Stress levels among college students have been on the rise for years [1]. According to a recent large-scale nationwide survey, rates of student stress continue to climb as more than half of students (57%) reported experiencing “more than average stress” [2]. In the workplace, it has been conservatively estimated that stress costs the United States economy up to US$125 billion annually [3]. Although not directly measured in dollars and cents, evidence for the negative impact of stress on college students can be observed through hampered academic performance, as 30% of students noted that stress caused them to receive a lower grade on an exam or course, fail or drop a course, or it interfered with thesis or practicum work [2].

Broadly, stress can be defined as any sort of negative event related to demand, threat, or harm. Following a stressful event is a biological and behavioral response geared toward altering the present situation or otherwise adapting to the stressor [4]. Along with hindering academic performance, stress is thought to be related to a host of negative emotional states and health outcomes, including depression, obesity, and cardiovascular disease [5-7]. Indeed, as levels of stress have risen among college students, so have issues related to mental health [2]. Not surprisingly, a survey of college counseling center directors indicated that a clear majority (90%) of centers reported an increase in severe psychological problems among students [8].

A primary source of stress for students is academics. Stress because of class attendance and homework were among leading stressors in one study of college students [9]. Further, research suggests that in addition to academic performance, students are also stressed by a pressure to succeed and about concerns regarding postgraduate planning [10]. Of course, in the college environment, stressors other than those academic in nature also exist. Interpersonal aspects of a student’s life, such as worrying about forming friendships, fitting in socially, and getting along with roommates, were reported as stressful elements by students [11]. In addition, environmental sources of stress, such as financial difficulties, and changes in eating and sleeping patterns also contribute to levels of student stress [11,12].

Until recently, the dominant method for sampling information about students’ lives came by way of daily and weekly diaries where details about students’ thoughts, experiences, behaviors, and activities could be recorded over a specified time range. Indeed, approaches such as this have shed light on various aspects of a college students’ life, including interpersonal student relationships, drinking behavior, and coping with stressors [13,14]. However, diary methods can be time intensive for participants and typically rely entirely on retrospective self-report of activities, a task that is known to be susceptible to various forms of bias—chiefly a bias due to cognitive and memory limitations [15]—resulting in inaccurate reports of the frequency and severity of events.

With the widespread adoption of mobile phones in recent years, new approaches have been developed to use mobile phones for studying real-time or nearly real-time behaviors and attitudes [16]. Mobile phones can be used to collect both ecological momentary assessments (EMAs), such as a brief stress inventory, and automatic passive sensing data (eg, audio and location data collected via microphones and phone GPS). Researchers have successfully related mobile phone sensing features to mental health in a clinical setting [17,18]. Wang and colleagues [19] were among the first to adapt this technology to better understand student mental health with the creation of the StudentLife continuous sensing app. With the StudentLife app, researchers have been able to capture daily fluctuations in students’ mental and emotional well-being by linking passive sensing features (eg, sleep, location, social interaction) to aspects of standard health-related questionnaires [19-21].

Based on prior research using primarily self-report measures, aspects of the college experience are clearly stressful for students ranging from interpersonal relationships to academic achievements. However, one issue with this work is that these measures are often obtained once per term and are thus subject to the limitations and biases of retrospective self-report measures, which makes it difficult to paint an accurate picture of how stress manifests itself in the daily lives of students. Recently, a proof-of-concept study using passive mobile phone sensing investigated the relationship between passive sensing measures and various mental health outcomes (eg, depression, loneliness, stress) [20]. This proof-of-concept study demonstrated the utility of mobile phone sensing apps despite having focused on a relatively small number of sensing-derived features. Here, we expand on this work by focusing on a considerably larger number of passive sensing features to comprehensively categorize a day in the life of a college student and also make use of recently developed advances in modeling, such complex, longitudinal data. As examples of the mobile sensing features become available, inferences can be made about the quality and quantity of an individual’s interpersonal relationships by conversation features or phone usage, about academic-related activity by time spent in study locations, about sleep through a combination of sensing features (eg, periods of movement, presence of light, phone usage), about exercise by the time spent in gymnasiums, and so on. Moreover, these features can be examined not only daily, but also at a finer grain within a day. Looking at the data more minutely could help fingerprint meaningful behavioral patterns in relation to stress. For example, it could be the case that phone usage decreases dramatically during evening hours when stressed, but not globally across the day. Thus, the purpose of this study is to further the understanding of stress dynamics on college campuses by leveraging a dataset rich in passive sensing features to accurately, and naturally, capture possible stressors in the lives of students. Whereas prior work has largely focused on a small number of features, we are able to use an array of mobile sensing features and then subsequently analyze these data with recently developed methods that both account for statistical dependencies inherent in longitudinal data and perform feature estimation and selection on high-dimensional data [22]. By doing so, we are able to identify a collection of mobile sensing features across the domains of social activity, location, and ambient noise that are related to stress levels across the academic term.

Before any analyses, the data were cleaned to remove participants who encountered technological complications with their mobile phone or who failed to respond to more than 50% of the MPSM survey used to measure stress. Additional days were discarded when extreme outliers were observed in the location data (distance >0.975 quantile). The aim here was to remove days when students may have taken a day trip during the term; spending the majority of the day traveling severely skewed location-based data. After this step, the remaining 72 participants had 43.1 days of data on average (SD 11.8). Across these participants, the overall rate of failure to respond to the MPSM survey prompts was 18.57% (576/3101). Next, with the cleaned dataset the relationship between stress (self-reported, range 1-5) and the MPSM was assessed using a mixed-effect model with random subject intercepts. Supporting the MPSM pilot data, MPSM and self-reported stress were strongly related (beta=2.037, SE 0.076, P<.001) providing further validity for the MPSM as a measure of stress. Of general interest was understanding how reported stress unfolded across the term. Thus, the relationship between stress and time was also assessed. A mixed-effect analysis incorporating fixed linear and quadratic time effects, random subject intercepts, and random slopes for both the linear and quadratic effects of time revealed a significant linear effect (beta=1.282, SE 0.509, P=.02) and a significant quadratic effect (beta=–1.203, SE 0.491, P=.02) of time on the MPSM measure of stress, indicating that stress increased across the term but also experienced a bump near the middle of term presumably reflecting stress brought on by midterm exams (Figure 2). This quadratic effect is similar to the patterns observed in past research [20].

Correlation matrices are used to visually assess relationship patterns between variables in high-dimensional data. However, in this dataset, looking at correlations between sensing features may be misleading due to the clustered and unbalanced nature of the data. Thus, Figure 3 was created to aid in visualizing the relationship between stress and the set of sensing features. The estimates in the figure represent the t values from a series of pairwise mixed-effect analyses regressing stress with each of the variables in the dataset. From Figure 3, one can see a few themes emerging. For example, it appears that the majority of sensing features seem to be inversely related to stress. Generally, it also appears that a variety of sensing features see a decrease in usage/occurrence during the evening epoch when stress is high.

Unlike mixed-effect models, GEE (and, as a result, PGEE) are not “full-likelihood” models [29]. Thus missing data must be accommodated differently, here imputed before model fitting. Missing MPSM data points were imputed using Kalman smoothing. Each subject’s trajectory of MPSM scores was treated as a structural time series model and Kalman smoothing was then used to impute the missing values in the time series [30]. In the resulting completed dataset, 10 skewed covariates were transformed using log or log(x+1) transformations (eg, distance traveled, unlock duration). Finally, the outcome variable and covariates were standardized [31] and analyzed using PGEE. Of the 61 features used in the analysis, six were found to be significantly related to levels of stress by the PGEE analysis. Time spent in dining centers (beta=–0.024, robust z=–2.968), distance traveled between 6 pm and 12 am (beta=–0.021, robust z=–2.670), and mean audio amplitude between 6 pm and 12 am (beta=–0.031, robust z=–2.074) were found to be inversely related to stress, whereas time spent in study locations (beta=0.071, robust z=3.569), proportion of time spent conversing between 9 am and 6 pm (beta=0.030, robust z=2.706), and the proportion of conversations occurring between 9 am and 6 pm (beta=0.021, robust z=2.616) were found to be positively associated with stress (Table 1).