗
|  |  | (0.160) | (0.160)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 81,457 | 81,457 | 81,457 | 81,457
$R^{2}$ | 0.140 | 0.158 | 0.227 | 0.236
Adjusted $R^{2}$ | 0.139 | 0.156 | 0.225 | 0.235
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

###  5.3 Robustness against co-visit detection parameters

To test the robustness of the prediction power of the models using the
dependency-based network effects, we test the adjusted $R^{2}$ of the models
using dependency networks generated using different parameters for the co-
visit detection algorithm. Similar to Supplementary Note 4.3, we test the
regression models under 25 pairs of parameters ($T_{s}=[1,2,3,5,unlimited]$
and $T_{c}=[1,3,6,12,24]$ hours). Figure S34 shows the adjusted $R^{2}$ values
of the models using dependency networks generated with the corresponding co-
visit detection parameters. Across all five metropolitan areas, we observe the
general trend of the performance of the models increasing with longer maximum
time differences and with smaller number of between-visit steps. This suggests
that, for detecting the impact of the COVID-19 pandemic on businesses, we need
to observe 1-step (thus direct) visitation patterns between POIs, regardless
of the interval time between the entry and exit.

(a) Step difference parameter

(b) Time difference parameter

Figure S34: Regression results for dependency weights when using different co-
visit detection parameters, continued for Los Angeles and Dallas. Except for
the networks generated using maximum time difference of 1 hour, the results
(adjusted $R^{2}$ and coefficient for Haversine distance) are relatively
similar as the results in Table S3.

###  5.4 Results using changes in visits during different time periods

To test whether the behavior-based dependency network effects significantly
improves the prediction performance of visitation losses to POIs regardless of
the time period, we test the same regression models with dependent variables
calculated from different periods during the pandemic. Tables S13 to S17 show
the regression models for predicting the change of visits during 2020/6/1 and
2020/8/31, compared to the pre-pandemic period (2019/9/1 to 2019/11/30). Thus,
the dependent variable is computed as:

$\tilde{v}_{i}=\big{(}\frac{v_{i}^{2020June\sim
2020August}}{v_{i}^{2019September\sim 2019November}}-1\big{)}*100(\%)$ (6)

In all metropolitan areas, the adjusted $R^{2}$ using the behavior-based
dependency network effects (model 3) outperforms models 1 and 2 by 50% to
100%, showing substantial improvement in predictability. The regression
coefficients for the behavior-based dependency network effects is
significantly larger (30 fold) than the distance based effects, similar to the
findings from the experiments in Tables S9 to S12.

Similarly, Tables S18 to S22 show the regression models for predicting the
change of visits during 2020/9/1 and 2020/11/30, compared to the pre-pandemic
period (2019/9/1 to 2019/11/30). In all metropolitan areas, the adjusted
$R^{2}$ using the behavior-based dependency network effects (model 3)
outperforms models 1 and 2 by 50% to 100%, showing substantial improvement in
predictability. The regression coefficients for the behavior-based dependency
network effects is significantly larger (30 fold) than the distance based
effects, similar to the findings from the previous experiments. Overall the
magnitude of the $R^{2}$ across all 4 models are smaller than those in the
previous experiments. This suggests that the dependency network observed
during one year prior to the dependent variable loses predictive power due to
structural changes in the urban form. Nevertheless, experiments using change
in visits during different time periods during the pandemic showed that the
behavior-based dependency network effects substantially improve predictability
compared to using the distance-based network effects.

Table S13: Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in New York. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -20.6 | -21.1 | -15.8 | -16.3
| (17.00) | (15.66) | (15.66) | (15.62)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 26.41∗∗∗ |  | 10.12∗∗∗
|  | (0.275) |  | (0.275)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 57.97∗∗∗ | 53.96∗∗∗
|  |  | (0.297) | (0.316)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 213,140 | 213,140 | 213,140 | 213,140
$R^{2}$ | 0.072 | 0.111 | 0.213 | 0.218
Adjusted $R^{2}$ | 0.071 | 0.110 | 0.212 | 0.217
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S14: Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in Boston. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -19.6 | -24.9 | -33.7∗ | -35.2∗∗
| (18.67) | (17.52) | (17.52) | (17.38)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 25.83∗∗∗ |  | 14.70∗∗∗
|  | (0.519) |  | (0.521)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 44.40∗∗∗ | 39.43∗∗∗
|  |  | (0.546) | (0.570)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 48,848 | 48,848 | 48,848 | 48,848
$R^{2}$ | 0.062 | 0.107 | 0.173 | 0.187
Adjusted $R^{2}$ | 0.059 | 0.104 | 0.171 | 0.185
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S15: Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in Seattle. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 3.507 | 2.605 | -1.16 | -1.55
| (16.98) | (16.36) | (16.36) | (16.27)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 8.777∗∗∗ |  | 6.400∗∗∗
|  | (0.303) |  | (0.296)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 19.09∗∗∗ | 17.98∗∗∗
|  |  | (0.338) | (0.340)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 41,451 | 41,451 | 41,451 | 41,451
$R^{2}$ | 0.106 | 0.124 | 0.170 | 0.180
Adjusted $R^{2}$ | 0.104 | 0.121 | 0.168 | 0.177
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S16: Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in Los Angeles. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 8.252 | 7.685 | 3.501 | 3.390
| (7.296) | (6.885) | (6.885) | (6.857)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 8.702∗∗∗ |  | 5.212∗∗∗
|  | (0.145) |  | (0.140)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 21.46∗∗∗ | 20.42∗∗∗
|  |  | (0.149) | (0.151)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 168,385 | 168,385 | 168,385 | 168,385
$R^{2}$ | 0.080 | 0.099 | 0.180 | 0.187
Adjusted $R^{2}$ | 0.079 | 0.098 | 0.179 | 0.186
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S17: Linear regression models predicting the change in visits to POIs during the pandemic (2019 June - August) in Dallas. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 38.63∗∗ | 33.88∗ | 12.24 | 10.28
| (18.73) | (18.16) | (18.16) | (18.11)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 8.472∗∗∗ |  | 5.673∗∗∗
|  | (0.269) |  | (0.265)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 20.41∗∗∗ | 19.47∗∗∗
|  |  | (0.283) | (0.285)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 81,457 | 81,457 | 81,457 | 81,457
$R^{2}$ | 0.062 | 0.073 | 0.118 | 0.123
Adjusted $R^{2}$ | 0.060 | 0.071 | 0.116 | 0.121
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S18: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in New York. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -11.7 | -12.4 | -11.4 | -11.9
| (9.700) | (9.413) | (9.413) | (9.382)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 9.426∗∗∗ |  | 6.109∗∗∗
|  | (0.163) |  | (0.162)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 22.57∗∗∗ | 21.12∗∗∗
|  |  | (0.196) | (0.199)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 213,140 | 213,140 | 213,140 | 213,140
$R^{2}$ | 0.081 | 0.095 | 0.135 | 0.140
Adjusted $R^{2}$ | 0.080 | 0.094 | 0.134 | 0.139
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S19: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Boston. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -13.4 | -15.8 | -19.8 | -21.2
| (15.04) | (14.94) | (14.94) | (14.90)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 8.396∗∗∗ |  | 6.962∗∗∗
|  | (0.427) |  | (0.429)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 11.95∗∗∗ | 10.84∗∗∗
|  |  | (0.469) | (0.472)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 48,848 | 48,848 | 48,848 | 48,848
$R^{2}$ | 0.081 | 0.088 | 0.093 | 0.097
Adjusted $R^{2}$ | 0.078 | 0.085 | 0.090 | 0.095
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S20: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Seattle. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 8.718 | 7.900 | 4.898 | 4.468
| (16.05) | (15.56) | (15.56) | (15.48)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 7.389∗∗∗ |  | 5.628∗∗∗
|  | (0.286) |  | (0.281)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 16.64∗∗∗ | 15.80∗∗∗
|  |  | (0.323) | (0.324)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 41,451 | 41,451 | 41,451 | 41,451
$R^{2}$ | 0.071 | 0.086 | 0.127 | 0.136
Adjusted $R^{2}$ | 0.069 | 0.083 | 0.125 | 0.133
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S21: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Los Angeles. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 9.110 | 8.471 | 4.076 | 3.920
| (7.274) | (7.055) | (7.055) | (7.024)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 7.655∗∗∗ |  | 5.468∗∗∗
|  | (0.144) |  | (0.142)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 15.62∗∗∗ | 14.69∗∗∗
|  |  | (0.151) | (0.152)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 168,385 | 168,385 | 168,385 | 168,385
$R^{2}$ | 0.053 | 0.069 | 0.109 | 0.117
Adjusted $R^{2}$ | 0.052 | 0.068 | 0.108 | 0.116
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S22: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Dallas. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 17.86 | 14.28 | -4.65 | -6.44
| (19.67) | (19.18) | (19.18) | (19.14)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 7.407∗∗∗ |  | 5.340∗∗∗
|  | (0.282) |  | (0.278)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 18.95∗∗∗ | 18.28∗∗∗
|  |  | (0.292) | (0.293)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 81,457 | 81,457 | 81,457 | 81,457
$R^{2}$ | 0.037 | 0.045 | 0.084 | 0.089
Adjusted $R^{2}$ | 0.035 | 0.043 | 0.083 | 0.087
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

###  5.5 Robustness of regression results when using different time periods to
generate dependency networks

The robustness checks conducted in Supplementary Notes 3.1 and 4.4 showed high
correlation in edge weights between different time periods. Nevertheless, in
this section, we tested whether the time periods used to generate the
behavior-based dependency networks affects the performance of the regression
models. Tables S23 to S27 show the regression models for predicting the change
of visits during 2020/3/1 and 2020/5/31, using the dependency network computed
from data between 2019/1/1 and 2019/4/30.

In all metropolitan areas, the adjusted $R^{2}$ using the behavior-based
dependency network effects (model 3) outperforms models 1 and 2 by around 50%,
showing substantial improvement in predictability. The regression coefficients
for the behavior-based dependency network effects is significantly larger
(around 5 fold) than the distance based effects, similar to the findings from
the previous experiments.

Similarly, Tables S28 to S32 show the regression models for predicting the
change of visits during 2020/3/1 and 2020/5/31, using the dependency network
computed from data between 2019/5/1 and 2019/8/31. Again, in all metropolitan
areas, the adjusted $R^{2}$ using the behavior-based dependency network
effects (model 3) outperforms models 1 and 2 by around 50%, showing the
robustness against the choice of time period to generated the dependency
networks. In summary, the results on the predictability of shocks using the
behavior-based dependency networks are robust against the choice of the time
periods used to generate the dependency networks.

Table S23: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in New York when using dependency network generated from data between 2019 January to April. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -38.3∗∗∗ | -38.9∗∗∗ | -40.3∗∗∗ | -40.8∗∗∗
| (5.251) | (5.033) | (5.033) | (5.009)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.089∗∗∗ |  | 3.614∗∗∗
|  | (0.084) |  | (0.081)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 13.63∗∗∗ | 13.44∗∗∗
|  |  | (0.100) | (0.100)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 206,108 | 206,108 | 206,108 | 206,108
$R^{2}$ | 0.166 | 0.175 | 0.234 | 0.241
Adjusted $R^{2}$ | 0.165 | 0.174 | 0.233 | 0.240
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S24: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Boston when using dependency network generated from data between 2019 January to April. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -22.0∗∗∗ | -24.0∗∗∗ | -33.1∗∗∗ | -34.6∗∗∗
| (6.518) | (6.277) | (6.277) | (6.242)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.779∗∗∗ |  | 4.102∗∗∗
|  | (0.185) |  | (0.178)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 12.30∗∗∗ | 12.00∗∗∗
|  |  | (0.202) | (0.201)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 46,643 | 46,643 | 46,643 | 46,643
$R^{2}$ | 0.147 | 0.159 | 0.210 | 0.219
Adjusted $R^{2}$ | 0.145 | 0.157 | 0.208 | 0.217
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S25: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Seattle when using dependency network generated from data between 2019 January to April. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -27.2∗∗ | -27.5∗∗ | -30.1∗∗∗ | -30.3∗∗∗
| (11.03) | (10.52) | (10.52) | (10.46)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.856∗∗∗ |  | 3.937∗∗∗
|  | (0.191) |  | (0.183)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 13.12∗∗∗ | 12.75∗∗∗
|  |  | (0.211) | (0.210)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 39,582 | 39,582 | 39,582 | 39,582
$R^{2}$ | 0.173 | 0.186 | 0.247 | 0.256
Adjusted $R^{2}$ | 0.171 | 0.184 | 0.245 | 0.253
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S26: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Los Angeles when using dependency network generated from data between 2019 January to April. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -18.6∗∗∗ | -19.3∗∗∗ | -20.9∗∗∗ | -21.3∗∗∗
| (4.828) | (4.563) | (4.563) | (4.542)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.651∗∗∗ |  | 3.561∗∗∗
|  | (0.097) |  | (0.092)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.26∗∗∗ | 13.91∗∗∗
|  |  | (0.102) | (0.102)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 162,861 | 162,861 | 162,861 | 162,861
$R^{2}$ | 0.138 | 0.150 | 0.230 | 0.237
Adjusted $R^{2}$ | 0.137 | 0.149 | 0.229 | 0.236
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S27: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Dallas when using dependency network generated from data between 2019 January to April. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 7.027 | 4.521 | -8.57 | -9.93
| (10.15) | (9.647) | (9.647) | (9.585)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 5.827∗∗∗ |  | 4.493∗∗∗
|  | (0.147) |  | (0.141)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.91∗∗∗ | 14.37∗∗∗
|  |  | (0.162) | (0.161)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 78,222 | 78,222 | 78,222 | 78,222
$R^{2}$ | 0.145 | 0.161 | 0.228 | 0.238
Adjusted $R^{2}$ | 0.143 | 0.160 | 0.227 | 0.237
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S28: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in New York when using dependency network generated from data between 2019 May to August. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -38.2∗∗∗ | -38.7∗∗∗ | -40.5∗∗∗ | -40.9∗∗∗
| (5.249) | (5.016) | (5.016) | (5.002)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 3.398∗∗∗ |  | 2.733∗∗∗
|  | (0.085) |  | (0.081)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.70∗∗∗ | 14.50∗∗∗
|  |  | (0.104) | (0.103)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 210,540 | 210,540 | 210,540 | 210,540
$R^{2}$ | 0.164 | 0.170 | 0.236 | 0.240
Adjusted $R^{2}$ | 0.163 | 0.169 | 0.235 | 0.240
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S29: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Boston when using dependency network generated from data between 2019 May to August. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -19.8∗∗∗ | -21.4∗∗∗ | -33.8∗∗∗ | -34.9∗∗∗
| (6.580) | (6.324) | (6.324) | (6.302)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 3.816∗∗∗ |  | 3.244∗∗∗
|  | (0.185) |  | (0.178)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 13.20∗∗∗ | 13.00∗∗∗
|  |  | (0.208) | (0.207)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 47,995 | 47,995 | 47,995 | 47,995
$R^{2}$ | 0.146 | 0.153 | 0.212 | 0.217
Adjusted $R^{2}$ | 0.144 | 0.151 | 0.210 | 0.215
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S30: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Seattle when using dependency network generated from data between 2019 May to August. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -21.9∗∗ | -22.5∗∗ | -26.3∗∗∗ | -26.6∗∗∗
| (10.61) | (10.07) | (10.07) | (10.03)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.667∗∗∗ |  | 3.622∗∗∗
|  | (0.190) |  | (0.181)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.01∗∗∗ | 13.64∗∗∗
|  |  | (0.210) | (0.210)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 40,800 | 40,800 | 40,800 | 40,800
$R^{2}$ | 0.172 | 0.184 | 0.253 | 0.260
Adjusted $R^{2}$ | 0.169 | 0.181 | 0.251 | 0.258
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S31: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Los Angeles when using dependency network generated from data between 2019 May to August. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -17.6∗∗∗ | -17.8∗∗∗ | -20.5∗∗∗ | -20.6∗∗∗
| (4.839) | (4.561) | (4.561) | (4.543)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.597∗∗∗ |  | 3.372∗∗∗
|  | (0.096) |  | (0.091)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.72∗∗∗ | 14.37∗∗∗
|  |  | (0.102) | (0.102)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 166,292 | 166,292 | 166,292 | 166,292
$R^{2}$ | 0.136 | 0.148 | 0.233 | 0.239
Adjusted $R^{2}$ | 0.135 | 0.147 | 0.232 | 0.238
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S32: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Dallas when using dependency network generated from data between 2019 May to August. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 8.334 | 5.849 | -8.60 | -9.90
| (10.10) | (9.581) | (9.581) | (9.530)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 5.621∗∗∗ |  | 4.216∗∗∗
|  | (0.149) |  | (0.143)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 15.68∗∗∗ | 15.16∗∗∗
|  |  | (0.164) | (0.165)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 80,431 | 80,431 | 80,431 | 80,431
$R^{2}$ | 0.141 | 0.156 | 0.228 | 0.236
Adjusted $R^{2}$ | 0.140 | 0.154 | 0.227 | 0.235
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

###  5.6 Robustness of regression results when using only short non-work stays

In this section, we test whether the behavior-based dependency network
generated using only short (i.e., non-work) stays yields similar performance
metrics in the regression models. Tables S33 to S37 show the regression models
for predicting the change of visits during 2020/3/1 and 2020/5/31, using the
dependency network computed with stays shorter than 4 hours. In all
metropolitan areas, the adjusted $R^{2}$ using the behavior-based dependency
network effects (model 3) outperforms models 1 and 2, showing improvement in
predictability. The regression coefficients for the behavior-based dependency
network effects are significantly larger (around 5 fold) than the distance
based effects, similar to the findings from the previous experiments. This
results suggest that our estimation results are robust against the limiting
the analysis to the use of short non-work trips.

Table S33: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in New York when using dependency network generated from stays shorter than 4 hours. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -41.1∗∗∗ | -41.8∗∗∗ | -42.7∗∗∗ | -43.2∗∗∗
| (5.230) | (4.943) | (4.943) | (4.928)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.217∗∗∗ |  | 2.896∗∗∗
|  | (0.084) |  | (0.080)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 16.66∗∗∗ | 16.26∗∗∗
|  |  | (0.105) | (0.106)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 208,329 | 208,329 | 208,329 | 208,329
$R^{2}$ | 0.165 | 0.174 | 0.254 | 0.258
Adjusted $R^{2}$ | 0.164 | 0.173 | 0.253 | 0.257
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S34: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Boston when using dependency network generated from stays shorter than 4 hours. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -20.6∗∗∗ | -22.6∗∗∗ | -36.6∗∗∗ | -37.5∗∗∗
| (6.562) | (6.261) | (6.261) | (6.236)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.844∗∗∗ |  | 3.456∗∗∗
|  | (0.183) |  | (0.176)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.16∗∗∗ | 13.68∗∗∗
|  |  | (0.205) | (0.206)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 47,466 | 47,466 | 47,466 | 47,466
$R^{2}$ | 0.148 | 0.160 | 0.225 | 0.231
Adjusted $R^{2}$ | 0.145 | 0.158 | 0.223 | 0.229
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S35: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Seattle when using dependency network generated from stays shorter than 4 hours. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -21.7∗∗ | -22.4∗∗ | -28.8∗∗∗ | -29.0∗∗∗
| (10.50) | (9.905) | (9.905) | (9.860)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.933∗∗∗ |  | 3.439∗∗∗
|  | (0.188) |  | (0.179)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 14.94∗∗∗ | 14.44∗∗∗
|  |  | (0.211) | (0.212)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 40,135 | 40,135 | 40,135 | 40,135
$R^{2}$ | 0.171 | 0.185 | 0.263 | 0.270
Adjusted $R^{2}$ | 0.169 | 0.183 | 0.261 | 0.268
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S36: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Los Angeles when using dependency network generated from stays shorter than 4 hours. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | -18.5∗∗∗ | -19.0∗∗∗ | -22.9∗∗∗ | -23.1∗∗∗
| (4.834) | (4.544) | (4.544) | (4.527)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 4.905∗∗∗ |  | 3.241∗∗∗
|  | (0.096) |  | (0.091)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 15.07∗∗∗ | 14.61∗∗∗
|  |  | (0.102) | (0.103)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 164,195 | 164,195 | 164,195 | 164,195
$R^{2}$ | 0.139 | 0.152 | 0.239 | 0.245
Adjusted $R^{2}$ | 0.138 | 0.151 | 0.238 | 0.244
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S37: Linear regression models predicting the change in visits to POIs during the pandemic (2019 September - November) in Dallas when using dependency network generated from stays shorter than 4 hours. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during the pandemic)
---|---
| (1) | (2) | (3) | (4)
Constant | 3.572 | 0.977 | -13.2 | -14.2
| (10.11) | (9.521) | (9.521) | (9.476)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 5.910∗∗∗ |  | 3.843∗∗∗
|  | (0.146) |  | (0.140)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 16.34∗∗∗ | 15.65∗∗∗
|  |  | (0.161) | (0.163)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 78,929 | 78,929 | 78,929 | 78,929
$R^{2}$ | 0.144 | 0.162 | 0.242 | 0.250
Adjusted $R^{2}$ | 0.143 | 0.160 | 0.241 | 0.248
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

###  5.7 Case study on school closure period

To further test the effectiveness of using the dependency network for
predicting the cascade of shocks, we used school holidays as a separate case
study. The assumption is that, places that are connected to schools (in our
case, college places) tend to have an additional decrease in visits than other
places that have less dependency on college POIs. To compute the change in
visits, we used the school semester period (September to November 2019) as the
post period and the summer break period (June to August 2019) as the pre-
period.

$\tilde{v}_{i}=\big{(}\frac{v_{i}^{2019September\sim
2019November}}{v_{i}^{2019June\sim 2019August}}-1\big{)}*100(\%)$ (7)

Figure S35 shows the changes in visits to POIs in the five cities during the
fall semester period compared to the summer break period. As the right panels
clearly show, College POIs have a significant (25% to 60%) increase in the
number of visits during the semester compared to the breaks. The same model
specification was used to test the effectiveness of using the dependency
network. Tables S38 to S42 show the regression results. Although the
predictability of the change in visits is generally lower than the pandemic
results (due to the smaller impacts of summer holidays compared to the
pandemic), in all five cities, the model performance is highest when we use
the behavior-based dependency network compared to when we use the distance-
based null network.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Figure S35: Change in visits to POIs in New York, Boston, Seattle, Los Angeles, and Dallas during the fall semester period. The left panels show the distribution of the change in visits, and the right panels show the average effects per POI category. Table S38: Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in New York. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during school semester)
---|---
| (1) | (2) | (3) | (4)
Constant | -5.92 | -2.48 | -4.70 | -3.06
| (14.83) | (14.42) | (14.42) | (14.39)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 15.11∗∗∗ |  | 7.714∗∗∗
|  | (0.240) |  | (0.247)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 26.13∗∗∗ | 23.74∗∗∗
|  |  | (0.235) | (0.247)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 212,008 | 212,008 | 212,008 | 212,008
$R^{2}$ | 0.015 | 0.033 | 0.069 | 0.073
Adjusted $R^{2}$ | 0.014 | 0.032 | 0.068 | 0.072
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S39: Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in Boston. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during school semester)
---|---
| (1) | (2) | (3) | (4)
Constant | 12.09 | 17.42 | 18.28 | 20.11
| (16.29) | (15.45) | (15.45) | (15.39)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 20.47∗∗∗ |  | 9.685∗∗∗
|  | (0.456) |  | (0.475)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 33.63∗∗∗ | 29.87∗∗∗
|  |  | (0.458) | (0.492)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 48,652 | 48,652 | 48,652 | 48,652
$R^{2}$ | 0.049 | 0.087 | 0.144 | 0.151
Adjusted $R^{2}$ | 0.046 | 0.084 | 0.141 | 0.148
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S40: Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in Seattle. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during school semester)
---|---
| (1) | (2) | (3) | (4)
Constant | -7.76 | -8.32 | -8.75 | -9.05
| (56.04) | (55.94) | (55.94) | (55.92)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 6.630∗∗∗ |  | 4.304∗∗∗
|  | (0.991) |  | (1.011)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 12.02∗∗∗ | 11.15∗∗∗
|  |  | (0.974) | (0.995)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 41,294 | 41,294 | 41,294 | 41,294
$R^{2}$ | 0.004 | 0.005 | 0.008 | 0.008
Adjusted $R^{2}$ | 0.001 | 0.002 | 0.005 | 0.005
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S41: Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in Los Angeles. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during school semester)
---|---
| (1) | (2) | (3) | (4)
Constant | 4.979 | 5.578 | 6.292 | 6.486
| (12.90) | (12.63) | (12.63) | (12.61)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 11.14∗∗∗ |  | 5.416∗∗∗
|  | (0.253) |  | (0.260)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 21.40∗∗∗ | 19.81∗∗∗
|  |  | (0.251) | (0.262)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 166,784 | 166,784 | 166,784 | 166,784
$R^{2}$ | 0.009 | 0.020 | 0.050 | 0.052
Adjusted $R^{2}$ | 0.008 | 0.019 | 0.049 | 0.051
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
Table S42: Linear regression models predicting the change in visits to POIs during the school semester (2019 September - November) compared to summer break (2019 June - August) in Dallas. | Dependent variable: $\tilde{v}_{i}$ (Change in visits during school semester)
---|---
| (1) | (2) | (3) | (4)
Constant | 15.96 | 32.60 | 25.89 | 33.77
| (45.82) | (41.70) | (41.70) | (40.70)
Distance effect $\sum_{j}\delta_{ij}\tilde{v}_{j}$ |  | 65.77∗∗∗ |  | 40.32∗∗∗
|  | (0.598) |  | (0.634)
Dependency effect $\sum_{j}w_{ij}\tilde{v}_{j}$ |  |  | 75.00∗∗∗ | 57.42∗∗∗
|  |  | (0.579) | (0.629)
Subcategory FE | Y | Y | Y | Y
PUMA FE | Y | Y | Y | Y
Observations | 81,103 | 81,103 | 81,103 | 81,103
$R^{2}$ | 0.006 | 0.135 | 0.177 | 0.216
Adjusted $R^{2}$ | 0.004 | 0.134 | 0.175 | 0.214
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01

##  6 Cascading impacts of hypothetical shocks

###  6.1 Leontief open model

To explore what the behavior-based dependency network can tell us about other
types of future shocks, we apply the network effects regression model to
simulate the spatial cascades of such shocks in different cities. More
specifically, re-writing and reorganizing the regression model in matrix form,
we obtain

$\vec{v}=W\vec{v}+\vec{f}$ (8)

where $\vec{v}$ is a vector of $\tilde{v}_{i}$ for all $N$ places, $W$ is an
$N\times N$ matrix where each element is
$\tilde{w}_{ij}=\hat{\beta}_{W}w_{ij}$, and vector $\vec{f}$ is an aggregation
of all fixed effects $\beta_{0}$, $\eta_{i}$, and $\theta_{i}$. This model
specification is known as the Leontief Open Model, which is a simplified and
linear economic model for an economy in which input equals output [8]. To
predict the propagation of shocks throughout places in the city, the shocks
are modeled in the fixed effect vector $f$ (e.g., all colleges experience an
external shock of $-50\%$ visits reduction due to uptake of online education),
and the production vector $\vec{v}$ is computed by solving the linear system
$\hat{\vec{v}}=(I-W)^{-1}\vec{f}$ via the generalized minimal residual
iteration method.

The shift to online education which occurred during the pandemic is reported
to have a continuing effect, with roughly 20 percent of school systems
planning to or have already started online school programs [12]. Previous
studies [1] as well as analysis in Figure 2 in the main manuscript have
pointed out that college campuses have a substantial impact on the local
economy. If online learning and remote education were permanent and increased
with the help of advanced technology (e.g., augmented reality), what impacts
would it have on other businesses and amenities?

Figure S36a shows the simulated effects of a 50% reduction in visits to
college POIs (gray points) on nearby non-college POIs (red points; darker red
indicates larger negative impacts). Impacted POIs are not limited to those in
proximity to college POIs, but also in locations that are popular with college
students, for example, Massachusetts Avenue which connects MIT and Harvard
University. For comparison, we simulated the shocks to non-college POIs using
the physical distance network $\hat{W}$, where $\hat{w}_{ij}$ is used as the
matrix elements instead of behavior-based dependency $w_{ij}$ in Figure S36c.
Comparing the simulation results using the dependency network and the null
network shows that neglecting the behavior-based dependencies results in a
substantial underestimation of the effects on POIs that are located further
away from colleges. Model parameters, $\beta_{W}=0.70$ and $\beta_{null}=0.15$
were derived from prior regressions on estimation of changes in visits during
pre-pandemic periods.

The effects of online education were heterogeneous for different place
categories located at different distances from colleges. Figure S36b shows the
90th percentile of impacts on POIs by category and distance (log scaled).
While most significant impacts occur within 0.5 km, places such as arts and
museums, food, and service places experience substantial long-distance
impacts. Furthermore, simulations assuming different levels of visit decrease
to colleges (e.g., -100%, -25%) show a similar long-distance cascade of shocks
(Figures S37 and S38). These persistent spatial cascades emphasize the
importance of considering behavior-based dependency relationships between
places to grasp the holistic impact of such urban shocks for resilient urban
planning.

(a) Map of effects using dependency network

(b) Category and distance effects using dependency network

(c) Map of effects using null network

(d) Category and distance effects using null network

Figure S36: Cascading impacts of a 50% visit reduction to colleges. a.
Simulated effects of a 50% reduction in visits to college POIs (gray points)
on nearby non-college POIs (red points; darker red indicates larger negative
impacts), using the fitted Leontief Open Model. Impacted POIs are not limited
to those in proximity to college POIs. b. Impacts of the 50% visit reduction
to colleges on places by category and distance (90th percentile decrease in
visits are shown, log scaled). c. and d. show results using the null networks.

(a) Map of effects using dependency network

(b) Category and distance effects using dependency network

(c) Map of effects using null network

(d) Category and distance effects using null network

Figure S37: Cascading impacts of a 100% visit reduction to colleges. a.
Simulated effects of a 50% reduction in visits to college POIs (gray points)
on nearby non-college POIs (red points; darker red indicates larger negative
impacts), using the fitted Leontief Open Model. Impacted POIs are not limited
to those in proximity to college POIs. b. Impacts of the 100% visit reduction
to colleges on places by category and distance (90th percentile decrease in
visits are shown, log scaled). c. and d. show results using the null networks.

(a) Map of effects using dependency network

(b) Category and distance effects using dependency network

(c) Map of effects using null network

(d) Category and distance effects using null network

Figure S38: Cascading impacts of a 25% visit reduction to colleges. a.
Simulated effects of a 25% reduction in visits to college POIs (gray points)
on nearby non-college POIs (red points; darker red indicates larger negative
impacts), using the fitted Leontief Open Model. Impacted POIs are not limited
to those in proximity to college POIs. b. Impacts of the 50% visit reduction
to colleges on places by category and distance (90th percentile decrease in
visits are shown, log scaled). c. and d. show results using the null networks.

###  6.2 Cascading effects of individual place closures

Further leveraging the network model, we are able to simulate the impacts of
POI closure scenarios and identify the seed nodes (POIs) that have the largest
cascading effects on other POIs if inflicted by other urban shocks. For each
node, we simulate the cascading impacts of a 100% visit change to a single
node $i$, by computing $\hat{\vec{\nu}}^{(i)}=(I-W)^{-1}\vec{e}^{(i)}$, where
$\vec{e}^{(i)}$ is a one-hot encoding vector of the initial shock that assigns
a change in visits of $+1$ to node $i$ and $0$ otherwise, and
$\hat{\vec{\nu}}^{(i)}$ is the resulting vector of the cascading impacts,
where each element measures the impacts of the initial shock to all nodes. The
total impacts of changes in the number of visits to all nodes can be computed
by multiplying
$\hat{\vec{\nu}}^{(i)}=(\hat{\nu}_{1}^{(i)},\ldots,\hat{\nu}_{N}^{(i)})$ with
the vector of total visits to each POI, $\vec{n}=(n_{1},\cdots,n_{N})$. Thus,
the total impacts of the initial shock to node $i$ can be computed by
$C_{i}=\sum_{j;j\neq i}\hat{\nu}^{(i)}_{j}n_{j}$. By further scaling the
impact to its own size $n_{i}$, we obtain the total relative cascading effect
as $\hat{C_{i}}=C_{i}/n_{i}$. $\hat{C_{i}}=0.3$ indicates that increasing the
number of visits to node $i$ by 100% ($=n_{i}$) results in a total of
30%$*n_{i}$ increase in visits across all other nodes. The mean relative
cascading impacts of each POI category, $\hat{C}_{category}$ are shown in the
y-axis of Figures S39 to S41. POI categories such as airports, supercenters,
colleges, furniture stores, theme parks, railway stations, and sports stadiums
have a high impact on other POIs in urban areas propagated through behavior-
based dependency networks.

When implementing policies to close down certain POIs for emergency response
(e.g., lockdowns during pandemics), it is important to understand the spatial
extent of the cascade. To quantify this, we defined the distance range of the
cascade by computing the average distance to impacted nodes, weighted by the
magnitude of the impacts. More specifically, we compute the weighted distance
range of POI $i$ by $\hat{d}_{i}=\sum_{j;j\neq
i}\hat{\nu}^{(i)}_{j}d_{ij}/\sum_{j;j\neq i}\hat{\nu}^{(i)}_{j}$.

The weighted distance range of impact for each POI category,
$\hat{d}_{category}$ are shown in the x-axis of Figures S39 to S41.
Supercenters and colleges have high cascading effects but are focused locally
($\sim$ 1.5km around the POI). On the other hand, the impacts of airports,
stadiums, theme parks, and gas stations are both large and far-reaching
($\sim$ 2.5km to 3.5km). Understanding the magnitude and spatial extent of the
cascading effects could be applied to design emergency management policies to
effectively close places while minimizing economic losses. The large magnitude
of the spatial cascades that occur due to behavior-based dependency networks
calls for new urban policy-making approaches that balance the benefits of
mobility restriction measures (e.g., preventing the spread of diseases) while
minimizing the total cascading economic impacts to urban places and amenities.

(a) New York

(b) Boston

Figure S39: Total cascading impact of closing places on other locations. Total
cascading impact of closing places on other locations, relative to its own
size (x-axis) and the weighted distance range of the impact (y-axis) for
different POI subcategories in New York and Boston.

(a) Seattle

(b) Los Angeles

Figure S40: Total cascading impact of closing places on other locations. Total
cascading impact of closing places on other locations, relative to its own
size (x-axis) and the weighted distance range of the impact (y-axis) for
different POI subcategories in Seattle and Los Angeles. (a) Dallas
Figure S41: Total cascading impact of closing places on other locations. Total
cascading impact of closing places on other locations, relative to its own
size (x-axis) and the weighted distance range of the impact (y-axis) for
different POI subcategories in Dallas.

##  7 Software

Analysis was conducted using Python, Jupyter Lab, and the following libraries
and software:

  * •

NumPy [4] for general computation on Python.

  * •

Pandas [9] for loading, transforming, and analyzing data tables.

  * •

Matplotlib [5] for creating plots and figures.

  * •

GeoPandas [7] for spatial analysis and plotting map figures.

  * •

networkx [3] for network analysis.

  * •

Statsmodels [13] for statistical modeling and econometric analysis.

  * •

A Python implementation of the R Stargazer multiple regression model creation
tool555https://github.com/mwburke/stargazer was used to create the regression
tables.

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