Change of human mobility during COVID-19:
A United States case study

Justin Elarde1, Joon-Seok Kim 1, Hamdi Kavak2, Andreas Züfle1, Taylor
Anderson1*

1 Department of Geography and Geoinformation Science, George Mason University,
Fairfax, VA, USA

2 Department of Computational and Data Sciences, George Mason University,
Fairfax, VA, USA

*<EMAIL_ADDRESS>
###### Abstract

With the onset of COVID-19 and the resulting shelter in place guidelines
combined with remote working practices, human mobility in 2020 has been
dramatically impacted. Existing studies typically examine whether mobility in
specific localities increases or decreases at specific points in time and
relate these changes to certain pandemic and policy events. However, a more
comprehensive analysis of mobility change over time is needed. In this paper,
we study mobility change in the US through a five-step process using mobility
footprint data. (Step 1) Propose the Delta Time Spent in Public Places
($\Delta$TSPP) as a measure to quantify daily changes in mobility for each US
county from 2019-2020. (Step 2) Conduct Principal Component Analysis (PCA) to
reduce the $\Delta$TSPP time series of each county to lower-dimensional latent
components of change in mobility. (Step 3) Conduct clustering analysis to find
counties that exhibit similar latent components. (Step 4) Investigate local
and global spatial autocorrelation for each component. (Step 5) Conduct
correlation analysis to investigate how various population characteristics and
behavior correlate with mobility patterns. Results show that by describing
each county as a linear combination of the three latent components, we can
explain 59% of the variation in mobility trends across all US counties.
Specifically, change in mobility in 2020 for US counties can be explained as a
combination of three latent components: 1) long-term reduction in mobility, 2)
no change in mobility, and 3) short-term reduction in mobility. Furthermore,
we find that US counties that are geographically close are more likely to
exhibit a similar change in mobility. Finally, we observe significant
correlations between the three latent components of mobility change and
various population characteristics, including political leaning, population,
COVID-19 cases and deaths, and unemployment. We find that our analysis
provides a comprehensive understanding of mobility change in response to the
COVID-19 pandemic.

##  1 Introduction

Human mobility plays a crucial role in spreading an infectious virus such as
SARS-CoV-2 and has been instrumental in the onset of the COVID-19 pandemic. In
response to this global crisis, non-pharmaceutical interventions (NPIs),
including stay-at-home orders and social distancing guidelines, have been
implemented [1], reducing physical contacts and resulting in significant
changes to normal mobility patterns [2]. These changes can be observed using
individual-level mobility data such as mobile phone data embedded with
Bluetooth and global positioning system (GPS), collected actively through Call
Detail Records (CDRs) and passively through the use of smartphone applications
(apps).

Individual-level mobility data are typically anonymized and aggregated to
various spatial resolutions to produce a range of different mobility
indicators (see Table 1). As part of their COVID-19 Data Consortium efforts,
SafeGraph Inc. [3] has made available a comprehensive set of mobility
indicators ranging from mean distance traveled to median dwell time at and
away from home for each census block group in the US. Descartes Labs Inc. [4]
makes available the median of the maximum distance traveled by users at the
national, state, and county levels. Through the Data for Good [5, 6] effort,
Facebook makes available the fraction of users who stay put in a 60x60 meter
tile.

By using indicators such as these, we can derive a mobility change measure by
comparing mobility as measured by an indicator for a specific point in time
and place with a baseline representing normal mobility as measured by the same
indicator (see Table 1).

Table 1: Publicly available mobility indicators and mobility change measures Name |  Mobility Indicators |  Geography |  US Spatial Granularity |  Mobility Change Measure |  Baseline
---|---|---|---|---|---
SafeGraph
[7, 8] |  candidate device count, origin CBG and POI destination, completely home device count, home dwell time, non-home dwell time, distance traveled from home |  US |  census block
group |  shelter in place index, relative foot traffic index |  average time spent at home/foot traffic from Feb. 20-27, 2020
Google
[9] |  N/A |  global |  county |  relative time spent at various POI groups compared to baseline |  median value for the corresponding day of the week, during the 5 week period Jan.3-Feb.6, 2020
Apple
[10] |  N/A |  global |  county, city |  relative number of direction requests compared to baseline |  volume of requests on Jan. 13, 2020
Foursquare
[11, 12] |  N/A |  US |  national and select states |  relative number of visits to different POIs compared to baseline |  average number of visits from Feb. 13-19, 2020
Descartes Labs Inc
[4, 13] |  number of samples, median of the max distance |  US |  national, state, and county level |  relative median max distance compared to baseline |  average median max distance from Feb. 17-Mar. 7, 2020
Facebook
[5, 6] |  fraction of users that stay put in a region |  global |  national, state, county, and city level |  relative number of trips to other 60m tiles compared to baseline |  average from Feb. 2-Mar. 29, 2020
Unacast
[14] |  N/A |  US |  county level |  relative distance traveled compared to baseline, relative number of visits to non essential retail and essential services compared to baseline, relative number of unique human encounters relative to baseline |  average from Feb. 2-Mar. 29, 2020

To preserve the privacy of users, many companies like Google and Apple have
not made available mobility indicators, but instead make available their
mobility change measures, which are based on some measured mobility indicator.
Google [9] makes available the percent change in minutes spent at various POI
groups like parks, residential, workplace, retail, and public transportation
each day compared to a baseline. Similar mobility change measures based on POI
visits are produced by Foursquare [11], Safegraph [7], and Unacast [14]. Apple
[10] makes available the percent change in volume of direction requests.
Unicast also makes available the absolute change in distance traveled compared
to a baseline and the absolute change in unique human encounters per sq km.
Safegraph [8] makes available their own mobility change measure, a shelter in
place index which measures the change in percent in the population that stays
at home each day compared to a baseline. Descartes Labs Inc. [4] makes
available the percent change in max distance traveled relative to a baseline.
In all of the above examples, the choice of baseline varies. In most cases,
these baselines are static and usually look at the average mobility measured
by the indicator of choice over a short period representing normal mobility
(usually January or February 2020).

Quantifying the spatial and temporal change in mobility has been critical for
evaluating the effectiveness of NPIs [15, 16, 17], explaining behavior related
to mobility patterns [18], supporting contact tracing efforts [19], and
developing realistic models that predict trajectories of the disease [20].
However, due to the challenges associated with analyzing big data with both
spatial and temporal dimensions, mobility change measures are typically either
1) mapped to show the increase or decrease in mobility at specific points in
time [13] or 2) plotted to show the change in mobility as a time series for a
specific study area [21]. In either case, studies tend to associate these
changes at specific points in time with certain NPIs and furthermore attempt
to determine the underlying explanations for the variation in the social
distancing behaviors [17]. However, A more comprehensive understanding of
mobility changes is needed.

Therefore, the objectives of this study are to (1) develop a novel mobility
change measure and (2) identify and describe common temporal and spatial
trends that are observed across all US counties over the period of a year
during the COVID-19 pandemic. We aim to explore three related hypotheses, as
follows:

  * •

Our first hypothesis is that mobility behavior during the pandemic varies
spatially and temporally, but we can quantify general mobility trends across
counties. To evaluate this hypothesis, we use principal component analysis
(PCA) approach based on truncated Singular Value Decomposition (SVD) to
decompose the mobility time series of all counties into latent components of
mobility behavior.

  * •

Our second hypothesis is that geographically close counties have similar
mobility change trends. By representing each county as a linear combination of
latent features of human mobility, we can map these features into geographic
space and measure their spatial autocorrelation.

  * •

Our third hypothesis is that the strength of mobility components correlate
with other population characteristics such as population density, income, and
political leaning. To evaluate this hypothesis, we test for a significant
correlation between mobility components and these explanatory variables for
the same county.

By exploring these hypotheses, we aim to uncover hidden spatial and temporal
patterns and provide a concise summary of human mobility behavior.

##  2 Methods

In this paper, we analyze mobility change in the US using high-resolution foot
traffic data (Figure 1). We first propose the Delta Time Spent in Public
Places ($\Delta$TSPP), which measures changes in mobility for each US county
from 2019 to 2020 (Section 2.2). In this study, any geographical region that
has a FIPs code including counties, cities, and boroughs is designated as a
county. Because of the high dimensionality of the data, we next use Principal
Component Analysis (PCA) to reduce the data into three latent components,
where each component is explained as a time series representing the change in
mobility in US counties (Section 2.3). Third, we use clustering analysis to
find which counties have similar weighted combinations of the three components
(Section 2.4). Fourth, we investigate local and global spatial autocorrelation
for each component (Section 2.5). And finally, we conduct correlation analysis
to investigate how various population characteristics and behavior correlate
with mobility patterns (Section 2.6).

Fig 1: Overview of methodology

###  2.1 Mobility Data Source

The data used in this study was obtained “from SafeGraph, a data company that
aggregates anonymized location data from numerous applications in order to
provide insights about physical places, via the Placekey Community. To enhance
privacy, SafeGraph excludes census block group information if fewer than five
devices visited an establishment in a month from a given census block group”
[3, 22].

As part of SafeGraph’s Data for Academics [23], SafeGraph offers a Social
Distancing Metrics Dataset [8] (archived on April 16, 2020). This dataset is
available at no cost for academic researchers for non-commercial work. In
general, SafeGraph obtains precise device location information from third-
party data partners such as mobile application developers. This information is
collected through APIs where app developers provide information about their
users [24]. The device’s home census block group (CBG) is determined based on
the nighttime location of devices over six weeks so that Social Distancing
Metrics including the CBG’s device count, the complete at home device count,
the median distance traveled from home, the median home dwell time, median
non-home dwell-time and more can be calculated. It should be noted that
SafeGraph’s Social Distancing Metrics are available from January 1, 2019,
through to April 16, 2021, and are no longer being updated. For this study, we
use data from SafeGraph’s Social Distancing Metrics from January 1, 2019, to
December, 31st 2020.

###  2.2 Human Mobility Measures

As an indicator to assess changes in human mobility in the US, we selected
SafeGraph’s measure of median_non_home_dwell_time from the Social Distancing
Metrics dataset, which is defined as the median time (minutes each day) that
all devices in a census block group (CBG) spend visiting public points of
interest (POIs) located outside the boundaries of their home geohash (using a
$153m\times 153m$ hash buckets). This includes minutes spent at public POIs
such as grocery stores, restaurants, bars, and movie theaters. We note that
this measure only includes public POIs that are captured among the 6.5 million
POIs in the SafeGraph Core Places database [7]. We aggregate this measure to
the county level by averaging the median_non_home_dwell_time for each CBG in
each county to give us an average_median_non_home_dwell_time for each county.

Our goal is to compare the average_median_non_home_dwell_time for each county
for each day in 2019 and the corresponding day in 2020. Weekly patterns
strongly affect mobility in the United States, where in general, lower
mobility is observed on the weekends, especially on Sundays. Since
corresponding days in 2019 and 2020 may not be corresponding days of the week,
we use the seven-day rolling average of the average_median_non_home_dwell_time
for both 2019 and 2020. That is, we calculate the mean
average_median_non_home_dwell_time for that day and the three days before and
after that day. We formally define this as Time Spent at Public Places (TSPP)
calculated for both 2019 and 2020 as follows:

######  Definition 1 (Time Spent at Public Places (TSPP))

Let $\mathcal{R}$ be a region, and let
$\mathcal{D}^{\mathcal{R}}=[d^{\mathcal{R}}_{1},...,d^{\mathcal{R}}_{N}]$
denote a time series of daily median_non_home_dwell_time for that region,
where $N$ is the number of days of interest. We define our Time Spent at
Public Places measure at the i-th day as:

$TSPP(\mathcal{D^{\mathcal{R}}})[i]=\frac{\sum_{j=0}^{6}d^{\mathcal{R}}_{i+j}}{7},$

where $i$ is an index of $D^{\mathcal{R}}$ and $1\leq i\leq N-7$. The
denominator denotes the size of a sliding window, i.e., 7 days, used for
calculating the mean.

Next, we look at the difference between the Time Spent at Public Places (TSPP)
measure calculated for the i-th day in the time series for each county in 2019
and the i-th day in the time series for the same county in 2020. We define
this as Change in Time Spent at Public Places measure or $\Delta$TSPP as
follows:

######  Definition 2 (Time Spent at Public Places ($\Delta$TSPP))

Let $\mathcal{R}$ be a region and let $\mathcal{D}^{\mathcal{R}}_{y}$ the time
series of 365 daily median_non_home_dwell_time values in $\mathcal{R}$ for all
days in year $y$. We define the daily change in TSPP as:

$\Delta
TSPP(\mathcal{R},y1,y2)=TSPP(\mathcal{D}^{\mathcal{R}}_{y1})-TSPP(\mathcal{D}^{\mathcal{R}}_{y2}),$

where $y1$ and $y2$ are a target year and a reference year to compare,
respectively. For short, $\Delta$TSPP is referred to $\Delta
TSPP(\mathcal{R},2020,2019)$ in this paper, where $\mathcal{R}$ is all
counties of the US.

We consider an increase in $\Delta$TSPP, where TSPP is higher in 2020 than in
2019, as a proxy for increased mobility, thus increasing the risk of exposure.
Although individual counties can provide the spatial and temporal
heterogeneity in the post-pandemic mobility behavior, there are thousands of
counties in the US, each with a unique mobility trend. Thus, we seek an
approach that can identify different mobility trends found commonly across all
3107 counties while handling both the dimensionality and variance of the data.

###  2.3 Mobility Feature Extraction: Principal Component Analysis

Principal Component Analysis (PCA) [25] is a commonly used technique to reduce
the dimensionality, yet maintain the variation, present in large multivariate
data and is a generalization of eigendecomposition for non-square and non-
maximum rank matrices. We define a data matrix $R\in{\rm I\\!R}^{m\times n}$
as a $m\times n$ matrix where $m=359$ corresponds to days the number of days
of the year (except for the first three and last three days due to the seven-
day sliding window) and where $n=3100$ corresponds to the number of US
counties (we remove seven outlier counties - see Appendix). Using singular
value decomposition (SVD), $R$ is factorized in the product of three matrices
$R=U\Sigma V^{T}$ where $\Sigma$ is a diagonal matrix containing the square
roots of the eigenvalues of $RR^{T}$, and the columns of $U$ ($V$) are the
eigenvectors of $RR^{T}$ ($R^{T}R$).

To reduce the dimensionality of $R$ we truncate the SVD to obtain only the
first $K$ dimensions. Thus, $\Sigma_{K}$ is a $K\times K$ diagonal matrix
containing the $K$ largest eigenvalues, $U_{K}$ is a $m\times K$ matrix
describing each of the $m$ days with $K$ latent features, and $V_{K}$ is a
$K\times n$ matrix describing each county with $K$ latent features.

The idea of using SVD in this context is to decompose the time series of each
county into a linear combination of $K$ archetypal time series called
principal components (PCs). SVD assumes that the $\Delta$TSPP is a linear
combination of latent features. This assumption holds since the average
$\Delta$TSPP that we observe is indeed derived from the mobility change of
individual people. By applying SVD to the set of $\Delta$TSPP time-series of
all counties of the US, we can find components of individual human behavior as
follows.

  * •

Reduced mobility during the entirety of March-December 2020 corresponding to
counties with individuals who have the ability and obedience to stay at home
for the remainder of 2020, such as people who worked remotely.

  * •

Reduced mobility only during Summer 2020 corresponding to individuals who stop
isolation after the first wave of infections in the US, either due to having
to go back to work or due to growing weary of mobility restrictions.

  * •

No reduced mobility, corresponding to individuals who cannot stay at home such
as health professionals or individuals who are not willing to follow stay-at-
home directions.

In addition to finding these three latent PCs, SVD further allows us to
describe each county as a linear combination of these components, which can be
interpreted as corresponding mobility behavior. In the case that some counties
are not well explained by any of the latent components, we calculate the
coefficient of determination for each county.

###  2.4 Clustering Analysis

Due to a large number of counties, it is difficult to determine which counties
exhibit similar mobility trends. Therefore, we cluster counties into groups of
counties that exhibit similar latent features of change of exposure. We first
plot each county into the PCA space where each point represents a county, and
each axis represents the weight of each PC in explaining the county’s
$\Delta$TSPP, normalized from 0 to 1. For clustering, we compared the K-means
algorithm [26] against other clustering algorithms and determined K-means to
be the most appropriate (see Appendix). The K-means algorithm partitions n
observations into k clusters by randomly initializing k points (means or
cluster centroids) and assigning each observation to their closest point. The
coordinate point is updated iteratively to reflect the mean center of
observations that belong to it. This approach requires the number of k points
to begin with. We choose  k=3 so that we can better understand which groups of
counties are better explained by each of the three latent components.

###  2.5 Spatial Autocorrelation Analysis

To test the impact of proximity in mobility change, we measure the spatial
autocorrelation of counties and their corresponding weights for each PC using
both Global Moran’s I [27] and Anselin’s Local Moran’s I [28]. The concept of
spatial autocorrelation is based on Tobler’s First Law of Geography which
states that things that are closer to each other are more similar than things
that are far apart [29]. Moran’s I calculates the degree to which features in
a dataset are positively spatially autocorrelated (neighboring features are
alike), negatively spatially autocorrelated (neighboring features are not
alike), or not spatially autocorrelated (attributes of features are
independent of location).

First, we compute a matrix of spatial weights to define each counties’
neighbors mathematically. We used Queens-case, meaning counties are considered
to be neighboring if their border shares at least one common vertex. After
building this matrix, we discovered that the only neighboring county to
Fairfax City is Fairfax County, which was identified as an outlier in the PCA
space and removed earlier in this analysis. To resolve this issue, Fairfax
City was also removed. Next, we calculate the fraction of the total variation
that is attributed to counties that are close together across the entire study
area to give us a measure of global spatial autocorrelation (Moran’s I) and
then decompose the measure for each feature to give us local spatial
autocorrelation (Anselin’s Local Moran’s I).

###  2.6 Correlation Analysis

We have covered both the spatial and temporal variation of mobility trends
across all of the counties in the US in response to the COVID-19 pandemic.
Next, we aim to identify some population variables that may explain the
variation. Thus, we use the Pearson’s R coefficient to calculate the
correlation between the weight of each PC and a variety of explanatory
variables, including income, political leaning, employment, and COVID-19 cases
and deaths for each county. Pearson’s R is a statistical measure of linear
association that returns a value between -1 and 1 that defines how strong the
correlation is, where the further away that value is from 0, the stronger the
correlation. We test for significance using a p-value. Since we hypothesize
that there is a linear relationship between the strength of the PCs in
explaining county mobility and different county variables, we did not
investigate non-linear relationships.

##  3 Results

###  3.1 General Mobility Trends

We calculate the TSPP for each of the 3107 counties to produce a time series
representing mobility in each county in 2019 and 2020. This can be aggregated
to the US. Fig 2 shows the Time Spent in Public Places
$TSPP(\mathcal{D^{\mathcal{R}}})$ for the region $\mathcal{R}$ corresponding
to all counties aggregated to the United States level, excluding Alaska,
Hawaii, and US territories, and for the sequence of days
$\mathcal{D}^{\mathcal{R}}$ ranging from Jan to Dec. for 2019 and 2020.

Fig 2: TSPP calculated for the United States in 2019 and 2020.
Fig 3: $\Delta$TSPP calculated for the US, Arlington County (VA), Tulare
County (CA), and Cambria County (PA).

We observe low mobility between January and March 2019, which is a seasonal
effect due to below-average temperatures and above-average snowfall in Winter
2018-2019 [30]. We also observe a lack of such seasonal mobility decrease
between January and March 2020 due to one of the warmest winters on record for
the contiguous United States. Starting March 2020, we observe a rapid drop in
mobility due to the COVID-19 pandemic. Interestingly, we also observe that
these drops swing back to normal by June 2020, exceeding the mobility of 2019.

Next, we look at the Change in Measure of Public Exposure. Fig 3 shows the
$\Delta$TSPP measure for the US and for three counties. We can visually
observe radically different mobility behavior among these counties. Arlington
County, VA, exhibits a large drop in mobility in March 2020 than other
counties. We also observe that this reduction in mobility persists throughout
the year 2020. In contrast, the mobility of Cambria County, PA, exhibits a
less extreme drop in mobility and quickly returns to and exceeds normal
mobility after June 2020, where $\Delta$TSPP is greater than or equal to 0.
Tulare County, California, exhibits a much less extreme drop in mobility, but
in general, maintains this reduction of mobility.

###  3.2 Principal Components of $\Delta$TSPP

####  3.2.1 Qualitative Interpretation

We find that $K=3$ principal components explain 59% of the variation in all of
the included time series where PC1 explains 35.6%, PC2 explains 15.3%, and PC3
explains 8.8% of the variance. Thus, using Matrix $V_{K}$, each county in the
U.S. is described as a linear combination of three PCs, with a loss of
$1-59\%=41\%$ of explained variance. This result shows that by describing each
county by only three archetypal behaviors, we can explain more than half of
the variance across the $359$ dimensions that each county is described by in
the full space.

Towards explainable machine learning, Fig 11 shows the three latent principal
components describing each county in the U.S. mapped back into the full
359-day space.

  * •

The mobility trend captured by PC1 (in red) begins with slightly higher
mobility in January and February 2020 compared with 2019. In March 2020, there
is a sharp deviation from the mobility observed in March 2019 as mobility
declines in response to the pandemic. For the remainder of 2020, mobility
remains consistently lower than mobility in 2019. We explain PC1 by
individuals who reduced their mobility in March 2020 and then maintained this
stay-at-home and social distancing behavior for the rest of the year. Counties
that are well explained by PC1 may be composed of individuals who are able to
work from home in April and continued working from home throughout the year.

  * •

The mobility trend captured by PC2 (in green) begins with a slightly lower
mobility in January and February 2020 than in comparison with 2019. In the
spring, mobility steadily increases until April 2020, when mobility declines
slightly in response to the COVID-19 pandemic. For the remainder of 2020,
mobility remains higher than mobility in 2019. The only time mobility is lower
than in comparison to 2019 is before the pandemic. Counties that are well
explained by PC2 may be composed of individuals who can’t or won’t comply with
stay-at-home orders (such as health care workers, essential workers, and other
individuals).

  * •

Finally, the mobility trend captured by PC3 (in blue) begins with more
mobility in January and February 2020 than in 2019. In response to the
pandemic, there is a sharp drop in mobility in March 2020 until it returned to
normal mobility in June 2019. Mobility then increases in late summer and
remains higher for the remainder of the year than in 2019. We explain PC3 by
individuals who have reduced mobility directly after the pandemic (March-June
2020) but then return to normal mobility. Counties that are well explained by
PC3 may be composed of individuals who were unable to work due to a shutdown
in March 2020, but returned to work in June 2020. Counties that are well
explained by PC3 may also be composed of individuals who were fearful during
the onset of the pandemic but experienced pandemic fatigue and became less
compliant with stay-at-home orders as the pandemic continued.

Fig 4: Three latent features describing mobility in the US mapped back into
the temporal space.

Abstractly speaking, we can interpret these three latent components as “Long
term mobility reduction” (PC1), “No mobility reduction” (PC2), and “Short term
mobility reduction” (PC3).

In the Singular Value Decomposition, Matrix $V$ provides us with the $K=3$
weights of these latent features for each county. In the following, Section
3.2.1 provides a qualitative spatial analysis of these three principal
components to understand which parts of the United States exhibit strong
weights for each of these latent features. We provide quantitative analysis to
show that the weights of these latent features are strongly spatially auto-
correlated with a number of significant spatial clusters.

####  3.2.2 Spatial Analysis

We provide a spatial analysis of the principal components of change of
exposure across all counties in the United States. Section 3.4 shows the
spatial distribution of each principal components, Section 3.2.2 analyses
clusters of counties having similar principal components, and Section 3.5
explores which counties are well-modeled by these components and which
counties still exhibit large unexplained variance using three principal
components only.

Matrix $V$ describes each county as a linear combination of the three
components. For example, Arlington County’s $\Delta$TSPP (See Fig 3) is
described as 98% PC1, 20% PC2, and 21% PC3, thus having a dominant first
component. In contrast, Tulare County’s $\Delta$TSPP (See Fig 3) is described
as 51% PC1, 16% PC2, and 33% PC3, thus having a stronger weight on PC3 than
Fairfax.

Fig 5 A to C maps the strength of each PC in explaining the mobility trend of
all 3100 counties. Based on visual analysis of the results, we find that the
counties on the east and west coast have a higher weight in PC1, counties in
the south-west and south-east have a higher weight in PC2, and counties in the
mid-west have a higher weight in PC3.

(a)

(b)

(c)

Fig 5: Spatial Distribution of the Three Principal Components of Change of
Public Exposure. (A) Principal Component 1: Reduced $\Delta$TSPP March-
December (B) Principal Component 2: Increased $\Delta$TSPP March-December (C)
Principal Component 3: Reduced $\Delta$TSPP March-June.

Stacking these three figures, Fig 6 presents a Red-Green-Blue (RGB) composite
map to show the linear combination of the components for each county where red
is PC1, green is PC2, and blue is PC3. Again, we predominantly observe red
colors, which correspond to PC2, which corresponds to long-term reduced
mobility at the west coast and the northeast coast. We can also observe a
strong influence of green, corresponding to PC2, which corresponds to no
reduction of mobility in the central United States. We also observe large
patches of purple (red and blue) corresponding to a mixture of PC1 and PC3 in
the midwest, New York, New Jersey, and other states, which corresponds to a
mixture of long-term and short-term reduction of mobility having an absence of
PC2.

Fig 6: RGB Map of Latent Features of Change of Exposure $\Delta$TSPP for all
counties in the United States

Since the three principal components only explain 59% of the variation among
the 358-dimensional representation of counties as a sequence of daily changes
in mobility, an important and open question is to ask which counties of the
U.S. are explained well by these components and which ones are not. That is,
which counties may be better explained by the remaining 355 components that we
truncated to reduce the dimensionality. Fig 7 shows the explained and
unexplained variance using the coefficient of determination. The counties with
positive values (green) are well explained by the three PCs. The counties with
negative values (red) are not well explained by the three PCs and would be
better explained by taking the simple average of the counties $\Delta$TSPP.

Fig 7: Spatial distribution of the explained variance ($R^{2}$) for all
counties across the US using three principal components

###  3.3 Clustering of Latent Features of $\Delta$TSPP

Fig 8 depicts the resulting feature vectors for all counties in the $K=3$
dimensional latent feature space from two angles (Fig 8A and B) for easier
interpretation. The colors in Fig 8 represent the result of the K-means
clustering analysis. We map the results of K-means analysis to see the spatial
distributions of the counties related to each cluster (Fig 9).

(a) Angle 1

(b) Angle 2

Fig 8: Counties plotted in PCA space. Fig 9: K-means analysis mapped
geographically

We can see that counties in the southwest and southwest, excluding Arizona,
New Mexico, Virginia, and West Virginia, belong primarily to Cluster 1 (in
green) and thus have similar weighted combinations of PCs. Counties along the
west and northeastern coast, as well as the Florida coast and southern Texas,
belong primarily to Cluster 2 (in pink). Counties that belong to the Rocky
Mountain region of the US as well as Maine, Vermont, much of New York, West
Virginia, Minnesota, and Wisconsin belong primarily to Cluster 3 (in purple).
Counties in many states in the midwest and southeast are a mix of belonging to
different clusters.

###  3.4 Spatial Autocorrelation of Mobility Behavior Between Counties

The results of the Global Moran’s I analysis for each of the three latent
features are presented in Table 2. We found a strong positive spatial
autocorrelation for all three features. The spatial autocorrelation of PC1 and
PC2 at $0.556$ and $0.544$, respectively, is higher than the spatial
autocorrelation of PC3 at $0.489$. For all three components, the positive
spatial autocorrelation is highly significant at p-values $<<10^{-28}$ having
Z-scores of 46 and greater. As we suspected from our qualitative analysis,
this result confirms that the patterns of $\Delta$TSPP that we observed in Fig
5 are indeed strongly positively spatially autocorrelated.

Component | Moran’s I | Z-score
---|---|---
PC1 | 0.556 | 52.4
PC2 | 0.544 | 51.3
PC3 | 0.489 | 46.1
Table 2: Global Moran’s I Measure of Spatial Autocorrelation for each
Principal Component

Next, we calculate Anselin’s Local Moran’s I [28] to help visualize clusters
of counties with similar neighbors and outlier counties with dissimilar
neighbors (Fig 10). The results of Anselin’s Local Morain’s I for PC1 are
presented in Fig 10A. We can identify clusters of counties with high weights
corresponding to PC1 that have neighbors with high weights. We refer to these
patterns as High-High (HH) clusters that are positively spatially
autocorrelated. In addition, we can identify the counties with low weights
corresponding to PC1 that have neighbors with low weights. We refer to these
patterns as Low-Low(LL) clusters that are positively spatially autocorrelated.
Anselin’s Local Moran’s I also uncover outliers, where we find counties with
high or low weights corresponding to PC1 that have oppositely weighted
neighbors. We refer to these patterns as Low-High(LH) outliers and High-Low
(HL) outliers that are negatively spatially autocorrelated. Counties with a
p-value of greater than .05 are considered insignificant. We present the
results of Anselin’s Local Moran’s I for PC2 and PC3 in Figs 10B and 10C.

(a) PC 1

(b) PC 2

(c) PC 3

Fig 10: Anselin’s Local Moran’s I (LISA) results. Correlation Variable | PC1 | PC1 P-value | PC2 | PC2 P-value | PC3 | PC3 P-value
---|---|---|---|---|---|---
Median Household Income | 0.63 | 0.00e+00 | -0.11 | 1.84e-09 | 0.22 | 2.39e-36
Per Capita Income | 0.55 | 1.02e-244 | -0.15 | 2.02e-16 | 0.19 | 5.13e-26
2020 Rep Vote Percent | -0.45 | 8.12e-152 | 0.38 | 2.90e-104 | -0.02 | 3.34e-01
2020 Dem Vote Percent | 0.44 | 3.61e-150 | -0.37 | 4.56e-99 | -3.23e-02 | 5.14e-01
2016 Rep Vote Percent | -0.42 | 5.79e-133 | 0.39 | 7.45e-112 | 0.02 | 1.72e-01
2016 Dem Vote Percent | 0.41 | 5.40e-125 | -0.33 | 1.93e-81 | -0.03 | 7.25e-02
ACS 2019 Pop Est | 0.38 | 4.50e-106 | -0.18 | 3.32e-25 | -0.02 | 2.32e-01
2012 Dem Vote Percent | 0.28 | 2.42e-56 | -0.39 | 1.11e-115 | 0.02 | 3.38e-01
2012 Rep Vote Percent | -0.28 | 4.62e-55 | 0.42 | 1.07e-130 | -0.02 | 3.55e-01
2008 Dem Vote Percent | 0.26 | 2.18e-47 | -0.44 | 2.48e-143 | 0.05 | 5.09e-03
2008 Rep Vote Percent | -0.24 | 1.03e-41 | 0.45 | 1.32e-157 | -0.05 | 4.78e-03
2000 Rep Vote Percent | -0.19 | 7.16e-27 | 0.30 | 1.99e-64 | 0.03 | 1.01e-01
2004 Dem Vote Percent | 0.19 | 1.01e-25 | -0.35 | 2.06e-89 | -1.49e-02 | 4.07e-01
2004 Rep Vote Percent | -0.18 | 3.74e-25 | 0.36 | 1.65e-97 | 0.02 | 3.41e-01
2000 Dem Vote Percent | 0.17 | 1.95e-21 | -0.23 | 4.50e-40 | -0.03 | 9.62e-02
Unemployment Rate | 0.11 | 1.42e-10 | -0.31 | 1.28e-69 | -0.02 | 2.65e-01
Deaths Per Thousand | 0.09 | 1.36e-07 | 0.15 | 2.64e-16 | -0.17 | 1.31e-21
Cases Per Thousand | -0.05 | 1.18e-02 | 0.25 | 5.15e-44 | -0.16 | 6.41e-20
Table 3: Correlation analysis results showing Pearson’s correlation and
respective p-values between each principal component (PC1-PC3) and other
population characteristics.

###  3.5 Explaining Variation in Mobility Patterns

We examine the correlation between the weight of each PC and other variables
for each county. The results are presented in Table 3. PC1 captures the
mobility trends in US counties that maintain decreased mobility from the onset
of the pandemic and beyond. We find that there is a strong positive
correlation between counties with a higher income (median household income and
per capita income) and a higher weight corresponding to PC1. This has been
supported in the literature in other studies that find that higher-income
counties and states are able to follow social distancing guidelines better and
stay-at-home orders [31].

We find a strong positive correlation between counties that are democratic
leaning and have a higher weight corresponding to PC1. In contrast, we find a
strong negative correlation between counties that are republican leaning in
the 2020 and 2016 election and have a higher weight corresponding to PC1. This
has been supported in the literature where it has been found that counties and
states that are democratic leaning better follow social distancing guidelines
and stay-at-home orders [32]. Interestingly, we find that the strength of the
correlations between PC1 weight and political leaning decrease as we use
political data from 2012, 2008, 2004, and 2000.

We also find positive correlations between counties with high population and a
higher weight corresponding to PC1. We do not find strong correlations between
counties with a higher weight corresponding to PC1 and normalized numbers of
cases and deaths corresponding to COVID-19. In any case, it is difficult to
properly quantify the relationship between total and normalized COVID-19 cases
and deaths and PC weight based on the uncertainty inherent to the data due to
inconsistent reporting.

PC2 captures the mobility trends in US counties that increase their mobility.
We find that the correlations between counties with a high weight of PC2 and
the variables are opposite that of PC1. Thus, there is a strong positive
correlation between counties that are republican leaning in the 2020 and 2016
election with a higher weight corresponding to PC2. PC3 captures the average
mobility trends in US counties. There does not appear to be nearly as strong
correlations between counties with a high weight corresponding to PC3 and the
variables.

##  4 Discussion and Conclusions

In this study, we calculate a novel indicator of mobility change which we call
the Time Spent at Public Places (TSPP) using Safegraph data [3]. We quantify
the change of mobility by calculating the running difference of this measure
between 2019 and 2020 for each county to estimate a measure of mobility change
($\Delta$TSPP) that describes each county as a time series of mobility change
of 365 days.

Confirming our first hypothesis, we find that mobility behavior during the
pandemic varies spatially and temporally, but that there are three main
mobility trends uncovered by our PCA analysis. PC1 captures the mobility
trends of counties that drop their mobility at the onset of the pandemic and
maintain reduced mobility through to the end of the year, the behavior of
which we refer to as “Long term mobility reduction”. PC2 captures the mobility
trends of counties that increase their mobility in 2020 or, in other words “No
mobility reduction”. PC3 captures the mobility trends of counties that drop
their mobility at the onset of the pandemic and then quickly return to normal
mobility, which we call “Short term mobility reduction”. PC3 can be considered
the average mobility trend across all counties. Confirming our second
hypothesis, we find that mobility trends are positively spatially
autocorrelated, meaning that counties that are geographically close exhibit
similar mobility trends. Finally, we partly confirmed our third hypothesis is
that we find some correlations between the variation in mobility trends and
underlying population behavior and characteristics.

While we obtained interesting results, there are certain limitations of the
data relevant to this study including sparse documentation of data collection,
data completeness, bias, geographic coverage, and open-access. First, although
SafeGraph has gone to unprecedented lengths to make the data public, perhaps
unsurprisingly as a corporate data provider, their methods and sources for
collecting device data and POI data are sparse. Detailed methods, sources of
data, and truth datasets are not available and thus cannot be independently
evaluated [33].

Data completeness is also difficult to assess. Our mobility indicator is based
on the median_non_home_dwell_time which measures the median time that devices
in the same CBG spend at public POIs that are included in SafeGraph’s Core
Places database. SafeGraph represents the location of over 6300 distinct
brands as POIs and this number changes over time as new brands are added.
These are chains of commercial POIs that include all major brands in the
United States (McDonald’s, AMC, Macy’s, Chevrolet, Whole Foods Market). Of the
brands that SafeGraph includes, they capture close to 100% of the brands’
locations [34]. About 80% of SafeGraph POIs have no brand associated as they
are single commercial locations (local restaurants, museums). It is not
possible to assess the actual completeness of SafeGraph’s POIs; specifically,
the total number of all POIs in the US versus the total number of POIs
represented in the Safegraph Core Places Dataset.

SafeGraph’s Social Distancing Metrics dataset is based on device users that
make up approximately 10% of the United States population, which is
significantly larger than typical household mobility surveys. Although there
are concerns that the sample is not a perfect representative of the
population, SafeGraph reports that their sample correlates very highly with
true census populations [35]. SafeGraph finds a Pearson’s R Correlation
Coefficient of 0.966 and a Sum Absolute Bias of 24.77 between the real county
population and the number of devices in the county counted by SafeGraph.
SafeGraph finds little to no race-level sampling bias, educational attainment-
level sampling bias, and household income-level bias with Pearson’s R
Correlation Coefficients of 1, 0.999, and 0.997 and Sum Absolute Biases of
3.70, 3.43, and 1.75, respectively. The code to run independent sampling bias
analysis on SafeGraph data is provided by SafeGraph [36].

We found that the geographic coverage of the data was complete at the county
level with 100% coverage. There were no counties that were excluded from the
dataset as a result of few POIs or lower device counts (see the Appendix). As
part of SafeGraph’s Data for Academics, academic researchers have no-cost
access to SafeGraph data for non-commercial work. The reliance on commercial
data means that there are limited safeguards to the data, and changes to data
and data access may occur beyond our control. For example, SafeGraph recently
stopped updating the Social Distancing Metrics dataset. However, SafeGraph
provided ample notice, and the archived data is still available for academic
researchers, ensuring the reproducibility of this study. Furthermore, we have
made available $\Delta$TSPP on this project’s GitHub Repository (see the
Appendix).

Our results are only applicable to the United States. Application of the same
methodology to other countries is yet to be conducted. Finally, our PCA
components capture ≈59% of the movement patterns, and the rest 41% is
unexplained with our approach. Additional work is needed to cover a better
percentage of variation without significantly increasing the PCA space. Future
work will also focus on exploring the correlation between the PCs and
additional variables, including commute, weather, and policy guidelines. This
study provides a more comprehensive and data-driven approach to examining how
human mobility has changed in response to the pandemic.

##  5 Acknowledgments

We thank the Editor and the reviewer for their valuable feedback.

##  6 Author Contributions

  * •

Conceptualization: J.E., J-S.K., H.K., A.Z., and T.A.

  * •

Methodology: J.E., J-S.K., H.K., A.Z., and T.A.

  * •

Investigation: J.E., J-S.K., H.K., A.Z., and T.A.

  * •

Software and visualization: J.E.

  * •

Validation: J.E., J-S.K., H.K., A.Z., and T.A.

  * •

Formal analysis: J.E., J-S.K., H.K., A.Z., and T.A.

  * •

Data curation: J.E.

  * •

Writing–original draft preparation: J.E., J-S.K., H.K., A.Z., and T.A.

  * •

Writing–review and editing: J.E., J-S.K., H.K., A.Z., and T.A.

  * •

Supervision: H.K., A.Z. and T.A.

  * •

Project administration: T.A.

  * •

Funding acquisition: H.K., A.Z., and T.A.

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##  7 Appendix

###  7.1 Implementation and Source Code

In this study, we used the Python programming language for data collection and
analysis. The main Python packages used were Pandas, Matplotlib, Scikit-Learn,
and Pysal. Pandas along with Matplotlib allowed for data pre-processing as
well as visualization. Scikit-Learn was used for the truncated SVD and the
clustering techniques. Finally, Pysal was used for performing both the local
and global spatial autocorrelation analysis. All additional packages used in
this research and our implementation can be found in our GitHub repository at
https://github.com/GMU-GGS-NSF-ABM-Research/Mobility-Trends.

###  7.2 Data Set and Data Processing Details

We have made our derived data $\Delta TSPP$ for every county fully available
on the GitHub repository. The following list of counties are removed from our
analysis as outliers with a standard deviation of four or greater in the PCA
space: Grant County, AR, San Mateo County, CA, Santa Clara County, CA, Howard
County, MD, Somerset County, NJ, Fairfax County, VA, Loudoun County, VA.

###  7.3 Analysis Details

####  7.3.1 Principal Component Analysis

Figure 1 presents the amount of explained variation for each feature in the
Principal Component Analysis. We find that three features are sufficient for
explaining variation.

Fig 11: Explained variance for different numbers of latent features.

####  7.3.2 Clustering Analysis

For clustering, we compare between the K-means algorithm [26] and hierarchical
clustering algorithm [37]. The K-means algorithm partitions n observations
into k clusters by randomly initializing k points (means or cluster centroids)
and assigning each observation to their closest point. Cluster centroids are
updated and iteratively reassigned until convergence. In contrast, either
agglomerative or divisive hierarchical clustering does not require the number
of clusters to be specified. Based on the distance between features, a
hierarchy of clusters is built from a set of single observations to one single
cluster of all observations.

In the case of the k-means analysis, we choose a k of three to better
visualize the counties that belong to each of the latent features. In the case
of hierarchical clustering, we tested different distance functions, including
Euclidean, Manhattan, and Cosine distance. We additionally tested various
linkage types including complete link, average link, single link, and Ward’s
method.

We found no difference between the clustering of counties using either the
hierarchical clustering or the k-means analysis and thus we select k-means
analysis due to computational efficiency.

Fig 12: Geographic coverage of the data including (A) distribution of mean
device counts per county, (B) distribution of sum of device counts per county,
(C) distribution of standard deviation of device counts per county, and (D)
distribution of sum of POIs per county.

####  7.3.3 Analysis of Geographic Coverage of the Data

To provide more information about the SafeGraph data that our study is based
on we calculated descriptive statistics of device counts for each county per
day. There is an average of 5433.76, a max of 414085.93, a min of 8.47 devices
per U.S. county per day, Figure 12A shows the distribution of the mean number
of observed devices (average over the $365*2=730$ days used in our study)
across all 3100 counties included in our study. We observe that the majority
of counties have thousands of observations per day, with some outlier counties
only have tens of observations per days and other counties having hundreds of
thousands of observations per day. Figure 12A additionally shows the
distribution of standard deviation of device counts (over 730 days) of all
counties. To understand the spatial distribution of POIs among counties in the
SafeGraph Places dataset we used a spatial join to count the total number of
POIs in each county, as shown in Figure 12C. There is an average of 1788.84, a
max of 195232, a min of 3, and a standard deviation of 5941.88 POIs across
counties. We found that geographic coverage at the county level is 100% for
both device counts and POIs, meaning no counties were excluded due to lack of
data.