# Formation of Social Ties Influences Food Choice:
A Campus-Wide Longitudinal Study

Kristina Gligorić  EPFLLausanne, Switzerland<EMAIL_ADDRESS>,  Ryen
W. White  Microsoft ResearchRedmond, Washington, United States
<EMAIL_ADDRESS>,  Emre Kıcıman  Microsoft ResearchRedmond, Washington,
United States<EMAIL_ADDRESS>,  Eric Horvitz  Microsoft ResearchRedmond,
Washington, United States<EMAIL_ADDRESS>,  Arnaud Chiolero  Population
Health Laboratory, University of FribourgFribourg, Switzerland
<EMAIL_ADDRESS>and  Robert West  EPFLLausanne, Switzerland
<EMAIL_ADDRESS>
(2021; October 2020; January 2021; January 2021)

###### Abstract.

Nutrition is a key determinant of long-term health, and social influence has
long been theorized to be a key determinant of nutrition. It has been
difficult to quantify the postulated role of social influence on nutrition
using traditional methods such as surveys, due to the typically small scale
and short duration of studies. To overcome these limitations, we leverage a
novel source of data: logs of 38 million food purchases made over an 8-year
period on the École Polytechnique Fédérale de Lausanne (EPFL) university
campus, linked to anonymized individuals via the smartcards used to make on-
campus purchases. In a longitudinal observational study, we ask: How is a
person’s food choice affected by eating with someone else whose own food
choice is healthy vs. unhealthy? To estimate causal effects from the passively
observed log data, we control confounds in a matched quasi-experimental
design: we identify focal users who at first do not have any regular eating
partners but then start eating with a fixed partner regularly, and we match
focal users into comparison pairs such that paired users are nearly identical
with respect to covariates measured before acquiring the partner, where the
two focal users’ new eating partners diverge in the healthiness of their
respective food choice. A difference-in-differences analysis of the paired
data yields clear evidence of social influence: focal users acquiring a
healthy-eating partner change their habits significantly more toward healthy
foods than focal users acquiring an unhealthy-eating partner. We further
identify foods whose purchase frequency is impacted significantly by the
eating partner’s healthiness of food choice. Beyond the main results, the work
demonstrates the utility of passively sensed food purchase logs for deriving
insights, with the potential of informing the design of public health
interventions and food offerings, especially on university campuses.

nutrition; behavioral analysis; causal analysis; university; public health

††copyright: acmlicensed††journal: PACMHCI††journalyear: 2021††journalvolume:
5††journalnumber: CSCW1††article: 184††publicationmonth: 4††price: 15.00††doi:
10.1145/3449297††ccs: Human-centered computing Empirical studies in
collaborative and social computing††ccs: Applied computing Health
informatics††ccs: Information systems Data mining††ccs: Information systems
Social networks††ccs: Mathematics of computing Causal networks

##  1\. Introduction

Nutrition plays a key role in people’s daily lives and is a major determinant
of long-term health (Delaney and McCarthy, 2011; Gakidou et al., 2017).
Interventions and policies that promote healthier diets are therefore
important public health priorities (Willett et al., 2019). In designing such
interventions, situational food norms, including social influences, play a
prominent role, as they are theorized to have a powerful effect on food intake
(Hetherington et al., 2006; Higgs and Thomas, 2016; Shepherd, 1999; Collins et
al., 2019; Mollen et al., 2013).

Despite the postulated importance of social factors, measuring how dietary
behaviors are affected by the behaviors of others remains challenging. On the
one hand, experimental studies to date have been limited to observing people
in small-scale scenarios with a short duration (Robinson et al., 2014;
Robinson and Higgs, 2013). On the other hand, observational studies have
relied on survey-based methods (Christakis and Fowler, 2007), employing
questionnaires (Wouters et al., 2010) and personal food journals (Cordeiro et
al., 2015b; Cordeiro et al., 2015a), which are costly to organize and prone to
biases (Bowling, 2005).

Furthermore, making causal inferences regarding the influence of social ties
on food intake faces the challenge of numerous confounding factors. Although
similarities in diet and eating behaviors among persons connected via social
links (e.g., friends, family and peers) have been observed in a number of
experimental and survey-based studies (Madan et al., 2010; Finnerty et al.,
2010; Patrick and Nicklas, 2005; Salvy et al., 2008; Stevenson et al., 2007;
Harmon et al., 2016), it is not clear whether the similarity in the
consumption patterns arises from social influence, or if confounding factors,
such as self-selection in tie formation (homophily) and environmental
influences, can explain the similarity (Aral et al., 2009; Shalizi and Thomas,
2011; Shalizi and McFowland III, 2016; Kossinets and Watts, 2006). In real-
world settings, it remains challenging to measure and disentangle properties
that are relevant in the context of food consumption, such as attributes of
the individuals and of the environment (e.g., food options available in
different locations and settings). Researchers have only recently been
addressing this gap by studying social media and other digital traces of human
behavior in the context of food consumption (Abbar et al., 2015; Pater et al.,
2016; Chancellor et al., 2016).

In order to shed new light on the influence of social factors on food choice,
we harness a novel data source: logs of 38 million food purchases made over an
eight-year period on a major university campus, linked to anonymized
individuals (students and staff) via the smartcards they use to make on-campus
purchases. The large scale and long duration of the data enables studies with
greater statistical power, compared to prior setups, and allows for reducing
the influence of confounding factors, and thus for identifying the causal
effect of social influence, by carefully selecting a suitable subset of
individuals whose food choice behaviors are monitored throughout the
individuals’ long-term transaction histories.

Based on this dataset, we design a longitudinal observational study to address
the question of how a person’s food choice is affected by eating with someone
else whose own food choice is healthy vs. unhealthy. To estimate causal
effects from the passively observed log data, we control confounds in a
matched quasi-experimental design. where we identify focal users who at first
do not have any regular eating partners but then start eating with a fixed
partner regularly, and we match focal users into comparison pairs such that
paired focal users are nearly identical with respect to covariates measured
before acquiring the eating partner, but the two focal users’ new eating
partners diverge in the healthiness of their respective food choice.

Research questions. Specifically, we seek to answer the following questions:

  1. (1)

How is the overall healthiness of a focal person’s food choice affected by the
healthiness of an eating partner’s food choice? Does the focal person’s food
choice change, and if so, in what direction?

  2. (2)

How is a focal person’s choice of specific food categories affected by the
healthiness of an eating partner’s food choice? Does the distribution over
food categories change, and if so, what items are purchased more, and what
items less?

Summary of main findings. Regarding question 1, we observe that, when a focal
person acquires a new eating partner, the healthiness of the focal user’s food
choice shifts significantly in the direction of their new eating partner’s
dietary patterns. In a difference-in-differences analysis of 415 comparison
pairs of focal persons (identified among a total of around 39,000 persons in
eight years’ worth of log data), which carefully controls for a number of
confounding covariates, we find clear evidence of social influence: focal
persons acquiring a healthy-eating partner change their habits significantly
more in the direction of healthy foods than focal persons acquiring an
unhealthy-eating partner. We quantify the robustness of this finding in a
sensitivity analysis, and we provide further evidence by observing a
dose–response relationship between the difference in exposures and the
difference in effects.

Regarding question 2, we observe that focal persons who start eating with
healthy-eating partners show an increase in the purchase of coffee and lunch
meals, items generally purchased in large numbers, with the strongest effect.
On the other hand, items purchased at higher rates by the matched
counterparts, who start eating with unhealthy-eating partners, loosely form a
cluster of potentially unhealthy items that should not be eaten in large
quantities (soft drinks, drinks from vending machines, condiments, pizza,
kebabs, and crêpes).

Implications. Students and staff consume large amounts of food on campuses,
daily and globally. The present work shows the value of employing novel
methods relying on population-scale digital traces to measure social influence
on food choice behaviors in this context. The derived insights have the
potential to support interventions aimed at encouraging more healthy and
sustainable dietary habits in university environments and beyond.

##  2\. Related work

###  2.1. Social influence and diet

Social influence on dietary habits is an active area of research (Higgs and
Thomas, 2016; Shepherd, 1999). Food consumption has been found to be
influenced by eating with others (Hetherington et al., 2006), and the food
choices of others, including people one does not know, have been observed to
influence food choices, even when not consciously recognized (Christie and
Chen, 2018; Robinson and Higgs, 2013). Particular attention has been given to
understanding the governing psychological mechanisms, including the seeking of
dish uniformity driven by the goal of regret minimization, or the seeking of
dish variety driven by self-presentation (Ariely and Levav, 2000; De La Haye
et al., 2013; Munt et al., 2017).

Although the underlying mechanisms are not fully understood, uniformity
seeking is observed across a range of studies. For example, it is observed
that the quantity dimension is used to communicate gender identity, and the
food-type dimension to ingratiate the co-eater’s preferences by matching the
other’s presumed choice, following gender-based stereotypes about food
(Cavazza et al., 2017). Such social norms, including the influence of peers,
have tremendous potential for understanding dietary patterns and designing
public health interventions (Collins et al., 2019; Mollen et al., 2013;
Robinson et al., 2013, 2014).

In our work, we monitor behaviors outside of experimental setups. While
previous efforts in this area have focused on specific behaviors (e.g., buying
a dessert or not), having access to a multi-year history of all transactions
made on a large campus allows us to observe behavioral changes for longer time
periods and in a more fine-grained way, by measuring a wide set of purchasing
behaviors that occur in the real world.

###  2.2. The special case of children and adolescents

A large fraction of the transactions recorded in our logs were made by
students, i.e., adolescents and young adults. Focusing on similar age groups,
social influence in dietary habits has been examined in the context of school
children (Finnerty et al., 2010; Patrick and Nicklas, 2005; Salvy et al.,
2008; Birch, 1980) and adolescents (Stevenson et al., 2007; de la Haye et al.,
2010, 2011), who are theorized to be most susceptible to social pressures. In
particular, effects of peer influence have been observed in children and
adolescents’ diets as well as activity patterns (Ball et al., 2010; Salvy et
al., 2012).

Systematic reviews of social network analyses of young people’s eating
behaviors and body weight reveal consistent evidence that school friends are
significantly similar in terms of their body mass index. Friends with the
highest body mass index appear to be most similar (Fletcher et al., 2011).
Prior work further reveals that the family context is essential when
implementing healthy eating interventions, as parents, not friends, are the
most prominent influencers of adolescents’ healthy eating (Kakaa et al., 2018;
Pedersen et al., 2015).

###  2.3. Contagiousness of unhealthy behavior

Previous work has particularly been focused on unhealthy behaviors and their
contagious effects, observing that obesity (Christakis and Fowler, 2007),
overeating (McFerran et al., 2010), fast food (Thornton et al., 2013), high-
fat (Feunekes et al., 1998; Hermans et al., 2009), and alcohol and snack
consumption (Pachucki et al., 2011; Wouters et al., 2010) are contagious. In
fact, the strongest evidence of social influence in food choices has been
found for unhealthy behaviors (e.g., snack foods) (Cruwys et al., 2015; Blok
et al., 2013). Beyond food consumption, peer influence and social norms have
been observed to play a role in unhealthy weight-control behaviors among
adolescent girls: self-induced vomiting, laxatives, diet pills, and fasting
were all shown to be contagious among adolescent girls (Eisenberg et al.,
2005). A rich literature exists on tackling the problem of unhealthy behaviors
through interventions with the goal of promoting healthy dietary habits and
physical activity (Fjeldsoe et al., 2011), losing weight (Jeffery et al.,
1993), reducing the risk of chronic illnesses (Gittelsohn et al., 2012), and
reducing food waste (Reynolds et al., 2019).

There is a heated debate about whether unhealthy behaviors are indeed
contagious, or whether the observed similarities should instead be attributed
to homophily, i.e., people’s tendency to form ties with others who are similar
to oneself to begin with. Disentangling social influence from homophily poses
a fundamental challenge. Without strong assumptions about the structure of
ties or the ability to measure confounding factors, homophily and contagion
are generically confounded (i.e., the effect of social influence cannot be
identified) (Aral et al., 2009; Shalizi and Thomas, 2011; Shalizi and
McFowland III, 2016).

Our work attempts to minimize the effect of confounding variables in
previously infeasible ways. Based on the rich transaction data, we measure a
set of relevant confounding variables and carefully control for them in our
quasi-experimental setup.

###  2.4. Nutrition monitoring and modeling based on digital traces

Social media has emerged as a promising source of data for studies on
monitoring food consumption. For instance, it has been shown that Twitter has
tremendous potential to provide insights into food choices at a population
scale (Abbar et al., 2015). Researchers have also studied specific dietary
issues and behaviors: reports of eating disorders (Pater et al., 2016;
Chancellor et al., 2016), dietary choices, and nutritional challenges in food
deserts, i.e., places with poor access to healthy and affordable food (De
Choudhury et al., 2016). Another active area of research has been focused on
improving methods for monitoring food consumption, relying on mobile phones
(Cordeiro et al., 2015b; Cordeiro et al., 2015a) and wearable devices, to
recognize when the eating activities take place (Thomaz et al., 2015).

Recent related research has also demonstrated the value of monitoring and
modeling of nutrition using other kinds of large-scale digital traces
(Groseclose and Buckeridge, 2017), such as grocery store purchase logs (Aiello
et al., 2019; Buckeridge et al., 2014), online recipes (Rokicki et al., 2018),
logging-based smartphone applications and wearables (Achananuparp and Weber,
2016; Bin Morshed et al., 2020), reviewing platforms (Chorley et al., 2016),
search engine logs (West et al., 2013; Vosen and Schmidt, 2011), social media
such as Twitter (Abbar et al., 2015; Mejova et al., 2016; Widener and Li,
2014) or Instagram (Sharma and De Choudhury, 2015; Ofli et al., 2017),
crowdsourcing platforms (Howell et al., 2016), and geo-location signals
(Sadilek et al., 2018).

Finally, large-scale passively sensed signals have been harnessed in
university campus environments to measure factors of well-being outside of
nutrition (Barclay et al., 2013; Madan et al., 2010; Nook and Zaki, 2015;
Sefidgar et al., 2019; Swain et al., 2020). Recent preliminary insights point
towards the feasibility and the potential of automatically inferring social
interactions from behavioral traces for campus-centric applications (Swain et
al., 2020).

To summarize, while large-scale digital traces are promising for monitoring
and modeling nutrition, little is known about how these passively sensed
behavioral signals can be used for understanding the factors that govern food
consumption in campus settings. Our longitudinal study aims to bridge this gap
by analyzing large-scale, long-term purchase data.

##  3\. Materials and methods

Figure 1. Distribution of purchases across item categories, across a campus.
Most purchased items are coffee and lunch meals.

###  3.1. Transaction log data

This work leverages an anonymized dataset of food purchases made on the École
Polytechnique Fédérale de Lausanne (EPFL) university campus. The data spans 8
years, from 2010 to 2018, and contains about 38 million transactions, of which
about 18 million were made with a badge that allows linking to an anonymized
person’s ID. The data includes 38.7k users, who, on median, are observed for a
time period spanning 578 days and make 188 transactions. Each transaction is
labeled with the time it took place, information about the sales location
(shop, restaurant, vending machine, or café), the cash register where the
transaction took place, and the purchase items. Items are associated with
unstructured textual descriptions (e.g., “coffee”, “croissant”, “Coca-Cola
can”). The unstructured textual descriptions were additionally manually mapped
to categorical labels (such as “meal”, “drink”, or “dessert”) by a research
assistant, who labeled the 500 most frequently purchased items, which account
for 95.4% of the total volume of item purchases observed in the dataset. The
distribution of purchases across categories is shown in Figure 1.

Purchases are not evenly spread over the course of the year, but, as expected,
are higher during semesters, and lower during the breaks between semesters
(Figure 2, left).

This work also leverages a smaller-size enriched transactional dataset
gathered during a campus-wide sustainability challenge, for which 1,031
consenting participants formed 278 teams in order to compete in taking
sustainable actions (e.g., taking the stairs instead of the elevator, or
consuming a vegetarian meal). This data was not used for our analyses, but
only for assessing the accuracy of our heuristic method for inferring frequent
eating peers (described next).

###  3.2. Inference of co-eating onset from proximity in transaction logs

Figure 2. Left: Annual distribution of food purchases. The trends mirror the
university schedule: the number of transactions drops at the end of the spring
semester (around week 25), and increases again at the start of the fall
semester (around week 40). A similar pattern is observed before the beginning
of the spring semester (around week 10). Right: Annual distribution of
detected onsets of social ties. The ties emerge disproportionally often when
classes start at the beginning of the fall semester (by a factor of 3.5 times,
compared to a baseline sampled at random from the distribution of purchases).

To measure the effect of the emergence of new social ties, we first infer
frequently co-eating persons based on the proximity in the transaction logs.
Frequently co-eating persons are likely to share a social tie, i.e., they are
persons likely to be friends, colleagues, or classmates who often eat
together. Previous work has shown that such social ties can be reliably
inferred from geospatial proximity (Crandall et al., 2010).

To infer frequent eating peers, we monitor a sequence of transactions made on
the same day with the badge in the queue of a fixed cash registry, in a given
shop. We identify situations when two individuals are adjacent in the queue
and make a transaction within one minute between each other, with no one in
between them. We use a lower threshold of 10 such high-confidence proximity
indicators to infer a likely social tie. The first appearance of proximity in
the logs is then considered to be the onset of co-eating. We observe a spike
in tie formation coinciding with the start of classes in the fall (Figure 2,
right).

Furthermore, we evaluate the precision of our heuristic by comparing the
inferred co-eaters with ground-truth team membership information from the
sustainability challenge. We observe that team membership in the
sustainability challenge, a ground-truth indicator of a social tie, is
correlated with sharing an inferred tie based on the transaction logs: out of
all the pairs of individuals from the sub-population taking part in the
sustainability challenge who are detected as frequent eating partners, 72% are
also members of the same team.

###  3.3. Inference of nutritional properties from raw transaction logs

We infer a set of summary nutritional properties from raw transaction logs by
relying on a set of pre-established criteria. We derive healthiness labels
based on food-pyramid recommendations (Walter et al., 2007). Products that
should be consumed in the least amounts possible, i.e., items at the top of
the Swiss food pyramid (with high amounts of saturated fats, salt, added
sugars, refined grains, and highly processed foods) were considered as
“unhealthy” (e.g., sodas, chips, candies, and chocolate bars). Other products
that are not at the top of the Swiss food pyramid are considered to be
“healthy” (including non-sweetened beverages, fruits, vegetables, whole
grains, meat, fish, and nuts). When insufficient information was available
from the name of the product, “unclassifiable” was selected.

Two professional epidemiologists specialized in nutrition independently
assessed each food item and categorized them into healthy vs. unhealthy vs.
unclassifiable. The reviewers had access to the unstructured textual
description of the item (e.g., “coffee”, “croissant”, “Coca-Cola can”). The
reviewers did not have access to any other meta-information about the items.
Disagreements were resolved by a third reviewer. Labels are used to create a
healthiness score of a set of purchases by averaging individual product
scores, coded numerically as $1$ for healthy (25% of items), $-1$ for
unhealthy (46% of items), and $0$ for unclassifiable (29% of items).

###  3.4. Matched incident user design with active comparators

Figure 3. Study design diagrams. We illustrate three potential observational
study designs to estimate the effect of eating with other persons on food
choices, (a) cross-sectional design, (b) incident user design, and (c)
incident user design with active comparators. At different points in time, a
person either does not have a regular eating partner (marked in gray), or she
does (marked in green, red, or blue). A cross-sectional design observes food
consumption at the start of the monitored period, a fixed time $t_{0}$, which
is the same across all participants. Incident user design isolates the effect
of the onset of co-eating with another person on subsequent food consumption.
In incident user design, time is tracked relative to the moment of onset
$t_{0}$, which may be different across participants. The active comparator
design additionally allows for comparisons of the effect of onset among
persons who all start to eat with someone, but their partners have different
characteristics (marked in red and blue). The present paper is based on an
incident user design with active comparators (presented in more detail in
Figure 4).

Recall that we are interested in determining whether and how eating with
others impacts the nature of food consumption. As depicted in Figure 3(a), a
naïve approach to answering those questions would be a cross-sectional design:
at any given absolute point in time, some people are regularly eating with
their peers (indicated with green) while others do not (indicated with gray).
Starting from a certain absolute point in time $t_{0}$, by identifying persons
with different habits, one could compare what is consumed by the persons who
do not have a regular eating partner with what is consumed by the persons
eating with a regular eating partner. One could also compare the food consumed
by persons who are eating regularly with partners who have different habits.

The problem with this setup is that those persons who do not eat with others
might have done so in the past (e.g., Person 1 in Figure 3(a)). Those who do
eat with others might have been doing it for a long time or might have just
initiated. Also, some people stop eating with others, whereas other people
continue. It could be that those who stop do so because they prefer the diet
they seek when eating alone (i.e., selection bias). Additionally, people who
eat with others might differ in fundamental ways from those who do not.

For these two reasons, looking at everyone at the same moment in a cross-
sectional way can be problematic. To overcome these challenges, we can turn to
an incident user design (Figure 3(b)), which restricts the population to those
people who newly initiate the treatment—starting to eat together with another
person. We are interested in the causal effect on food consumption of
initiating eating with a peer. Among people who had no regular eating partners
in the past, what is the causal effect of starting to eat with a peer? In this
way we isolate the causal effect of initiation. We restrict the observed
population so that none of the persons have a history of eating with someone.
Note how Person 1 in Figure 3(b) starts eating together with a regular
partner, but then after a while no longer has a regular eating partner. This
is not an issue because we are interested in the effect of the onset.

Figure 4. The matched incident user design with active comparators on which
the present study is based. We identify comparison pairs of focal persons 1
and 2, who are indistinguishable in the pre-treatment period and have no
regular eating partners, until the moment of co-eating onset, when they each
acquire a regular eating partner. Focal person 1 starts regularly eating with
a healthy-eating partner, while focal person 2 starts regularly eating with an
unhealthy-eating partner. The comparison pair of focal users is then observed
in the pre-treatment period (no regular eating partner) and post-treatment
period (regular eating partner). The effect of the co-eating onset is
estimated using a difference-in-differences analysis.

As opposed to the cross-sectional design, where time is absolute, the incident
user design offers the flexibility of tracking time relative to an onset
$t_{0}$ that may be different for different participants. Although this design
allows us to compare different treatments, the problem with this setup, which
persists from the above-described cross-sectional design, is that, if the
comparison group is “no treatment” (i.e., no initiation of co-eating), it is
not apparent when the follow-up should start for the “no treatment” group.
Additionally, selection bias remains and is not accounted for, as people who
do not initiate might in other fundamental ways differ from those who do
initiate.

Our study design addresses these challenges by implementing a variant of
incident user design, incident user design with active comparators (Figure
3(c)). Here, before initiation, no user included in the study had a regular
eating partner (i.e., was treatment-free). We compare the effect of initiating
to eat with partners who have different habits among persons who all initiate
to eat with someone (illustrated with blue and red in Figure 3(c)). Active
comparator designs tend to involve significantly less confounding (Yoshida et
al., 2015; Lund et al., 2015; Johnson et al., 2013), as people who eat with
different kinds of others are more alike among themselves than when compared
to people who do not have regular eating partners.

Our study design is illustrated in more detail in Figure 4. We identify
persons (referred to as focal persons) who had no regular eating partners and,
at a moment $t_{0}$ specific to that focal person, initiate eating with
someone (referred to as eating partner). Here, as defined in Section 3.2, a
person qualifies as a focal person’s potential eating partner if the two were
observed making subsequent purchases in the same queue within one minute of
one another on at least 10 occasions in the entire dataset, and the onset of
co-eating is defined as the first one of these occasions. We then isolate pre-
treatment and post-treatment periods of the focal person’s food purchases
comprising all transactions made six months before the first purchase together
(moment $t_{0}$) and six months after, respectively. We ensure that the focal
person does not initiate eating with anyone else in the pre- and post-
treatment six months. The length of the pre-treatment period is chosen so that
it is feasible to expect that an individual will be present on campus given
the typical stay in the logs (the total observed 12 months of pre- and post-
treatment correspond to one school year).

Figure 5. Daily fraction of purchases annotated as potentially unhealthy,
tracked over five years. A seasonal pattern emerges. Drops in the daily
fraction of unhealthy purchases coincide with between-semester breaks.

Some persons initiate co-eating with a person who has a positive healthiness
score in the aligned pre-treatment period. In contrast, some initiate co-
eating with a partner who has a negative score. These are the two groups that
we seek to compare (we refer to the two types of partners as healthy-eating
partner and unhealthy-eating partner).

For a focal person who starts to eat together with a partner who has a healthy
dietary pattern, an active comparator (or counterpart), will be another focal
person who starts to eat together with a partner who has an unhealthy dietary
pattern. The potential counterparts start to eat with their partner in the
same month as the other counterpart. This is done in order to control for
temporal confounds that might arise from a seasonal variation of food
popularity: as seen in Figure 5, unhealthy foods are especially popular at
certain times of the year. The healthiness of the partner’s dietary pattern is
determined according to its numeric value (greater or less than zero), and not
relative to the focal person.

Comparing incident users with active comparators is an important step towards
reducing the impact of biases. However, in the assignment of the type of
treatment, there can still be confounding. For example, it might be the case
that only people who already have healthy habits start eating together with a
partner who has healthy habits, due to a preference for similar others. The
influence of the partners would then be indistinguishable from the impact of
selection biases caused by homophily.

Hence, we turn to a matched incident user design with active comparators. We
introduce an improvement over the previously discussed setup, where the
incident users are matched to the potential active comparators while
additionally controlling for pre-treatment covariates. Our goal here is to
balance potential confounding variables within pairs, to be able to observe
how the onset of co-eating with partners with different dieting patterns is
associated with subsequent changes in the focal person’s dieting pattern. We
achieve this by performing a propensity-score-based causal analysis. We
approximate randomized treatment assignment by modeling the propensity to
experience the assigned intervention, relying on a number of pre-treatment
covariates describing the focal persons’ eating profiles. Due to the balancing
property of propensity scores (Rosenbaum and Rubin, 1983), matching on
propensities results in similar covariate distributions between groups that
differ in their assigned interventions.

The covariates capture important dimensions of the pre-treatment dietary
pattern of the focal person: where the food is purchased (what is the shop
where the person most frequently buys food), when the food is purchased (what
is the fraction of items occurring during lunchtime), what types of items are
purchased (what fraction of purchased items are meals, and what is their
estimated healthiness), and how often the person purchases food on campus
(number of transactions). We measure these confounding covariates up to time
$t_{0}$.

Figure 6. Distribution (before matching) of propensity to start eating with a
healthy-eating partner.

Figure 7. Importance of most indicative features for predicting treatment
assignment, i.e., initiation of eating with a healthy- vs. unhealthy-eating
partner (shop names anonymized). Most important feature: pre-treatment
healthiness score of focal person’s purchases, which indicates homophily.

We use a random forest model that predicts the type of treatment based on pre-
treatment covariates of the focal person (area under the ROC curve: 0.87).
This implies that past purchases allow us to accurately predict whether the
tie will be formed with a healthy- or an unhealthy-eating partner, and that
confounding is a real problem that needs to be addressed. The distribution of
the propensity to start eating with a partner who has a high healthiness score
is presented in Figure 7. We also examine the feature importances in
predicting the treatment assigned, i.e., the initiation of eating with a
partner who has a healthy or unhealthy eating pattern (Figure 7). We observe
that the focal person’s pre-treatment healthiness score is in fact the most
important predictor of the type of partner the focal person will start to eat
with, pointing at homophily.

Focal persons in the two sets are then matched while ensuring that two
potential matches have propensity scores (likelihoods of receiving the
treatment) within a caliper of 0.1. The size of the caliper was chosen so that
balance in covariates is achieved. Moreover, an exact match on the sign of the
mean pre-treatment healthiness score and the most frequented shop is required
to achieve tight control. We then create matched pairs based on possible
candidates by performing maximum weight matching on the weighted bipartite
graph, where nodes are focal persons, and the weights use similarity based on
the Mahalanobis distance in covariates. We maximize the total similarity to
find a maximal matching.

Figure 8. Histogram of the number of high confidence indicators of eating
together with their respective partners, for matched focal persons.

Figure 9. Histogram of the partner’s pre-treatment healthiness score, across
matched persons. Orange bars correspond to healthy-eating partners, blue bars
to unhealthy-eating partners. A margin of 0.1 is ensured to differentiate the
treatments.

The result is a set of matched pairs of focal persons, indistinguishable up to
the moment of initiation, who initiated co-eating with partners with different
dietary patterns in the same month. This approach yielded 415 matched pairs of
830 focal persons who started to eat with different partners. We require at
least 10 high confidence indicators of eating together with the partner
(Figure 9). Partners’ distribution of pre-treatment healthiness scores is
shown in Figure 9.

Our matched analysis then moves on to comparing focal people who initiate co-
eating with a person with a healthy dieting pattern, to their counterparts who
have the same dieting patterns up to the moment of initiation, but initiate
co-eating with a partner who has an unhealthy dieting pattern. The post-
treatment patterns are then compared across treatments within the matched
population.

Table 1. To ensure that matched persons are comparable, we evaluate the balance of their pre-treatment covariates, via the standardized mean difference (SMD) across covariates in the two matched groups. Pre-treatment covariate | SMD before matching | SMD after matching
---|---|---
Preferred shop (i.e., where the largest fraction of | exact match required
pre-treatment transactions is made) |
Pre-treatment percentage of lunchtime transactions | 0.109 | 0.045
Pre-treatment percentage of meal transactions | 0.207 | 0.075
Pre-treatment mean healthiness score | 0.301 | 0.023
Pre-treatment mean weekly number of transactions | 0.071 | 0.023

Before moving on to the analysis of the outcomes, we ensure that the matched
persons are comparable by measuring the balance of their pre-treatment
covariates (Table 1). We use the standardized mean difference (SMD) across
covariates in the two groups to measure the balance. We observe that matching
greatly reduces the SMD, as the largest SMD across covariates (the one of the
pre-treatment healthiness score of the focal person) changes from 0.301 before
matching, to 0.023 after matching. Groups are considered balanced if all
covariates have SMD lower than 0.2 (Kıcıman et al., 2018), a criterion that is
satisfied here.

##  4\. Results

Recall our research question: we want to understand how a person’s food
choices are affected by the healthiness of a co-eating partner’s food choices.
Do people’s choices change and, if so, in what direction (i.e., towards more
or less healthy)?

###  4.1. Regression analysis of pooled data

Figure 10. The effect of the focal person’s pre-treatment covariates, the
partner’s pre-treatment healthiness score, and the number of detected high-
confidence indicators of eating together on the focal person’s post-treatment
healthiness of purchased items. The effects are estimated with linear
regression ($R^{2}=0.194$); 95% confidence intervals are approximated as two
standard errors. Significant coefficients ($p<0.05$) are marked with an
asterisk (*). The focal person’s own healthiness score and their eating
partner’s healthiness score are the only two statistically significant factors
associated with the focal person’s post-treatment healthiness score.

First, we aim to determine if there are any significant differences between
the outcomes of the matched focal persons. Is the pre-treatment healthiness of
the partner predictive of post-treatment healthiness of the focal person? We
start by performing a regression estimation of the effect of the partner’s
pre-treatment healthiness score on the focal person’s post-treatment score.

We fit a model where the focal person’s post-treatment healthiness score is
the dependent variable. We include the focal person’s pre-treatment
healthiness score, the partner’s pre-treatment healthiness score, the number
of high-confidence indicators of eating together, and the focal person’s pre-
treatment covariates as the independent variables. The focal person’s pre-
treatment covariates (number of transactions, percentage of transactions that
are meals, percentage of lunchtime transactions, and the pre-treatment
healthiness score) are already controlled for by matching, but they are
included in the model to account for possible residual confounding. The
predictors and the outcome are standardized, so the coefficients are
interpreted as increases in the healthiness score per standard deviation of
the predictor.

In Figure 10, fitting the linear regression, we measure a significant positive
effect of 0.13 (95% CI [0.07, 0.19]) of the partner’s pre-treatment
healthiness score. The focal person’s own pre-treatment healthiness is the
strongest predictor of post-treatment healthiness (coefficient 0.43, 95% CI
[0.36, 0.49]). This is the first indicator that the pre-treatment score of the
partner is associated with the focal person’s patterns.

###  4.2. Contingency-table analysis

Next, to obtain fine-grained insights about patterns taking place at the pair
level, we analyze the outcomes with a contingency table. We binarize the
outcome to look for either an increase or no increase post-treatment, compared
to pre-treatment. Four possibilities exist for any matched pair: both
increased, only one or the other increased, and none increased. The
contingency table is presented as Table 2. The table counts the frequency of
the four possible results. Using a chi-squared test, we reject the null
hypothesis of no treatment effect ($p=0.00017$).

It is particularly informative to observe the discordant pairs (off-diagonal
entries in the contingency table) among the matched pairs. Such pairs
correspond to situations when the outcome (increase or no increase) differs in
the matched pair. The intuition is the following: if there is no effect, the
two types of discordant entries should be balanced. However, we observe that
in 103 pairs, the focal person with a positive intervention increased, and the
focal person with a negative intervention did not. The reversed situation, in
comparison, occurs in 67 pairs. We test the null hypothesis of no effect in a
paired randomized experiment using McNemar’s test (Lachenbruch and Lynch,
1998), which relies directly on the evidence that comes from the discordant
pairs (their number and the ratio between them). Here, too, we reject the null
hypothesis of no treatment effect ($p=0.007$).

Table 2. Contingency table counting number of pairs of matched focal persons in each condition. Post-treatment healthiness score is compared to pre-treatment score to determine if there was an increase; in columns, for focal persons who start to eat with healthy-eating partners, and in rows, for their matched counterparts, i.e., focal persons who start to eat with unhealthy-eating partners. | Focal person with a |
---|---|---
| healthy-eating partner |
| Increase | No increase | Total pairs
Focal person with an | Increase | 126 | 67 | 193
unhealthy-eating partner | No increase | 103 | 119 | 222
Total pairs | 229 | 186 | 415

###  4.3. Difference-in-differences analysis

We move on to further exploit the matched setup in order to estimate the
difference-in-differences (Lechner, 2011) effect for pairs of matched focal
persons. The idea is to first calculate the difference between post-treatment
and pre-treatment healthiness scores for each focal person separately. Then,
we can calculate the difference in treatment effects between two matched focal
persons in each pair. Averaging the differences in differences across all
pairs yields the overall treatment effect.

Regression model. In practice, following the standard approach, we estimate
the difference-in-differences effect via a regression model. Here, each focal
user adds two data points (one pre-treatment, one post-treatment), each of
which specifies, as predictors, the type of partner with whom the focal user
started to eat as a treatment (healthy-eating or unhealthy-eating) and the
time period (pre- or post-treatment); and, as the outcome, the healthiness
score of the focal user’s food choice during the respective period. Each
matched pair thus contributes four data points, and the modeled dataset
consists of $4\cdot 415=1{,}660$ data points. Formally, the model takes the
following form:

(1)
$y_{it}=\alpha+\beta\cdot\text{healthy\\_treatment}_{i}+\gamma\cdot\text{treated}_{t}+\delta\cdot(\text{healthy\\_treatment}_{i}\cdot\text{treated}_{t})+\text{error}_{it},$

where the dependent variable $y_{it}$ is the focal user $i$’s healthiness
score in period $t$, and the independent variables indicate whether $i$’s
partner has a positive or negative pre-treatment healthiness score
($\text{healthy\\_treatment}_{i}$ = 1 or 0, respectively) and whether the
respective data point captures the pre- or post-treatment period
($\text{treated}_{t}$ = 1 or 0, respectively). The coefficient $\delta$ of the
interaction term, then, is the difference-in-differences effect of starting to
eat with a healthy- vs. unhealthy-eating partner.

Results. Calculating the average difference-in-differences effect with a
linear regression across all matched focal persons, we observe a larger post-
treatment increase in focal persons with healthy-eating partners compared to
the post-treatment increase in matched counterparts, $\delta=0.051$ (95% CI
$[0.021,0.076]$, $R^{2}=0.07$). This means that, accounting for possible
temporal drifts between post-treatment and pre-treatment that are not
associated with the initiation, focal persons starting to eat with a healthy-
eating partner significantly diverge from their matched counterparts starting
to eat with an unhealthy-eating partner. Quantitatively, the effect size of
$\delta=0.051$ means that, compared to matched counterparts who start eating
with an unhealthy-eating partner, focal persons who start eating with a
healthy-eating partner increase their healthiness score by an additional 5.1%
of the full range spanning from a neutral healthiness score (i.e., 0) to the
maximum healthiness score (i.e., 1).

Similarly, to estimate the effect of social tie formation on the absolute
number of healthy and of unhealthy purchased items, we repeat the regression
analysis described in Eq. 1, but now with different dependent variables that
capture the total number of healthy and the total number of unhealthy items
purchased by focal user $i$ in period $t$. We observe that the focal persons
who start to eat with a partner with a healthy pattern purchase an additional
5.71 (95% CI $[3.21,8.21]$, $R^{2}=0.17$) healthy items, and an additional
$-1.13$ (95% CI $[-3.04,0.78]$, $R^{2}=0.12$) unhealthy items in the six
months following the tie formation, compared to their matched counterparts.

Sensitivity analysis. The above finding relies on the assumption that there
are no unobserved variables that create the differences between the matched
focal persons that could explain away the measured effect. Sensitivity
analysis is a way of quantifying how the results of our calculations would
change if the assumptions were violated to a limited extent. If the
conclusions of the study would change little, then the study is insensitive to
a violation of the assumptions, up to the specified limited extent. In
contrast, if the conclusions would change substantially, then the study is
sensitive to a violation of the assumption.

The key assumption made in our analysis is that the treatment assignment is
not biased, or in other words, that after balancing the pre-treatment
covariates, the co-eating initiation with a healthy-eating vs. an unhealthy-
eating partner is randomized (i.e., it is effectively decided by a coin flip).
We measure by how much that assumption needs to be violated in order to alter
our conclusion that there is a significant difference-in-differences effect on
the healthiness of purchased items among the matched focal persons.
Specifically, sensitivity analysis lets us answer the following question: if
there is a violation of randomized treatment assignment (i.e., a deviation
from fair 50/50 coin flip), how large would it need to be in order to alter
the conclusion that the null hypothesis of no difference between focal persons
can be rejected? This notion is quantified by the sensitivity $\Gamma$, which
specifies the ratio by which the treatment odds of two matched persons would
need to differ in order to result in a $p$-value above the significance
threshold. We always have $\Gamma\geq 1$, with larger values of $\Gamma$
corresponding to more robust conclusions.

For the chosen $p=0.05$, we measure a sensitivity of $\Gamma=1.17$, which
implies that, within matched pairs, an individual’s probability of being the
treated one could take on any value between $1/(1+\Gamma)=0.46$ and
$\Gamma/(1+\Gamma)=0.54$ without changing our decision of rejecting the null
hypothesis of no effect. In other words, if the assignment of the treatment
after matching were not approximating the ideal 0.5, but a third variable made
some people more likely to initiate eating with a healthy-eating or an
unhealthy-eating partner, the randomized treatment assignment would have to be
violated by deviating from the fair 0.5 by at least four percentage points.

Figure 11. Sensitivity analysis. For the sensitivity $\Gamma=1.17$, the
amplification $(\Lambda,\Delta)$ is plotted (see text for explanation).
Horizontal and vertical dashed lines indicate $\Gamma$, i.e., the asymptotic
value of $\Lambda$ for $\Delta\rightarrow\infty$, and vice versa.

Additionally, we conduct an amplification of the sensitivity analysis
(Rosenbaum and Silber, 2009). Amplification is particularly relevant when the
concern is not about a violation of the randomized treatment assignment, but
rather about the potential existence of a specific unobserved covariate. It
then becomes useful to consider possible combinations of $\Lambda$ and
$\Delta$, two parameters describing the unobserved covariate, that would
result in the measured $\Gamma$. The strength of the relationship between the
unobserved covariate and the difference in outcomes within the matched pair is
defined by $\Delta$, whereas $\Lambda$ defines the strength of the
relationship between the unobserved covariate and the difference in
probability of being assigned a treatment. With these definitions, the
sensitivity $\Gamma$ can be expressed in terms of $\Lambda$ and $\Delta$, as
$\Gamma=(\Lambda\Delta+1)/(\Lambda+\Delta)$.

The result of sensitivity analysis amplification is presented in Figure 11.
For combinations of $\Lambda$ and $\Delta$ in the orange area, significant
effects would be detected (leading to $p<0.05$), whereas for the combinations
in the blue area, no significant effects would be detected (leading to
$p>0.05$). An infinite number of $(\Lambda,\Delta)$ combinations fall on the
border; e.g., $(\Lambda,\Delta)=(2.0,1.6)$ corresponds to an unobserved
covariate that doubles the odds of treatment and multiplies the odds of a
positive pair difference in the outcomes by 1.6.

Overall, we conclude that the study design is insensitive to small biases
(Rosenbaum, 2017).

(a)

(b)

Figure 12.  Dose–response relationship. (a) Histogram of pre-treatment
differences in healthiness scores between partners of paired focal users. (b)
Difference-in-differences effect between focal persons in matched pairs,
stratified by the pre-treatment differences in healthiness scores between the
partners they were exposed to.

###  4.4. Dose–response relationship

Next, we analyze the dose–response relationship in our matched setup. Similar
focal persons initiate eating with differing partners. We observe systematic
changes in the dieting patterns of the focal persons after the tie formation.
But do more drastic difference-in-differences effects occur when the
differences between partners are more drastic? In the case of a true causal
effect, one would expect a dose–response effect where focal persons diverge
more post-treatment if their partners diverged more pre-treatment.

Although large differences in the pre-treatment scores between matched focal
persons’ partners are rare (Figure 12), Figure 12 shows evidence of a
dose–response relationship: the difference-in-differences effect is stronger
when the partners are more different (i.e., the more extreme difference in
partners leads to more extreme effect estimates). If there were other
confounding factors that could explain the observed difference-in-differences
effects, and those factors had nothing to do with the onset of eating
together, we would not expect to find a dose–response relationship. The
observed dose–response relationship thus further supports the conclusion of a
causal effect.

Figure 13. Post-treatment increase in healthiness score, stratified by pre-
treatment healthiness score of focal person (with 95% bootstrapped confidence
intervals). The difference is shown separately for focal persons who start
eating with a person with a positive (orange) vs. negative (blue) healthiness
score. The difference is monitored in the first 3, 6, and 12 post-treatment
months (left, center, and right panel, respectively).

###  4.5. Stratification by pre-treatment healthiness

Additionally, we would like to understand for whom the treatment is effective.
Are there changes across the board with respect to the initial healthiness, or
only for specific sub-populations? For whom is the intervention most
efficient? We again monitor the differences between post- and pre-treatment
healthiness scores, but now stratified into quartiles by pre-treatment
healthiness score of the focal person (Figure 13). Moreover, we repeat this
analysis for post-treatment observation periods of varying length (3, 6, and
12 post-treatment months). In the aligned, post-intervention period, persons
who start eating with partners with healthy dieting patterns are characterized
with consistently higher healthiness scores compared to the matched
counterparts, across strata of the focal person’s pre-treatment healthiness
score. Note that the fact that the slopes are decreasing may be a simple
regression to the mean. The key observation is that, within each stratum, when
comparing the outcomes in orange and blue, people who initiate eating with a
healthy-eating partner (orange) see a greater post- vs. pre-treatment
difference compared to people who initiate eating with an unhealthy-eating
partner (blue).

###  4.6. Analysis of affected food-item categories

Figure 14. Estimated difference-in-differences effects of co-eating onset with
healthy- vs. unhealthy-eating partner on frequency of purchased food
categories (with 95% confidence intervals approximated as plus/minus two
standard errors). Categories with a significant effect are marked in orange
(positive) and blue (negative), whereas categories with no significant effect
are marked in gray.

Finally, we set out to understand the influence of new co-eating partners on
the rates at which categories of food items are subsequently purchased. Since
we observed that the behaviors are modified, we now ask: what items are eaten
more, and which less? What foods being purchased and eaten in group settings
on campus have the largest influence on others?

To estimate category-specific difference-in-differences effects, we repeat the
regression analysis described in Eq. 1, but now with a different dependent
variable $y_{cit}$, which captures the number of items from food category $c$
purchased by focal user $i$ in period $t$. By fitting a separate regression
for each food category $c$, we obtain category-specific effects $\delta_{c}$.

The estimated effects $\delta_{c}$, together with 95% confidence intervals,
are presented in Figure 14. We observe that the focal persons initiating to
eat with a healthy-eating partner purchase more coffee, lunch meals, coffee
from vending machines, soup, fruit, dessert, tea, salad, and wraps, compared
to their matched counterparts, who purchase more soft drinks, drinks from
vending machines, water, condiments, pizza, kebabs, and crêpes. The values on
the $x$-axis can be interpreted as the number of purchased items by which the
matched focal persons diverge in the post-treatment period. For example, in
the six months following tie formation, people who start eating with healthy-
eating partners purchase, on average, around two additional meals and around
four additional coffees, compared to the matched counterparts. The matched
counterparts who start eating with unhealthy-eating partners, by contrast, on
average purchase around one additional soft drink in the six months following
tie formation.

Coffees and lunch meals are the items that see the largest increase after tie
formation with a healthy-eating partner. These items are in general purchased
in large numbers (Figure 2). Conversely, items with the strongest effect among
the matched counterparts, with the exception of water, loosely form a cluster
of potentially unhealthy items that should not be eaten in large quantities.
The remaining items with a significant positive effect, soups, fruits,
desserts, tea, salad buffet, and wraps are overall less indicative of an
unhealthy dietary pattern.

##  5\. Discussion and conclusions

We report on a longitudinal observational study of the effect of the formation
of social ties on food choice, leveraging a novel source of data: logs of
millions of food purchases made over an eight-year period on a major
university campus. To estimate causal effects from the passively observed log
data, we control confounds in a matched quasi-experimental design: we identify
focal persons who start regularly eating with a fixed partner and match focal
persons into pairs such that paired focal persons are nearly identical with
respect to covariates measured before acquiring the partner, but the new
eating partners diverge with respect to the healthiness of their respective
food choice behaviors (before tie formation with the focal person).

We observe that the people who acquire a healthy-eating partner change their
habits significantly more toward healthy foods than those acquiring an
unhealthy-eating partner. We further identify foods whose purchase frequency
is impacted significantly by the partner’s healthiness of food choice: coffees
and lunch meals are the items that see the largest increase on behalf of those
who initiate eating with a healthy-eating partner, whereas the matched
counterparts, with the exception of water, increase purchases of items that
loosely form a cluster of potentially unhealthy items that should not be
consumed in large quantities: soft drinks, drinks from vending machines,
condiments, pizza, kebabs, and crêpes.

Our findings show that digital traces can be used as a valuable tool for
monitoring dietary habits, and can provide valuable insights into the effects
of social ties on dietary choices. This work establishes the feasibility of
relying on transactional logs in order to monitor food consumption and derive
meaningful insights about behavioral patterns taking place at a population
scale. Such digital traces can complement small-scale field experiments,
making it possible to observe large populations over long time periods.

By relying on a novel transactional dataset and using carefully designed
quasi-experimental methodology, we confirm theories of social influence on
food choice postulating that social influence plays a prominent role and has a
powerful effect on food intake (Hetherington et al., 2006; Higgs and Thomas,
2016; Shepherd, 1999; Collins et al., 2019; Mollen et al., 2013). Conforming
to the behavior of others is adaptive, and individuals find it rewarding
(Higgs and Thomas, 2016). Hence, dietary choices are expected to converge with
those of our close social connections.

Additionally, eating norms are known to reduce the intake of unhealthy foods
(Robinson et al., 2013) in specific contexts. For example, exposure to social
eating norms is known to result in a reduction in the weight of consumed high-
energy snack foods (Robinson et al., 2013). The fact that persons exposed to a
partner eating healthy foods eat fewer items that should not be eaten in large
quantities (soft drinks, drinks from vending machines, condiments, pizza,
kebabs, and crêpes) compared to the counterparts indicates the presence of
such positive influence of others.

Finally, we contribute to the rich literature about social influences in
eating by demonstrating that, beyond studying social modeling in specific
situations (Vartanian et al., 2015), the naturally or experimentally occurring
event of tie formation is an important dimension to consider in order to
understand the mechanisms of social influence and their potential for
influence and interventions.

Implications. The most imminent utility of measuring the impact of social tie
formation on food choice relying on large-scale passively sensed transaction
signals lies in its potential to inform public health interventions on
campuses. Designing large-scale nutritional interventions is challenging and
logistically complicated. Additionally, it is difficult to predict their
impact through experimentation due to ethical concerns stemming from the
danger of eliciting undesirable effects. This work shows how observational
insights based on passively sensed data can be used to evaluate the impact of
potential interventions by estimating the impact of similar interventions that
occur naturally, without external experimentation.

For instance, in order to incentivize healthy eating habits, university or
corporate stakeholders might consider launching programs with disclosure and
consent that help students or staff connect onsite with “lunch buddies” and
incentivize consumption of meals in a company. Such programs leveraging peer-
led nutritional interventions (Yip et al., 2016) would need to take into
consideration self-selective disclosure and consent as confounding factors.
First, by relying on passively sensed observational data and evaluating the
impact of similar interventions, it would be possible to anticipate the impact
on the involved individuals ahead of implementing any interventions in the
real world. Second, it would be possible to optimize the pairing of people, by
estimating on whom the effect of tie formation with others could be strongest.
Finally, being informed about what products are most likely to be purchased in
modified quantities after tie formation, the stakeholders could optimize the
offering of products.

The question of whether the estimated impact of such naturally occurring
interventions is identical to the true causal effect, and whether it is
expected to mirror the impact of intentional externally induced interventions,
remains. In what follows, we discuss the assumptions that would need to hold,
and the limitations that should be considered.

Causal assumptions. We discuss what assumptions are necessary for our study
design to let us isolate the causal effect of social-tie formation on food
consumption. In particular, we consider the assumptions of the potential-
outcomes framework (Rubin, 2005) and the extent to which they can be assumed
to hold in the present work.

Stable unit treatment value. Units are assumed not to interfere with each
other. In other words, the treatment assignment of one unit does not affect
the outcome of another unit, i.e., there is no “spillover” or “contagion.”
Recall that we require initiation with no more than one peer during the
monitored pre- and post-treatment periods. While this restriction ensures that
there are no spillovers, our study is unable to capture complex network
interactions occurring in on-campus settings. Future work should therefore
generalize beyond the studied setup by identifying time-varying treatments and
dynamic treatment regimes using g-formula methods (Young et al., 2011; Taubman
et al., 2009).

Consistency. The potential outcome under a treatment is assumed to be equal to
the observed outcome when the actual treatment is received. In other words,
the counterfactual outcome for treated units is the observed outcome for
controls. While our study design attempts to compare people who are similar up
to the moment of receiving the treatment by modeling the propensity to be
treated, the assumption that the outcome of the matched person would be
exactly the outcome of the treated person is untestable.

Positivity. The probability of every treatment for every set of covariates is
assumed to be non-zero. In our study, it is reasonable to assume there are no
people who could never possibly receive a given treatment.

Ignorability. Finally, the ignorability assumption refers to the absence of
unmeasured confounding. By performing a sensitivity analysis, we have
attempted to assess the possible impact of unobserved biases if the ignorable
treatment assignment assumption is violated. This analysis leads us to
conclude that our findings are insensitive to small biases.

Limitations. This study is subject to certain limitations, some of which
suggest promising directions for future work. Inherent to observational
studies, we recognize the inability to infer true causality. Controlling for
all the possible confounds is fundamentally infeasible. Still, we make a step
towards understanding the effects of a certain “treatment” on food consumption
by developing a quasi-experimental design based on propensity-score matching
and difference-in-differences methods, whereby we seek to minimize biases due
to observed confounding variables, enriched with a quantification of the
danger of unobserved confounding variables via sensitivity analysis. Our work,
therefore, provides insights based on passively sensed behavioral signals that
go far beyond simpler correlational analyses.

We note that the inference of social ties might be imperfect. However, the
fact that a large fraction of ties forms precisely at the beginning of the
academic year (with the fall semester), when students are exposed to new
fellow students (Figure 2), and the fact that there is a correlation with
ground-truth team membership points towards reliability. In addition, we note
that we might potentially be detecting the onset of co-eating with a delay
(i.e., it actually occurs earlier than detected) if peers eat together as part
of a larger group and are not directly adjacent in the queue, or if they use
cash for the transaction. That said, we note that any potential delay in
estimating the onset would lead to more conservative estimates of the effect
of partnering up, as potential changes in the patterns would be counted as
purchases before the tie formed.

Construct validity. We also consider the issue of the construct validity of
our study design, i.e., the degree to which the obtained indirect measurements
(transaction logs of food consumption) are reflecting the true phenomenon that
is intended to be measured (actual food consumption). It is reasonable to
assume that students and staff indeed consume the food that they purchase.
However, one cannot eliminate the possibility of persons borrowing the card,
or paying for items consumed by other people. Conversely, people on campus may
consume food not recorded in the purchase logs (e.g., food purchased using
cash, or food prepared at home or in off-campus restaurants). Future work
should determine the extent to which the assumption that purchasing implies
consumption, and vice versa, holds.

External validity. Future work should also determine external validity, that
is, to what extent behaviors measured on campus reflect other settings off
campus, e.g., food consumption—and the complex interplay with food consumption
of their social ties at home—in families or in restaurants. People who
primarily eat home-cooked food might present a skewed representation of their
diet in the studied cafeteria purchase logs, and the fact that individuals
might consume food prepared at home introduces unobserved variables into our
analyses. For example, people who do not have regular eating partners in
extended periods might eat alone because they prefer to eat a peculiar type of
food that they cook at home and that is not served on campus, or measured via
purchase logs.

Ethical considerations. Nutrition is a potentially sensitive personal
behavior. To protect user privacy, the log data used here was accessed
exclusively by EPFL personnel involved in this project, and stored and
processed exclusively on EPFL servers. The data was obtained with approval
from EPFL’s Data Protection Officer and was anonymized before it was made
available to the researchers for analysis. Finally, we note that our work was
conducted retroactively on data that had been collected passively in order to
support campus operations. Thus, our analysis did not influence users in any
way.

Future work. This study opens the door for future research directions and
potential follow-up studies of the mechanisms of social influence beyond those
described, such as the role of the campus-wide sustainability challenge (cf.
Section 3.1), and if eating with a healthy-eating partner is correlated with
other behavioral changes (e.g., switching cafeterias). Future work should
further understand the measured behavioral changes by understanding the
underlying mechanisms and the social contexts in which the foods are consumed
in modified quantities (e.g., socializing by meeting for a cup of coffee
versus consuming a meal together). Future work should demonstrate whether
modified habits are retained in those individuals who return later to eating
alone for long stretches, or, if habits are not retained, how the individual
regresses to the state they were in before the tie formation, and if so, what
is the rate of the decay back.

Beyond food. To the best of our knowledge, this is the first study to leverage
large-scale transactional data to retrospectively evaluate the impact of
implicit dietary behavioral interventions. We show that purchase logs are
useful as an effective sensor to detect behavioral changes in individuals who
interact with others. Beyond food purchase logs on campus, this work
highlights how careful quasi-experimental comparisons leveraging passively
sensed data can be used to measure complex interactions between individuals.
The methodology of isolating influence through matched pairwise comparisons
has the potential to allow for detecting behavioral changes also in areas
relevant to other social computing scenarios. Ambitious questions of how
individuals impact behaviors or skills of one another in the context of
purchasing decisions, exercise habits, coaching or counselling, travelling,
sleep patterns, online interactions, collaborative writing, or coding practice
could all be tackled by identifying the onset of such interactions, and
comparing outcomes in similar matched persons while controlling for confounds.

Code and data. Although the transaction logs cannot be shared publicly, for
transparency we make all analysis code, as well as the food-item and
healthiness-score annotations, publicly available: https://github.com/epfl-
dlab/tie-formation-food

###### Acknowledgements.

We would like to thank Nils Rinaldi, Aurore Nembrini, and Philippe Vollichard
for their help in obtaining and anonymizing the data. We are also grateful to
Jonas Racine and Kiran Garimella for early help with data engineering, and to
our reviewers for their helpful suggestions. This project was funded by the
Microsoft Swiss Joint Research Center.

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