# Heterogeneous network approach to predict individuals’ mental health

Shikang Liu  Department of Computer Science and Engineering, University of
Notre Dame  Fatemeh Vahedian  Department of Computer Science and Engineering,
University of Notre Dame  David Hachen  Department of Sociology, University of
Notre Dame  Omar Lizardo  Department of Sociology, University of California,
Los Angeles  Christian Poellabauer  Department of Computer Science and
Engineering, University of Notre Dame  Aaron Striegel  Department of Computer
Science and Engineering, University of Notre Dame  Tijana Milenković
Department of Computer Science and Engineering, University of Notre Dame  Eck
Institute for Global Health, University of Notre Dame  Center for Network and
Data Science (CNDS), University of Notre Dame  Corresponding author (email:
<EMAIL_ADDRESS>
###### Abstract

Depression and anxiety are critical public health issues affecting millions of
people around the world. To identify individuals who are vulnerable to
depression and anxiety, predictive models have been built that typically
utilize data from one source. Unlike these traditional models, in this study,
we leverage a rich heterogeneous data set from the University of Notre Dame’s
NetHealth study that collected individuals’ (student participants’) social
interaction data via smartphones, health-related behavioral data via wearables
(Fitbit), and trait data from surveys. To integrate the different types of
information, we model the NetHealth data as a heterogeneous information
network (HIN). Then, we redefine the problem of predicting individuals’ mental
health conditions (depression or anxiety) in a novel manner, as applying to
our HIN a popular paradigm of a recommender system (RS), which is typically
used to predict the preference that a person would give to an item (e.g., a
movie or book). In our case, the items are the individuals’ different mental
health states. We evaluate four state-of-the-art RS approaches. Also, we model
the prediction of individuals’ mental health as another problem type - that of
node classification (NC) in our HIN, evaluating in the process four node
features under logistic regression as a proof-of-concept classifier. We find
that our RS and NC network methods produce more accurate predictions than a
logistic regression model using the same NetHealth data in the traditional
_non-network_ fashion as well as a random-approach. Also, we find that the
best of the considered RS approaches outperforms all considered NC approaches.
This is the first study to integrate smartphone, wearable sensor, and survey
data in an HIN manner and use RS or NC on the HIN to predict individuals’
mental health conditions.

##  1 Introduction

Mental disorders such as depression and anxiety have been recognized as
critical public health issues. Mental disorders are one of the leading causes
of both injury and disability for people around the world [78, 11]. According
to the World Health Organization (WHO), in 2015, 322 million people were
living with depression (4.4% of the global population) and 264 million people
were living with anxiety (3.6% of the global population) [50]. Moreover,
depression and anxiety are major contributors to suicides [50]. Although early
interventions significantly reduce the risk of developing mental disorders,
about two-thirds of people do not seek appropriate treatments due to a lack of
awareness of their mental illness [6, 1]. One way to overcome this issue is to
develop predictive models to enable individuals to recognize their risks of
mental disorders. Fortunately, smartphones, wearable sensors, and online
social media provide a wealth of data relevant to individuals’ mental health
[22, 61, 14]. Using such data, health care providers could alert people who
are at risk for depression and anxiety to get timely treatment.

In terms of developing models to predict mental health, existing studies can
be categorized into three different groups according to the types of data that
they use [46, 22]: 1) one group of studies rely on smartphone usage data [9,
54, 2], such as incoming and outgoing call frequency and duration; 2) another
group of studies use wearable sensor data, such as physical activity, skin
conductance, and heart rate [77, 52, 26]; and 3) the remaining group of
studies use social media behavioral data, such as text or image content on
social media platforms [81, 14, 1].

However, existing studies have several limitations. First, among group 1 and
group 2 studies, most are conducted on a limited number of individuals (fewer
than 50) and a limited time period (less than one month) [46] except for one
that collects smartphone data from 111 individuals for seven months [9].
Critically, the small number of individuals may not be representative of a
larger population and thus the obtained results might not be generalizable. In
addition, data collected from a short time period may be affected by special
events such as holidays and thus the obtained results might not be reliable.
Group 3 studies do not suffer from a limited number of individuals or a short
time period because data is collected online, but the prediction performance
of their models may be affected by low data quality resulting from fake
accounts and noise in text and image contents [22, 81]. Second, all of the
existing studies focused on a single type of data except for two [61, 9].
Models using a single type of data are often less accurate than models
integrating multiple types of data [9, 61]. For example, it was shown that
combining different types of data including information on individuals’
personality traits, weather conditions, and smartphone data yields more
accurate performance in predicting individuals’ stress levels than individual
data types [9]. Third, among the existing studies, only three [80, 40, 42]
have utilized a network approach to model and analyze data by capturing
relationships between entities. Clearly, there is a shortage of network-based
methods that could utilize relations between entities to make mental health
predictions [81]. Developing new approaches of this type is essential because
networks are powerful models of complex real-world systems, including social
networks, and because social networks play an important role in individuals’
mental health conditions [60, 68, 62, 44]. Moreover, networks allow for data
integration in an elegant way and can be used to make predictions about
individuals’ health-related traits [31, 84]. For instance, a network approach
was used to model multiple types of clinical data of patients in order to
diagnose diseases [31].

To address the limitations of the existing studies, we propose the following
contributions.

We leverage a rich data set from the NetHealth study to predict individuals’
mental health conditions. The NetHealth study collected smartphone data,
wearable sensor (Fitbit) data, and individuals’ trait data from surveys from
approximately 700 undergraduate student participants at the University of
Notre Dame during 2015 to 2019 [41, 55, 18]. The NetHealth data is more
representative of a large population since it contains a larger number of
individuals (student participants) than previous studies. In addition, the
NetHealth data covers a longer time period than the data from the existing
studies and thus may be more reliable. Moreover, the NetHealth study contains
multiple types of data for the same set of individuals, which allows us to
have a more comprehensive and thus hopefully more accurate understanding of
the individuals’ mental health conditions compared to the existing studies
that only focused on a single type of data.

In this study, we aim to predict individuals’ mental health conditions by
integrating multiple types of data including individuals’ social interactions,
i.e., their SMS communications collected from smartphones, health-related
behaviors collected via Fitbits, and individuals’ traits (e.g., personalities)
collected from surveys (Figure 1). We divide these data collected from the
three sources (smartphones, Fitbits, and surveys) into five dimensions:
individuals’ social interactions (i.e., SMS communications), personality
traits, social status, physical health, and well-being, with each of the last
four dimensions consisting of several components (Figure 1). To predict
individuals’ mental health conditions, we first divide individuals into
training and testing sets. In the prediction task, we leverage all
individuals’ information as shown in the left box of Figure 1 as well as the
training individuals’ mental health conditions to train a predictive model.
Then we use the trained model to predict the testing individuals’ mental
health conditions.

To integrate the different types of information, we model the NetHealth data
as a heterogeneous information network (HIN), which is an effective tool to
fuse information by considering multiple types of nodes and edges [65]. As a
promising paradigm, HIN analysis has been applied to a variety of
computational and applied tasks, such as recommendation systems in predicting
movie ratings [63], node classification in predicting authors or venues in
academic networks [16], clustering in visualization tasks [79, 73], link
prediction in inferring future co-authorships [83], and network alignment in
predicting protein function from biological data [27]. In our study, we apply
HIN analysis to the task of mental health prediction. Figures 2 and 3 show the
network schema and visualization of our HIN, respectively. Our constructed HIN
consists of six node types (individual, personality traits, social status,
physical health, well-being, and mental health). For the individual node type,
different nodes correspond to different student participants of the NetHealth
study. For each of the other five node types (personality traits, social
status, etc.), different nodes correspond to different personal
characteristics of the given type, i.e., different values of the components
listed under the given dimension in Figure 1. For example, a node of the
personality traits type represents some combination of an individual’s
agreeableness, conscientiousness, extroversion, neuroticism, and openness. As
an illustration, one combination, i.e., a node of the personality traits type,
may be low agreeableness - low conscientiousness - low extroversion - low
neuroticism - low openness, and another combination, i.e., another node of the
personality traits type, may be high agreeableness - high conscientiousness -
high extroversion - high neuroticism - high openness. See Section 2.1 for
details. Clearly, there are multiple nodes of each type because there are
multiple possible combinations of personal characteristics of the given type,
and each combination corresponds to one node of that type. We connect the
nodes of the network by forming six edge types. We construct the individual -
individual edge type by connecting two individuals if they communicate through
SMS at least once during our study period. We construct edges of the other
five types by connecting the individual node type to each of the other five
node types if the given individual has the given combination of personal
characteristics of the given type. See Section 2.1 for details.

We construct the HIN in this way in order to be able to predict an
individual’s mental health state (likelihood of being depressed or anxious) by
relying on the information about: 1) the individual’s combinations of the four
traits (personality traits, social status, physical health, and well-being),
2) the individual’s position in their social network (i.e., which other
individuals they are linked to), 3) combinations of the four traits of the
individual’s (direct or indirect) network neighbors, and 4) mental health
states of the individual’s (direct or indirect) network neighbors. For
example, we argue that if an individual is linked (directly or indirectly) to
many other individuals with whom she/he shares many combinations of the four
traits, and if these individuals are depressed or anxious, then the individual
in question is also likely to be depressed or anxious. So, our HIN offers an
elegant and convenient yet important way to model influence between
individuals.

More specifically, we have recognized that we can model the problem of mental
health prediction from our HIN in a novel manner, as applying to the HIN a
popular paradigm of a recommender system (RS). RS is widely used to suggest a
personalized list of items (e.g., movies, books, or new friends) to
individuals based on their preferences to help them find the most relevant
items [58]. In other words, for an individual $i$, based on the history of
$i$’s behaviors (e.g., rating movies, liking contents on social media, or
friendships with other individuals), an RS approach calculates a personalized
ranking score on a set of new items (i.e., movies, contents, or friends,
respectively) and suggests the top-ranked items to $i$. [58, 74]. In our case,
items are the individuals’ different mental health states, i.e., we predict
what mental health state an individual is likely to have.

Unlike their homogeneous counterparts that consider a single type of
individual-item interaction (i.e., edge), HIN-based RS approaches take
advantage of multiple node and edge types [63]. Multiple types of HIN-based RS
approaches exist. One major approach category is based on matrix
factorization. For example, DEDICOM, one of the earliest such approaches, is
able to capture correlations between different types of nodes through matrix
factorization. Such correlations are captured by including multiple edge types
into the learning task at hand [4]. RESCAL can be considered as a
mathematically relaxed version of DEDICOM and was shown to perform better in
recommendation tasks [48]. DMF further used novel objective functions compared
to DEDICOM and RESCAL to learn latent feature parameters, which led to
additional improvement of the prediction performance in recommendation tasks
[17]. Another major approach category incorporates into the recommendation
process the notion of a metapath, which follows a specific sequence of
multiple types of nodes and edges of a HIN to capture additional HIN
information for recommendation. For example, HeteRec learns metapath-based
latent features (representations or embeddings) of nodes (individuals and
items) through a Bayesian ranking optimization technique [82]. Similarly,
HERec learns node features through metapath-based random walks, but those are
then transformed by fused functions and integrated into a matrix factorization
framework with the goal of deriving more informative node features for
recommendation [63]. Unlike the above methods that cannot deal with weighted
graphs (i.e., edges), SemRec aimed to account for edge weights, and it did so
via weighted metapaths in RS to generate better recommendations [66].
Different from the many traditional RS methods that are based on matrix
factorization, MCRec used a deep neural network with a co-attention mechanism
to leverage the metapath-based context for recommendation [32]. Unlike the
above methods that did not consider social (i.e., individual-individual)
interaction data, DSR accounted for edges between individuals and used an
extended social similarity regularization, which imposed constraints on both
similar and dissimilar nodes in its RS framework [34]. Similarly, SimMF
integrated both social interactions and attribution information of individuals
and items to make recommendations; it did so via metapath similarity measures
[64].

Of all HIN-based RS methods mentioned above, we apply four prominent or recent
ones, namely DMF [17], HERec [63], RESCAL [48], and DEDICOM [4], to the HIN to
predict edges between nodes of the individual type and nodes of the mental
health type, denoted as target edges in our HIN (Figure 2).

In addition, to evaluate the power of RS, we model the problem of mental
health prediction in an alternative manner, as node classification (NC) in our
HIN. NC predicts labels of nodes based on their features that characterize
positions of nodes in a network [8]. In our case, node labels are individuals’
different mental health states. In our study, we extract four prominent
features of individuals from our HIN: graphlets [45], colored graphlets [27],
DeepWalk [51], and Metapath2vec++ [16]. Then, we put network features into a
logistic regression classifier to make predictions, which is a common approach
in NC [24]. Note that we choose these four features for the following reasons.
The first two are based on homogeneous and heterogeneous graphlets,
respectively, where graphlets are small subgraphs, i.e., Lego-like building
blocks, of complex networks [45, 27]. The graphlet-based features, which
intuitively capture how many subgraphs of each type a node participates in,
were extensively demonstrated to be powerful measures of the network position
of a node in numerous tasks [47]. The last two are prominent homogeneous and
heterogeneous network embedding methods, respectively. Network embedding has
received significant attention in the last several years, owing to of its
ability to _automatically_ learn low-dimensional latent node features that
likely preserve the original high-dimensional network structure [51, 16, 83,
67].

To evaluate the prediction performance of the four RS and four NC network
methods, we compare them against a logistic regression classifier using the
same NetHealth data in a non-network fashion [46], and against a random guess
method [21]. To our knowledge, this is the first study to use smartphone,
wearable sensor, and survey data in an HIN model and use RS or NC on the HIN
to predict individuals’ mental health conditions.

Our findings are as follows.

  * •

For both depression and anxiety prediction, among all network methods, DMF (an
RS method) makes the most accurate predictions. Compared to the random guess
method, for both depression and anxiety, all RS and NC methods except for
RESCAL and DEDICOM are significantly more accurate. Compared to the non-
network method, for depression, DMF and DeepWalk are significantly more
accurate, graphlets, colored graphlets, and Metapath2vec++ are marginally more
accurate, HERec is comparable, and RESCAL and DEDICOM are significantly less
accurate; and for anxiety, DMF is significantly more accurate, DeepWalk is
marginally more accurate, HERec, graphlets, colored graphlets, and
Metapath2vec++ are marginally less accurate, and RESCAL and DEDICOM are
significantly less accurate. Our results indicate that (at the minimum) the
best of the network methods outperforms the random guess method and the non-
network method. In addition, the best RS method outperforms all NC methods.
This confirms the power of networks and RS in particular in predicting mental
health.

  * •

We explore whether the different types of methods (RS, NC, non-network)
identify different sets of depressed/anxious individuals. If this is true, we
might be able to make more accurate predictions by combining the different
method types. Specifically, we study overlaps between depressed/anxious
individuals correctly predicted by three representative methods: the most
accurate RS method (DMF), the most accurate NC method (DeepWalk), and the non-
network method. For depression, we find that DMF’s and DeepWalk’s predictions
significantly overlap. Additionally, DeepWalk’s and the non-network method’s
predictions also significantly overlap. But DMF’s and the non-network method’s
predictions do not significantly overlap. For anxiety prediction, we observe
similar results. The reasons for these observations could be: 1) DMF and
DeepWalk are both network methods and differ only in one aspect - they are
different types of methods (RS versus NC); 2) DeepWalk and the non-network
method both use the logistic regression to make predictions and differ only in
one aspect - DeepWalk uses network features while the non-network method does
not; and 3) DMF differs from the non-network method in two ways: the former is
a network method and it does not use logistic regression to make predictions,
while the latter is a non-network method that uses logistic regression. In
other words, it could be that the more similar the two approaches are in terms
of their methodologies, the more similar their predictions. Our results
suggest that because of the non-significant overlap between DMF’s and the non-
network method’s predictions, by combining the two methods, we might be able
to make more accurate predictions. Exploring this is beyond the scope of this
paper and is the subject of our future work.

  * •

In our prediction approaches mentioned above, we have integrated all types of
information about individuals, represented by the different edge types in the
HIN, into our (RS and NC) network methods to make mental health predictions.
To study whether some edge types might be more informative (i.e., have more
predictive power) than others, we investigate the effect of using all possible
combinations of edge types (including all edge types) on the prediction
performance. For this analysis, we focus only on DMF as the most accurate of
all analyzed methods in the above evaluations. We consider a series of DMF
instances that correspond to all possible combinations of all five non-target
edge types from our HIN (the target edge type needs to be always included by
default). For example, on the one extreme, we consider each of the five non-
target edge types alone, and on the other extreme, we consider all five non-
target edge types combined (which has been the case in the above evaluations).
An example of an edge type combination in-between these two extremes is the
combination of the individual - individual, individual - physical health, and
individual - personality traits edge types. We find that for depression, the
combination of the individual - physical health and individual - well-being
edge types is significantly more accurate than the rest of the combinations,
including the combination of all edge types. For anxiety, the combination of
the individual - personality traits and individual - well-being edge types is
marginally more accurate than six other edge type combinations, including the
combination of all edge types, and is significantly more accurate than the
rest of the combinations. Our results indicate that we can make more accurate
predictions using some subset of edge types than using all edge types.
Exploring the reasons behind this observation is beyond the scope of this
paper and is the subject of our future work.

Figure 1: The summary of our data and the goal of our study. Figure 2: Network
schema of the HIN that we construct from the NetHealth data. Circles denote
our six node types. Connections between circles denote our six edge types. The
red line indicates the target (individual - mental health) edge type that we
try to predict. Figure 3: Network visualization of the HIN constructed from
the NetHealth data. Node colors represent the six node types from the network
schema in Figure 2. The table below the visualization summarizes the number of
nodes or edges of each type and the total number of nodes or edges across all
types. For detailed explanation behind the numbers of nodes and edges of the
given type, see Section 2.1.

##  2 Methods

###  2.1 HIN construction

Specific data used in this paper. The data used in this paper come from the
NetHealth study, an institutional review board-approved effort that collected
smartphone, Fitbit, and survey data from approximately 700 undergraduate
student volunteers at the University of Notre Dame, who entered the study as
freshmen in August 2015 [55, 18]. Smartphone data was collected via a
monitoring application (CIMON) installed on individuals’ (student
participants’) smartphones that periodically synchronizes SMS logs [30].
Notably, we did not collect information about the content of the messages.
Instead, we collected information on who communicates with whom and when.
Health behavioral data was collected through Fitbit Charge HR devices. In this
study, we consider two specific Fitbit metrics, individuals’ step counts and
their sleep duration. We conducted periodic surveys that asked questions about
individuals’ demographics, personality traits, mental health, and other
subjects. From surveys, we extract 15 characteristics that can be divided into
five categories: 1) personality traits: agreeableness, conscientiousness,
extraversion, neuroticism, and openness, as measured by the Big-Five
personality test [23]; 2) social status: gender, race, religion, and parents’
educations; 3) physical health: sleep quality measured by the Pittsburgh Sleep
Quality Index (PSQI) [10]; 4) well-being: body image, happiness, health,
loneliness [12], and self-esteem [59]; and 5) mental health: depression
measured by the Center for Epidemiological Studies Depression Scale (CES-D)
test [38] and anxiety measured by the State-Trait Anxiety Inventory (STAI)
test [70].

Selection of the study time period and pool of individuals. In this paper, we
select one year from August 2015 to August 2016 as the study period since our
previous study showed that the majority of individuals are actively involved
in the NetHealth study during this period but not during other periods [41].
This period covers 52 weeks, of which 31 are school weeks and 21 are break
weeks. In this study, we focus only on school weeks because our previous study
showed that school weeks have meaningful social network structures, while
break weeks do not [41]. The NetHealth data contain SMS logs of 615 iPhone
users and 96 Android users. In this study, we only consider iPhone data since
we encountered problems with Android data consistency. Finally, we keep only
SMS data where both the sender and receiver are among the 615 iPhone users,
i.e., the participants of our study. In other words, we discard SMS data where
the sender or receiver is not a participant of the NetHealth study (e.g., is a
participant’s family member or friend).

We use the following three criteria established in our previous study [41] to
select individuals who have high-quality data:

  1. 1.

Students’ first SMS activity date was before or on the start date of our
considered study period and their last SMS activity was on or after the end
date of our considered study period, i.e., students actively sent or received
SMSs during the one-year study period.

  2. 2.

Students have high-quality Fitbit data, i.e., their Fitbit data are valid. By
“valid”, we mean that a student wore the Fitbit at least 80 percent of the
time in more than half of the days during the one-year study period.

  3. 3.

Students completed the survey taken in July 2015, which was conducted before
students entered the school, and the survey taken in January 2016, which was
conducted during our study period. The reasons why we need both surveys are
discussed below.

274 out of the 615 individuals satisfy the three criteria and thus form the
final pool of individuals considered in this study.

The HIN. One of the key contributions of this study is to establish an HIN
using the NetHealth data. An HIN is a network consisting of multiple types of
nodes and edges [73]. In this study, we construct an HIN consisting of six
node types and six edge types (listed below). Formally, the HIN can be
represented as $G=(V,E)$, where $V=\bigcup_{i}V_{i}$, $i\in\\{1,2,3,4,5,6\\}$,
i.e., $V$ is the union of all nodes over all six node types, and
$E=\bigcup_{j}E_{j}i$, $j\in\\{1,2,3,4,5,6\\}$ i.e., $E$ is the union of all
edges over all six edge types.

The node types include individual, personality traits, physical health, social
status, well-being, and mental health, as follows (also, see Figures 2 and 3).

  * •

The individual node type represents students who participate in the NetHealth
study. There are 274 nodes of the individual node type.

  * •

The personality traits node type represents a combination of five personality
characteristics including agreeableness, conscientiousness, extroversion,
neuroticism, and openness, extracted from the survey taken in January 2016. We
use data from this survey because it is the only one conducted during our
study period. The distributions of personality characteristics scores are
shown in Supplementary Figure S1. We combine these five characteristics
because they belong to the same type of the individuals’ information, as also
suggested by domain experts who have conducted the NetHealth study. The
individuals’ personality characteristics scores vary from person to person.
For example, the individuals’ agreeableness scores could be 2.1, 2.2, 3.4,
4.2, 4.8, etc. Combining such absolute score values across the different
personality characteristics and over all individuals would generate a huge
number of possible combinations. To address this in an elegant way, for each
personality characteristic, we divide the individuals, i.e., their scores,
into three groups, as is typically done [61]: the high-score group (the top 25
percent of the scores), the medium-score group (the middle 50 percent of the
scores), and the low-score group (the lowest 25 percent of the scores). Then,
we form nodes of the personality traits type by combining the group labels of
the five personality characteristics. For example, a node of the personality
traits type may be low agreeableness - medium conscientiousness - medium
extroversion - medium neuroticism - high openness. The number of all possible
combinations of the five personality characteristics is $3^{5}=243$. Note that
some possible combinations are not present in the NetHealth data. So, the
number of combinations that correspond to scores of at least one individual in
our data, i.e., the number of nodes of the personality traits type, is $114$.

  * •

The social status node type represents a combination of four social status
characteristics including gender, race, religion, and parents’ education,
extracted from the survey taken in July 2015. We use social status data from
this survey because it is the only one containing the individuals’ social
status information. (This is the reason why we need both surveys in the third
criterion when choosing which pool of individuals to consider.) The
distributions of the 274 individuals’ social status scores are shown in
Supplementary Figure S2. For example, a node of the social status type may be
female - white - Catholic - both parents received bachelor’s degrees. Given
two possible genders, five possible races, four possible religions, and three
possible options for parents’ education, the number of all possible
combinations of the four social status characteristics is $2\times 5\times
4\times 3=120$. The number of combinations that correspond to scores of at
least one individual in our data, i.e., the number of nodes of the social
status type, is $55$.

  * •

The physical health node type represents a combination of three physical
health characteristics including sleep quality, average sleep duration, and
average step counts. We obtain the individuals’ sleep quality scores from the
survey taken in January 2016 and their average sleep duration and average step
counts during the study period from the Fitbit data. The distributions of the
scores are shown in Supplementary Figure S3. To combine sleep quality, average
sleep duration, and average step counts, we divide scores of each physical
health characteristic into three groups: the high-score group (the top 25
percent of the scores), the medium-score group (the middle 50 percent of the
scores), and the low-score group (the lowest 25 percent of the scores). Then,
we form nodes of the physical health type by combining the group labels of the
three physical health characteristics. For example, a node of the physical
health type may be low sleep quality - medium average sleep duration - high
step counts. The number of all possible combinations of the three physical
health characteristics is $3^{3}=27$. The number of combinations that
correspond to scores of at least one individual in our data, i.e., the number
of nodes of the physical health type, is $27$.

  * •

The well-being node type represents a combination of five well-being
characteristics including body image, happiness, health, loneliness, and self-
esteem, extracted from the survey taken in January 2016. The distributions of
the scores are shown in Supplementary Figure S4. To combine the five well-
being characteristics, we divide scores of each characteristic into three
groups: the high-score group (the top 25 percent of the scores), the medium-
score group (the middle 50 percent of the scores), and the low-score group
(the lowest 25 percent of the scores). Then, we form nodes of the well-being
type by combining the group labels of the five well-being characteristics. For
example, a node of the well-being type may be low body image - medium
happiness - medium health - medium loneliness - high self-esteem. The number
of all possible combinations of the five well-being characteristics is
$3^{5}=243$. The number of combinations that correspond to scores of at least
one individual in our data, i.e., the number of nodes of the well-being type,
is $87$.

  * •

The mental health node type represents a mental health condition: either
depression or anxiety. (Technically, we analyze each of depression and anxiety
via its respective HIN.) For depression, we use one node to denote having
“depressed” condition, and another node to denote having “non-depressed”
condition. Similarly, for anxiety, we use one node to denote having “anxious”
condition, and another node to denote having “non-anxious” condition. The
individuals’ depression and anxiety scores are collected from the survey taken
in January 2016. We consider individuals whose depression scores are above 15
as depressed, which is suggested in the literature [36, 33, 60]. Out of the
274 individuals, 67 individuals (24.5%) are depressed according to this
criterion. We consider individuals whose anxiety scores are above 40 as
anxious, which is suggested in the literature [25, 35, 13]. Out of the 274
individuals, 106 individuals (38.7%) are anxious according to this criterion.

The six edge types in our HIN include individual - individual, individual -
personality traits, individual - social status, individual - physical health,
individual - well-being, and individual - mental health, as follows (also, see
Figures 2 and 3).

  * •

The individual - individual edge type is constructed by connecting two
individuals if they have communicated through SMS at least once within our
study period. This results in 1354 edges between our 274 individuals. We
assign a weight to each edge, corresponding to the total number of SMSs
exchanged between two given individuals within the study period.

  * •

The remaining five edge types are constructed by connecting the individual
node type to the other five node types (personality traits, physical health,
social status, well-being, and mental health). Here, an edge is formed if the
given individual has the given combination of personal characteristics of the
given type. For example, if an individual has low agreeableness - low
conscientiousness - low extroversion- low neuroticism - low openness, we
connect the individual to the node of the personality traits type representing
such combination. In our data, an individual can only have one combination of
personal characteristics of a given node type (e.g., for the personality
traits node type, if an individual is linked to a node corresponding to low
agreeableness - low conscientiousness - low extroversion - low neuroticism -
low openness, he/she cannot be linked to a node corresponding to high
agreeableness - high conscientiousness - high extroversion - high neuroticism
- high openness or to any other combination). Therefore, an individual is
connected to exactly one node of each of the five node types. Thus, for each
of the five edge types, the number of edges is the same as the number of the
individuals, i.e., 274. The individual - mental health edge type is considered
as the target edge type since this is what we try to predict.

###  2.2 Network methods that we adapt to the task of predicting mental health
conditions

We model the problem of predicting individuals’ mental health conditions as RS
and NC.

RS methods. RS is widely used to suggest a personalized list of items (e.g.,
movies, books, or new friends) to individuals based on their preferences, in
order to help them find the most relevant items [58]. In this study, we use
four RS methods: DMF [17], RESCAL [48], DEDICOM [4], and HERec [63].

The first three methods are of the multi-relational matrix factorization
(MRMF) type [37]. In MRMF, the target edge type is to be predicted and the
remaining types of edges as used as side information. For example, if the task
is to recommend movies to individuals, the individual - movie edge type is
used as the target edge type and other types of edges such as movie - genre,
movie - actor, etc. are used as side information. An MRMF model is trained
using a proportion of target edges as well as side information, and then the
model is used to predict the rest of the target edges. MRMF computes latent
features of all types of nodes, which are used to map individuals to items
(the edge type to be predicted) that the individuals will prefer. However,
instead of using only one edge type, as in standard factorization schemes
[29], MRMF allows for the creation of additional latent features based on
other side information (other edge types). By operating on latent features
between a pair of nodes, we can obtain a value denoting the probability that
the given node pair has an edge. MRMF optimizes the loss function to minimize
the difference between probability values of all node pairs (represented by a
matrix) and the adjacency matrix representing real edges. The three MRMF
methods that we consider use different loss functions (that is, they differ in
how they mathematically define the difference between probability values of
all node pairs and the adjacency matrix) and different optimization methods
(that is, they differ in how they minimize their respective loss functions)
[75, 76]. We use all three MRMF-based RS approaches to predict target edges
(i.e., edges of the individual - mental health type). For more details on the
three MRMF RS methods, see Supplementary Section S1.

As a different approach type, HERec works as follows. First, it learns latent
features of nodes from the HIN through metapath-based random walks. For this
step, to mimic as closely as possible the case studies in the HERec paper
[63], i.e., to give HERec the best-case advantage, we consider all possible
metapath types from the individual node type to the individual node type via
each of the other five considered node types. That is, we consider the
following five types of metapaths: individual - well-being - individual,
individual - personality traits - individual, individual - social status -
individual, individual - physical health - individual, and individual - mental
health - individual. Second, to derive more effective (i.e., better-informed)
node representations, HERec uses fused functions to transform the latent node
features from the the previous step into a more suitable form for
recommendations. For this second step, we consider the personalized non-linear
fusion function, which was shown to yield the best performance in the
recommendation task among three functions considered in the HERec paper [63].
Third, HERec blends the transformed features into a matrix factorization
framework to predict rating scores of individuals. For this step, we model the
problem of rating prediction as the task of predicting individual - mental
health links (i.e., target edges). Namely, we use HERec to predict rating
scores of all individuals, sort the predicted scores from highest to lowest,
and select a cutoff where individuals with scores above the cutoff will be
predicted as depressed (anxious) and those with scores below the cutoff as
non-depressed (non-anxious). Note that HERec has the node feature dimension as
input parameter. The method uses the default value of 30 for this parameter.
To give HERec the best-case advantage, we evaluated additional values of this
parameter, namely 10 and 20, i.e., lower-dimensional features than used in the
HERec paper, because our data has fewer nodes than the data from the HERec
study. However, we found that reducing the dimension decreased HERec’s
perfrmance. So, we ended up reporting results for the default setting, as this
option yielded the best accuracy.

When we predict target edges of the individual \- mental health type using the
four RS methods discussed above, we randomly divide the individuals into 80%
training individuals and 20% testing individuals. This step is conducted using
stratified sampling to ensure that the split data maintain the percentage of
the individuals who are depressed (or anxious). We use target edges of
training individuals as well as the other types of edges to train an RS model,
and then use the model to predict target edges of testing individuals. In
other words, we hide a proportion of target edges and use the remaining edges
to train the model, and then use the model to predict the hidden target edges.
Formally, given the HIN $G=(V,E)$, let $I\in V$ and $M\in V$ denote the sets
of all individuals and all mental health conditions, respectively. Then, the
goal is to predict {$i_{test}$–$m$}, i.e., the target edges of the testing
individuals, where $i_{test}\in I$ and $m\in M$. To predict an individual as
depressed or non-depressed, we calculate probability values of the two target
edges that connect the individual to the node representing “depressed”
condition and the node representing “non-depressed” condition, respectively.
We predict an individual as anxious or non-anxious in the same manner. Of the
two target edges, we select the one with the higher probability value as the
final prediction.

NC methods. We model the problem of mental health prediction in an alternative
manner, as NC that uses the structural information encoded in the network to
predict nodes’ labels. For example, in a social network consisting of
individuals with known labels being smoker or non-smoker and individuals with
unknown labels, the NC method predicts the latter as smokers or non-smokers
based on their network features, i.e., their network “relationships” with the
former [8]. Network features characterize properties of nodes in a network,
such as nodes’ network positions and their neighborhood information. In order
to make mental health predictions using NC methods, our first step is to
extract the individuals’ network features from our constructed HIN. We learn
the individuals’ network features based on all edge types except for the
target edge type. Instead, we use the target edge type to label the
individuals according to their mental health states, for the purpose of NC
training and testing (see below). For example, if an individual connects to a
node representing the “depressed” condition, we assign a “depressed” label to
the individual. We extract four features for the individuals: graphlets [45],
colored graphlets [27], DeepWalk [51], and Metapath2vec++ [16]. Among these
four, graphlets and DeepWalk learn features of nodes from a homogeneous
network containing a single node type and a single edge type; in other words,
when applied to our HIN, they ignore the different node and edge types and
consider the network as homogeneous. Colored graphlets and Metapath2vec++
learn features of nodes from a heterogeneous network consisting of multiple
types of nodes and edges. We use the two homogeneous network methods because
1) these methods are widely used to extract features of nodes from a network
and 2) there is a limited number of methods that extract nodes’ features from
a heterogeneous network. In more detail, graphlets are small connected non-
isomorphic induced subgraphs of a network [45]. Based on the notion of
graphlets, the graphlet degree vector (GDV) is a network feature that
summarizes a node’s extended network neighborhood. In this study, we use both
homogeneous graphlets [45] and heterogeneous graphlets [27] to calculate
nodes’ GDVs. The DeepWalk method [51] uses random walks to generate node
sequences in a homogeneous network. The node sequences are put into a skip-
gram language model to learn network features. The Metapath2vec++ method [16]
formalizes metapath-based random walks which are restricted to only
transitions between certain types of nodes. Then, Metapath2vec++ leverages a
heterogeneous skip-gram model to learn nodes’ features vectors from the
metapath-based random walks. For more details on the four NC methods, see
Supplementary Section S1.

In NC, we use the same training and testing individuals that we have used in
RS in order to compare the different types of network methods in an unbiased
way. After learning the individuals’ network features, the second step in NC
is to train a classifier (e.g., logistic regression, random forest, or support
vector machine) based on training individuals’ network features and node
labels and make predictions on testing individuals’ node labels. Node labels
in NC and target edges in RS are conceptually equivalent. We model target
edges as node labels in NC and this is why we do not include target edges when
learning network features of individuals. In this study, we use logistic
regression as a proof-of-concept classifier, because this particular
classifier is often used to predict individuals’ mental health conditions [46,
39, 56]. The output of a logistic regression classifier is a set of
probability scores, one score per individual. For each logistic regression
classifier used in this study (one classifier per network feature), we choose
a probability cutoff where individuals with probability scores above the
cutoff value will be classified as depressed/anxious, and those with
probability scores below the cutoff value will be classified as non-
depressed/non-anxious. For each logistic regression classifier used in this
study, we choose a cutoff value such that the proportion of the individuals
who are predicted as depressed/anxious is equal to the proportion of the
individuals who are actually depressed/anxious, as is typically done [20].

RS and NC are mathematically different since they work in different ways as
discussed above. But ultimately, their inputs and outputs are the same, which
makes them directly comparable.

Comparison of RS and NC with a non-network method and a random guess method.
To investigate the effectiveness of the RC and NC network methods, we compare
the network methods to each other as well as to a non-network method [46] and
a random guess method [21]. For the non-network method and the random guess
method, we use the same training and testing individuals that we have used in
RS and NC.

We implement the non-network method as follows, making it as fairly comparable
to our RS and NC network methods as possible. The non-network method is also a
logistic regression classifier that utilizes the same NetHealth data as our
network methods do but in a non-network fashion. Specifically, the non-network
method uses the 15 characteristics collected from the surveys (Section 2.1),
average step counts and average sleep duration collected from Fitbits, and
numbers of SMS messages sent or received during the study period collected
from smartphones. For each of these data types, we divide individuals into
three groups: the high-score group, the medium-score group, and the low-score
group, which is the same approach that we have used when forming nodes of our
HIN (Section 2.1). We do this to ensure that the step of dividing individuals
to groups is consistent and is thus not a factor that can account for
differences in the results.

The random guess method works as follows. For example, in the depression
prediction task, suppose that $x\%$ of the individuals are depressed and
$(1-x)\%$ of the individuals are non-depressed. To make predictions, the
random guess method randomly chooses $x\%$ of all individuals and predicts
them as depressed, and it predicts the remaining individuals as non-depressed.

###  2.3 Evaluation methodology

We use 5-fold cross-validation to evaluate the performance of the four RS and
four NC methods, the non-network method, and the random guess method. We
divide all individuals into five equal-sized subsets, such that each subset
contains the same proportion of depressed/anxious individuals as present in
the considered pool of individuals. We use one of the subsets as the testing
set and the union of the other four subsets as the training set. We repeat
this process five times until every subset has served as the testing set. We
calculate the average and standard deviation of evaluation measures (defined
below) over the five runs. Moreover, we make a prediction about an individual
when the individual is part of the testing set. This way, we are able to
predict mental health conditions for all individuals through the cross-
validation process.

Given a prediction for an individual, there are four outcomes [19]. Taking
depression as an example, a true positive (TP) represents an individual who is
depressed and is also predicted as depressed. A false negative (FN) represents
an individual who is depressed but is predicted as non-depressed. A true
negative (TN) represents an individual who is non-depressed and is also
predicted as non-depressed. A false positive (FP) represents an individual who
is non-depressed but is predicted as depressed.

In our study, we consider the following four evaluation measures:

  1. 1.

$Precision={TP\over(TP+FP)}$: of all predictions, how many are correctly
predicted as depressed.

  2. 2.

$Recall={TP\over(TP+FN)}$: of all depressed people, how many are correctly
predicted as depressed.

  3. 3.

$F1\,score={2TP\over(2TP+FP+FN)}$: the harmonic mean of precision and recall.

  4. 4.

$Accuracy={(TP+TN)\over(TP+TN+FP+FN)}$: of all predictions, how many are
correctly predicted (as either depressed or non-depressed).

To statistically compare the performance of the different methods when
predicting the individuals’ mental health conditions, we use the Wilcoxon
signed-rank test, which is a non-parametric test used to compare paired
samples to assess whether their distributions differ [57]. Since for each
method we compare its prediction performance against the rest of the methods
that we evaluate, we adjust p-values via false discovery rate (FDR) estimation
to account for multiple test correction [49]. In this study, we use the
adjusted p-value threshold of 0.05.

We explore whether the most accurate RS method (DMF), the most accurate NC
method (DeepWalk), and the non-network method identify different sets of
individuals as depressed/anxious. If this is true, we might be able to make
more accurate predictions by combining the different method types. For each
pair of the three methods, we examine whether sets of depressed/anxious
individuals correctly predicted by the two methods are significantly
overlapping through a hypergeometric test. Suppose that $S$ is the set of all
depressed individuals, $A$ is the set of depressed individuals correctly
predicted by one of the two methods, $B$ is the set of depressed individuals
correctly predicted by the other method, and $O$ is the overlap between $A$
and $B$. Then, the $p$-value (i.e., the probability of obtaining the overlap
of size —O— or greater) is:

$P(X\geq|O|)=1-\sum_{i=0}^{|O|-1}\frac{{S\choose
i}{|S|-|A|\choose|B|-i}}{{|S|\choose|B|}}$ (1)

We say that the overlap is significant if its $p$-value is $<$ 0.05.

##  3 RESULTS

In this study, we investigate three research questions:

  * •

Q1: How do RS, NC, non-network, and random approaches compare to each other in
terms of accuracy of predicting individuals’ mental health?

  * •

Q2: Do the most accurate RS method, the most accurate NC method, and the non-
network method identify different sets of anxious/depressed individuals, i.e.,
are they complementary to each other?

  * •

Q3: What is the impact of using different types of information about the
individuals, represented by different edge types in the HIN, on the
performance of mental health prediction?

Q1: How do RS, NC, non-network, and random approaches compare to each other in
terms of accuracy of predicting individuals’ mental health?

Depression prediction. Among all network methods that we evaluate, DMF, an RS
method, is the most accurate and is significantly (p-value$<$0.05) more
accurate than the rest of the network methods in terms of all evaluation
measures (Figures 4(a), 4(b) and Supplementary Figure S5). Our results
indicate that the most accurate RS method (DMF) outperforms all NC methods.
However, this observation could be due to the classifier used in NC. Instead
of the logistic regression classifier, using other classifiers such as random
forest and support vector machine might improve the performance of NC. Recall
that the reason why we have used logistic regression is that this particular
classifier is typically used in the field of mental health prediction [46, 39,
56].

When we compare the RS and NC network methods to the random guess method, we
find that all network methods, except RESCAL and DEDICOM, are significantly
(p-value$<$0.05) more accurate in terms of all evaluation measures (Figures
4(a), 4(b) and Supplementary Figure S5). The most accurate method that we
evaluate, DMF, achieves gains of 115% in terms of precision, 150% in terms of
recall, 131% in terms of F1 score, and 21% in terms of accuracy over the
random guess method. Note that when we compare an approach, say DMF, to the
random guess method, we measure the gain (i.e., relative change) of DMF over
the random guess method as
$\frac{Performance_{\,DMF}-Performance_{\,random}}{Performance_{\,random}}$.
For example, if $Performance_{\,DMF}$ is 0.612 and $Performance_{\,random}$ is
0.245, the gain is $\frac{0.612-0.245}{0.245}=1.5=150\%$. RESCAL and DEDICOM
do not accurately predict depression - RESCAL and DEDICOM show similar (i.e.,
not significantly different) values as the random guess method, in terms of
all evaluation measures (Figures 4(a), 4(b) and Supplementary Figure S5). Note
that the superiority of DMF over the other two RS methods (RESCAL and DEDICOM)
is not surprising: DMF was already shown to perform better than RESCAL in
recommendation tasks [17]. In turn, RESCAL was already shown to perform better
than DEDICOM in recommendation tasks [48]. Therefore, we expected DMF to work
the best of these three RS approaches. However, it is surprising that in our
task of predicting mental health, RESCAL and DEDICOM produce random-like
results. Also, it is at least somewhat surprising that DMF is superior than
the fourth considered RS approach, HERec, given that the latter is a more
recent approach than the former. Examining why RESCAL and DEDICOM produce
random-like results and why DMF is superior to HERec is non-trivial, given the
heuristic-like nature of these methods in the recommendation task, without
many if any theoretic guarantees. As such, this is out of the scope of the
current study.

(a) Depression

(b) Depression

(c) Anxiety

(d) Anxiety

Figure 4: Method performance when predicting depression and anxiety with
respect to precision and recall. Each column shows the prediction performance
of the corresponding method averaged over five runs of the 5-fold cross-
validation; the error bar represents the corresponding standard deviation. The
column corresponding to the random guess method is marked in red and its
average precision or recall is shown by the red line. The column corresponding
to the non-network method is marked in blue and its average precision or
recall is shown by the blue line. RS denotes “recommender system”. NC denotes
“node classification”. Analogous results for F1-score and accuracy are shown
in Supplementary Figure S5 for depression and in Supplementary Figure S6 for
anxiety.

When we compare the network methods to the non-network method, we find that:
1) DMF and DeepWalk are significantly (p-value$<$0.05) more accurate in terms
of all evaluation measures (Figures 4(a), 4(b) and Supplementary Figure S5);
2) graphlets, colored graphlets, and Metapath2vec++ are marginally (i.e., not
significantly) more accurate in terms of all evaluation measures (Figures
4(a), 4(b) and Supplementary Figure S5); 3) HERec is comparable in terms of
all evaluation measures (Figures 4(a), 4(b) and Supplementary Figure S5); and
4) RESCAL and DEDICOM are significantly (p-value$<$0.05) less accurate in
terms of all evaluation measures (Figures 4(a), 4(b) and Supplementary Figure
S5). The most accurate method that we evaluate, DMF, achieves gains (as
defined above) of 41% in terms of precision, 64% in terms of recall, 52% in
terms of F1 score, and 11% in terms of accuracy over the non-network method.

In summary, our results show that for depression, the best RS method
significantly outperforms all NC methods. In addition, six out of the eight
network methods significantly outperform the random guess method. Moreover,
both the best RS method and the best NC method significantly outperform the
non-network method. This confirms the power of network methods and RS in
particular in predicting depression.

Anxiety prediction. Among all network methods that we evaluate, DMF, an RS
method, is the most accurate and is significantly (p-value$<$0.05) more
accurate than the rest of the network methods in terms of all evaluation
measures (Figures 4(c), 4(d) and Supplementary Figure S6). Our results
indicate that the most accurate RS method (DMF) outperforms all NC methods.

When we compare the RS and NC network methods to the random guess method, we
find that all network methods, except RESCAL and DEDICOM, are significantly
(p-value$<$0.05) more accurate than the random guess method in terms of all
evaluation measures (Figures 4(c), 4(d) and Supplementary Figure S6). The most
accurate method that we evaluate, DMF, achieves gains of 72% in terms of
precision, 101% in terms of recall, 86% in terms of F1 score, and 43% in terms
of accuracy over the random guess method. RESCAL and DEDICOM do not accurately
predict anxiety - RESCAL and DEDICOM show similar (i.e., not significantly
different) values as the random guess method, in terms of all evaluation
measures (Figures 4(c), 4(d) and Supplementary Figure S6).

When we compare the network methods to the non-network method, we find that:
1) DMF is significantly (p-value$<$0.05) more accurate in terms of all
evaluation measures (Figures 4(c), 4(d) and Supplementary Figure S6); 2)
DeepWalk is marginally more accurate and HERec, graphlets, colored graphlets,
and Metapath2vec++ are marginally less accurate in terms of all evaluation
measures (Figures 4(c), 4(d) and Supplementary Figure S6); and 3) RESCAL and
DEDICOM are significantly (p-value$<$0.05) less accurate in terms of all
evaluation measures (Figures 4(c), 4(d) and Supplementary Figure S6). The most
accurate method that we evaluate, DMF, achieves gains of 20% in terms of
precision, and 40% in terms of recall, 29% in terms of F1 score, and 16% in
terms of accuracy over the non-network method.

In summary, the results for anxiety are similar to those for depression. This
confirms the power of network methods and RS in particular in predicting
anxiety in addition to depression.

Q2: Do the most accurate RS method, the most accurate NC method, and the non-
network method identify different sets of anxious/depressed individuals, i.e.,
are they complementary to each other?

To answer Q2, we examine the overlap of sets of depressed/anxious individuals
correctly predicted by DMF, DeepWalk, and the non-network method. We find that
among the three methods, DMF identifies the largest number of
depressed/anxious individuals (Figures 5(a) and 5(b)), which is reflected by
its highest prediction accuracy (Figure 4). Using DMF, we predict as depressed
41 out of all 67 actually depressed individuals and as anxious 77 out of all
106 actually anxious individuals. The other two methods combined correctly
predict additional 11 depressed individuals and 20 anxious individuals who are
missed by DMF. Most of the depressed/anxious individuals are correctly
predicted by at least one of the three methods; only 15 out of all 67
depressed individuals and 9 out of all 106 anxious individuals are not
correctly predicted by any of the three methods.

(a) Depression

(b) Anxiety

Figure 5: Sizes of overlaps between individuals correctly predicted as (a)
depressed and (b) anxious by the best RS network method (DMF), the best NC
network method (DeepWalk), and the non-network method.

Results regarding the overlap between predictions of DMF, DeepWalk, and the
non-network method are qualitatively similar for depression and anxiety
(Figures 5(a) and 5(b)). Taking depression as an example, we find that the two
sets of depressed individuals correctly predicted by DMF and DeepWalk overlap
significantly (p-value$<$0.05) (Figure 5(a)). This could be because DMF and
DeepWalk are both network methods and differ only in one aspect - they are
different types of methods (RS and NC). Moreover, the two sets of depressed
individuals correctly predicted by DeepWalk and the non-network method overlap
significantly (p-value$<$0.05) (Figure 5(a)). This could be because the two
methods both use logistic regression to make predictions and differ only in
one aspect - DeepWalk uses network features while the non-network method uses
non-network features. However, the two sets of depressed individuals correctly
predicted by DMF and the non-network method do not significantly overlap
(Figure 5(a)). This could be because DMF differs from the non-network method
in two ways: the former is a network method and it does not use logistic
regression to make predictions, while the latter is a non-network method that
uses logistic regression. In other words, it could be that the more similar
the two approaches are in terms of their methodologies, the more similar their
predictions.

Since the two sets of depressed/anxious individuals correctly predicted by DMF
and the non-network method do not significantly overlap, the combination of
the two methods’ ideas may be able to correctly predict more of the
depressed/anxious individuals. Thus, we could potentially use ensemble
learning algorithms to combine DMF and the non-network method to achieve more
accurate predictions [15, 53].

Q3: What is the impact of using different types of information about the
individuals, represented by different edge types in the HIN, on the
performance of mental health prediction?

To answer Q3, we train a series of instances of DMF, which is the most
accurate method we have evaluated thus far (when considering all types of
information about individuals). Each instance is trained by using the target
(i.e., individual - mental health) edge type and one or more of the other five
non-target edge types. We analyze all possible combinations of the five non-
target edge types. Each DMF instance uses one of the combinations. In total,
we train 31 DMF instances corresponding to 31 possible combinations of the
five non-target edge types. In this section, edge types are denoted as
follows: I: individual - individual, P: individual - personality traits, S:
individual - social status, F: individual - physical health (where “F” stands
for mostly Fitbit-based physical health data), and W: individual - well-being.
Then, the different edge type combinations are denoted by the corresponding
combinations of the I, P, S, F, and W acronyms.

Depression prediction. We find that among all combinations, the FW
combination—representing the combination of the individual - physical health
and individual - well-being (W) edge types—is the most accurate in terms of
all evaluation measures (Figure 6 and Supplementary Figure S7). In more
detail, the FW combination is significantly (p-value$<$0.05) more accurate
than the rest of combinations, including the combination of all five non-
target edge types (“All”), in terms of all evaluation measures (Figure 6 and
Supplementary Figure S7). Potential reasons why the FW combination is more
accurate than the “All” combination are as follows. First, DMF is an MRMF
method (Section 2.2). MRMF typically contains a large number of parameters and
may be prone to overfitting, meaning that MRMF may fit well on the training
data but not predict well on the testing data [71]. The complexity (the number
of parameters) of the “All” combination is higher than the complexity of the
FW combination. Thus, the higher number of parameters of the former may cause
its overfitting, which in turn may cause its lower prediction performance.
Second, some edge types in the “All” combination may be less informative than
the individual - physical health (F) and individual - well-being (W) edge
types in the FW combination when predicting depression. Using edge types that
may be suboptimally informative may lower the prediction performance compared
to using only edge types that are optimally informative. In other words, it
might not be surprising that using some subset of all data types might be more
informative/accurate than using all data types. Specifically, in our
evaluation, since each of the F and W edge types alone is more accurate than
any one of S, I, and P edge types alone (Figure 6), it might not be surprising
that the FW edge combination is more accurate than the All combination.
Importantly, it _is_ the case that the other edge types alone, namely S and I
(although not P), are performing significantly better than at random (Figure
6), meaning that they do contain some predictive power. So, it is the subject
of our future work to understand how to significantly improve upon the FW
combination while incorporating the S and I (and possibly even P) edge types,
i.e., how to get a truly synergistic, multiplicative effect when integrating
the different data types. In Section 4, we discuss a possible direction
towards achieving this goal.

Figure 6: Performance of DMF (the best network method) when using different
combinations of data (i.e., edge types) to predict depression, with respect to
precision. In this figure, edge types are denoted as follows. I: individual -
individual, P: individual - personality traits, S: individual - social status,
F: individual - physical health, W: individual - well-being. “All” denotes the
combination of all edge types, and it corresponds to the DMF method shown in
Figure 4(a). Each column shows the prediction performance of the corresponding
edge type combination averaged over five runs in the 5-fold cross-validation;
the error bar represents the corresponding standard deviation. Columns are
sorted from left to right according to their heights from high to low, i.e.,
edge type combinations are sorted from left to right in decreasing order of
their prediction performance. Columns to the left of the vertical blue line
are the six top performing combinations that we focus on in the text. The
horizontal red line shows the precision of the random guess method.

Besides FW, there exist five other combinations that all have comparable
(i.e., not significantly different) prediction performance to each other and
are all significantly (p-value$<$0.05) more accurate than the rest of the
combinations in terms of all evaluation measures (Figure 6 and Supplementary
Figure S7). So, these five combinations can all be considered as the second
best result, inferior only to the FW combination. These combinations are FSW,
“All” (the combination including all types of edges), IFSW, PFSW, and IPFW. We
find that all of these combinations contain the individual - well-being (W)
and individual - physical health (F) edge types. This agrees with the
literature - well-being traits such as body image and self-esteem [72, 69], as
well as physical health traits such as physical activity [28] and sleep [5, 3]
are correlated with depression, which validates our HIN-based predictive
framework.

Anxiety prediction. For anxiety, we find that among all combinations, the PW
combination—representing the combination of the individual - personality
traits (P) and individual - well-being (W) edge types—is the most accurate in
terms of all evaluation measures (Figure 7 and Supplementary Figure S8).

Figure 7:  Performance of DMF (the best network method) when using different
combinations of data (i.e., edge types) to predict anxiety, with respect to
precision. In this figure, edge types are denoted as follows. I: individual -
individual, P: individual - personality traits, S: individual - social status,
F: individual - physical health, W: individual - well-being. “All” denotes the
combination of all edge types, and it corresponds to the DMF method shown in
Figure 4(c). Each column shows the prediction performance of the corresponding
edge type combination averaged over five runs in the 5-fold cross-validation;
the error bar represents the corresponding standard deviation. Columns are
sorted from left to right according to their heights from high to low, i.e.,
edge type combinations are sorted from left to right in decreasing order of
their prediction performance. Columns to the left of the vertical blue line
are the seven top performing combinations that we focus on in the text. The
horizontal red line shows the precision of the random guess method.

Unlike for depression, the best combination for anxiety, PW, is only
marginally more accurate than six other combinations including FW, PFW, PSW,
IPW, “All” (the combination of all types of edges), and IPFW. In other words,
the PW combination and the six other combination all have comparable (i.e.,
not significantly different) performance in terms of all evaluation measures.
Plus, all seven combinations are significantly (p-value$<$0.05) more accurate
than the rest of the combinations in terms of all evaluation measures (Figure
7 and Supplementary Figure S8). Focusing on the seven best combinations, the
individual - personality traits (P), individual - well-being (W), and
individual - physical health (F) edge types are frequently included. This
finding agrees with the literature that personality traits [7], well-being
traits such as self-esteem [69], and physical health traits such as physical
activity [43] and sleep [3] are correlated with anxiety, which further
validates our HIN-based predictive framework.

Unlike for depression, for anxiety, the All combination _is_ one of the best-
scoring combinations. However, it is still not significantly better than the
other six best-scoring combinations. So, just like for depression, for
anxiety, it is also the subject of our future work to understand how to get a
multiplicative effect with our HIN data integrative framework. The promise to
improve is certainly there, especially because multiple individual edge types,
namely P, W, and I (although not F and S) are all performing better than at
random when used alone (Figure 7), meaning that each of them has some
predictive power. Hence, it should be possible to use these three combined,
possibly also with F and S, to get the IPW combination, possibly also the All
combination, to perform significantly better than the other edge combinations.
Again, in Section 4, we propose a step in this direction.

An additional observation is that the FW combination, the most accurate
combination in depression prediction, is the second-best combination in
anxiety prediction. This indicates that physical health (F) and well-being (W)
are good predictors of both depression and anxiety. On the other hand, the PW
combination, the most accurate combination in anxiety prediction, is not among
the best combinations in predicting depression. This indicates that
personality traits (P) may not be a key factor in predicting depression, while
they are a good predictor of anxiety. These results suggest that depression
prediction and anxiety prediction have both similarities and differences. This
might be explained by a reasonably large overlap between the depressed
individuals and the anxious individuals in our data. Namely, of the 67
depressed individuals and 106 anxious individuals, 51 individuals are both
depressed and anxious ($p$-value$<$0.05). So, this overlap could explain the
similarities between the depression prediction and anxiety prediction results.
On the other hand, a number of individuals are depressed but not anxious and
vice versa, which could explain the differences between the depression
prediction and anxiety prediction results.

##  4 Conclusion

In this paper, we integrate individuals’ smartphone, wearable sensor, and
survey data into an HIN and apply state-of-the-art RS and NC methods to the
HIN to predict the individuals’ mental health conditions. Our results indicate
that among all of the network methods, DMF, an RS method, is the best, i.e.,
RS is better than NC as evaluated in our study. DMF outperforms the non-
network method as well as the random guess method in terms of all evaluation
measures. This confirms the power of network-based analyses of NetHealth data
and RS in particular in predicting mental health. This study can be extended
in several ways. 1) Because the NetHealth study has collected time series
data, adding temporal information such as dynamic social interaction data [42]
into our HIN could perhaps yield a truly multiplicative effect of data
integration, i.e., lead to improvement compared to using the currently best-
performing FW and PW data type combinations for depression and anxiety,
respectively. Note that doing this is non-trivial, as traditional RS and NC
methods are designed for static HINs. This is why we have not considered the
data’s temporal nature in the current study and why instead we plan to do so
in our future work. 2) In this study, we focus on the task of mental health
prediction as a proof-of-concept. But our HIN framework could be generalized
to predict any of the individuals’ traits available in the NetHealth data. In
other words, our framework could be generalized to predict any edge type and
not just the individual - mental health edge type, as we do in the current
study. To do that, we would just need to treat a desired edge type as the
target edge type and the rest of the edge types (including the individual -
mental health edge type) as side information. 3) Our framework could also be
generalized to new and larger data sets containing more participants and more
types of data when such data sets become available. To do that, we would just
need to model the new data set as a new HIN that may contain a larger number
of nodes and edges and more node and edge types than the HIN constructed in
this study, and then apply RS and NC methods to the new HIN. 4) Because of the
non-significant overlap between DMF’s and the non-network method’s
predictions, ensemble learning methods could be developed to combine the two
methods’ ideas in order to further improve prediction performance compared to
each of the methods individually. Exploring this is beyond the scope of this
paper and is the subject of our future work.

##  5 Acknowledgement

This work was funded by the National Institutes of Health (NIH) 1R01HL117757,
National Science Foundation (NSF) CAREER CCF-1452795, and Air Force Office of
Scientific Research (AFOSR) YIP FA9550-16-1-0147 grants. We thank the entire
NetHealth team for their useful discussions during weekly meetings. We
especially thank the following team members: Rachael Purta for helping us
access the Fitbit data, Afzal Hossain for help with the SMS data, and Louis
Faust for assistance with understanding the Fitbit and survey data.
Importantly, we thank all NetHealth study individuals for generously
volunteering and consenting to share their data, without whom our study would
not have been possible.

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