Conceptual clarifications

Social contagion refers to the spread or transmission of behaviors, emotions, or attitudes through a population, group or network. Social contagion theory is thus a theory of social influence, but with a specific focus: to what degree does the presence of X (e.g., school-related stress) in a population influence the probability of X in an individual who in some way interacts with this population?

The definition of stress in this study draws on Lazarus’ & Folkman’s [19] transactional model of stress and coping. The model posits that stress reactions arise from individuals’ appraisals of a situation. Primary appraisals refer to whether a situation – a potential stressor – is judged to pose a threat to the person’s safety or well-being. Secondary appraisals refer to whether the person assesses that they can cope with the situation, given their available resources. If a situation is deemed both threatening and difficult to cope with, emotional, behavioral, cognitive and/or stress reactions can occur. School-related stress thus refers to stress reactions triggered by situations in school. In qualitative studies, adolescent students largely use the term stress to describe negative experiences (i.e., as distress; see [20,21]), and report that school-related stress manifests as worry or rumination, unpleasant emotions and psychosomatic problems [10,22,23].

Social contagion of school-related stress

A key precondition for stress contagion is that stress reactions are observable. Only if stress reactions can be detected, consciously or unconsciously, by others will they influence other students. Behavioral stress reactions are often readily observable, as in restlessness, pacing, fidgeting, or irritability. Emotional stress reactions may be less visible, but research suggests that emotion recognition among humans tends to be at least moderately accurate among people in the same group [24].

Importantly, qualitative research provides some evidence that stress is often openly displayed in school, and that students can perceive when their classmates experience stress. For instance, Spencer et al. [3] write that American high school students reported “pervasive stress to be the norm” and that ”girls who were not showing signs that they were experiencing high levels of stress” were interpreted as “not working hard enough”. Studies of Swedish secondary students corroborate this picture: Låftman et al. [9] write about “a culture of stress in the school”, with one informant stating that students “get stressed out too much”, while Perming et al. [10] report that most of the students “could give examples of how stress manifests itself in others; for example, they seem to be tense, walk fast” and be “easily irritated or angry”.

Beyond this basic precondition, there are at least three mechanisms through which stress can spread in school. First, classmates’ stress reactions are a potentially useful source of information [25]. If others are stressed about a test, it may indicate that the test is consequential and that there may be negative consequences if one fails. In other words, classmates’ appraisals of the situation, expressed through their stress reactions, may influence a student’s primary appraisal of the same situation as threatening. This first mechanism is a form of object-related contagion, where the object of others’ stress is also the object of my stress. Second, if my classmates are stressed about a school task, I may worry about their well-being, even if I do not feel stress about that specific task. Thus, the classmates themselves can become the object of my stress. This is a form person-related stress transmission [25]. Third, emotional contagion theory [26] posits that emotions can spread directly from person to person. This transmission is largely automatic and unconscious and occurs when the ego mimics the facial expression of others (i.e., mimicry), and this then influences the emotional states of the ego.

Institutional background

Swedish compulsory school lasts 10 years (ages 6–16) and is divided into three stages: elementary school (grades 0–3), middle school (grades 4–6), and lower secondary school (grades 7–9). Our data were collected at the end of middle school (grade 6) and the end of lower secondary school (grade 9). The transition from middle to lower secondary school often involves a change in school and classroom composition. While students generally remain with the same classmates throughout grades 4–6 and grades 7–9, the transition in between can entail enrollment in a new and larger school (e.g., 3–6 classes per grade, compared to 1–3 classes in middle school) where students are redistributed into partly new class configurations and face a more complex school environment. The transition to lower secondary school also implies an intensification of academic demands and associated performance-related stress. School-related stress generally peaks in the final year of compulsory school (grade 9) [27], reflecting both developmental factors and the importance of students’ compulsory school leaving grades for access to upper secondary school.

Participants

We used data from the Evaluation Through Follow-Up (ETF) project, collected by the University of Gothenburg in collaboration with Statistics Sweden [28,29]. The ETF project has collected nationally representative and longitudinal data on different cohorts of Swedish students since the 1960s. In this study, we used data from the two most recent cohorts with complete compulsory school data: cohorts born in 1998 and 2004 and surveyed in grades 6 (age 12–13) and 9 (age 15–16), with data collected between 2011 and 2020.

Approximately 10 000 students were selected in each cohort through cluster sampling, with schools as the primary sampling unit and all students in the selected schools invited to participate. The sample was drawn based on students’ school registration in grade 3, but the surveys were conducted in grades 6 and 9, meaning some students attended different schools when they were surveyed. In the 1998 cohort, 8,007 students (87%) responded to the grade 6 survey and 4,573 (47%) to the grade 9 survey. In the 2004 cohort, 5,190 students (53%) responded to the grade 6 survey and 2,523 (26%) to the grade 9 survey. All participating students were included in the analysis. Non-participating students were excluded. 51.7% of the participants were girls. The average age was 13.0 year (SD = 0.18) in grade 6 and 16.0 years (SD = 0.19) in grade 9.

We examined whether attrition between waves was related to school-related stress (S3 Text and S4 Table). In unadjusted models, both individual stress and class-level stress in grade 6 weakly predicted non-response in grade 9. However, these associations vanished after adjusting for the basic demographic covariates that are included in the main analyses (see below), indicating that attrition is driven by observed and measured characteristics rather than by stress itself.

School-related stress

School-related stress is in ETF measured using a single item: “How well do the following statements describe your situation at school? I feel stressed”. Response options were [5] “Always / almost always”, [4] “Often”, [3] “Sometimes”, [2] “Rarely”, and [1] “Never/almost never”. Compared to more comprehensive instruments, single items may have lower reliability and content validity. We nonetheless believe the item was useful in this context, for three reasons. First, as evidenced by qualitative research [9,10,20–23], the key term – (school-related) stress – clearly resonates with students, indicating face validity. In these studies, students also describe the different sources (assessments, expectations, time pressure) and manifestations (physiological, psychosomatic, emotional) of stress in ways that resemble both the generic definition of stress in the transactional model [19] and the different facets of stress captured by more comprehensive psychometric instruments [1]. Second, the item is strongly correlated with measures of psychosomatic (r = 0.47–0.53, depending on grade) and emotional (r = 0.56) problems, as well as with school-related worry (r = 0.51–0.52), indicating criterion validity (see S5 Text and S6 Table). Third, Lindblad et al. [30] showed that a similar global item was highly correlated with both factors extracted from a detailed 11 item stress scale, tested on Swedish adolescents.

Multiverse analysis: defining the model space

The first step in multiverse analysis is defining the model space, that is, identifying the different model ingredients that result from combining different reasonable analytical decisions [18]. In defining the model space, we drew on previous research on social contagion effects (see below). We only considered model ingredients that were possible given the available data. Additionally, we assumed that the goal of the analysis was to identify causal contagion effects. Correlation between individual and peer outcomes, such as similarities in stress levels among students in a class, can arise from three different processes [13]. (a) Correlated effects: students may be similar because they have similar pre-existing characteristics (homophily/selection) or because they share common environmental exposures (confounding); (b) Simultaneity: the individual student may be affected by his or her peers, but may simultaneously influence these peers (i.e., reverse causation). (c) Social contagion effects: individual students’ outcomes are directly influenced by their peers’ outcomes.

The challenge in research on social contagion is to disentangle the social contagion effect from the other sources generating similarity between individual and group outcomes [13]. Researchers have used different strategies to this end, with the perhaps most notable analytical choice concerning the type of statistical model. Other important choices concern restrictions on the sample, the link function used in the model, the measurement of individual and peer characteristics, and the control variables to be included.

Defining the estimand

Our target estimand [31] is the average causal effect of classmates’ stress on individual student stress: the expected change in a student’s stress level associated with a one-unit increase in the average stress level of their classmates. The four model types we employ use different sources of identifying variation, but all target this same causal parameter under varying assumptions about correlated effects and simultaneity.

Type of model

Unit fixed effects (FE) model.

Unit-FE models only utilize variation in treatment and outcomes within units between measurement points for estimation. This model estimates the average effect of changes in classmates’ stress on individual stress among students who experience variation in exposure over time. Since the exposure – classmates’ stress – is continuous, virtually all (98.3%) students do experience some variation. By design, unit FE addresses correlated effects – both selection into classrooms and confounding – as long as these are time-invariant, but does not resolve simultaneity, as it cannot distinguish whether changes in classmates’ stress induce changes in individual stress or vice versa. Unit-FE models are, moreover, sensitive to dynamic effects, and can produce biased estimates if past treatments directly affect current outcomes or past outcomes directly affect current treatment [32]. Unit FE models are popular in economics, sociology and political science, with Hanushek et al. [33] and Raabe & Wölfer [34] being examples of studies using this approach to study social contagion.

In this study, the unit-FE model was specified as follows:

Where the change in stress of student i in class c and grade t between grades 6 and 9 is modelled as a function of the corresponding change in their classmates’ stress (), a vector of covariates (X; described below), a grade fixed effect (τ; capturing all temporal changes that are common to all students), a unit fixed effect (α), and an error term () that is assumed to be uncorrelated with classmates’ stress. The key parameter of the model is , which captures the contemporaneous effect of (a change in) classmates’ stress on individual stress.

Lagged dependent variable (LDV) model.

LDV-models estimate the average effect of classmates’ stress on individual stress by including lagged values of the outcome variable as a control. The lagged outcome adjusts for time-invariant selection and confounding that influence baseline stress, thereby addressing correlated effects that operate through these pathways [35]. It does not, however address time-varying confounding between measurement waves [36]. The model partially mitigates simultaneity by conditioning on pre-existing stress levels, but simultaneity bias remains a concern because classmates’ stress and individual stress are measured concurrently in grade 9. The works of Christakis & Fowler [37] are examples of the use of LDVs in the context of social contagion research.

In this study, the LDV model was specified as follows:

Where is the stress score of student i in grade 6. The key parameter is , which reflects the contemporaneous effect of classmates’ stress on individual stress in grade 9. Since the model does not adjust for past values of classmates’ stress, also captures any lagged effects of classmates’ stress that are mediated by current classmates’ stress.

Prospective cohort model.

Prospective models estimate the average effect of classmates’ stress on individual stress by using lagged classmates’ stress to predict current individual stress, typically while controlling for lagged individual stress. This temporal ordering – where classmates’ stress is measured before the outcome – directly addresses simultaneity concerns by ensuring that individual stress cannot cause classmates’ stress [38]. The model adjusts for correlated effects to the extent these are captured by baseline individual stress, but remains vulnerable to time-varying confounding between measurement waves and to unobserved selection or confounding not reflected in baseline controls. Prospective models are popular in epidemiology and psychology [39], with examples of such approaches in social contagion research being Alho et al. [40] Mendoza & King [41].

The prospective model was specified as follows:

Where is the stress score of student i’s classmates in grade 6. The key parameter is , which reflects the lagged effect of classmates’ stress.

School fixed effects (FE) model.

In schools with more than one class, school-FE models estimate the average effect of classmates’ stress on individual stress by comparing students across classes within the same school, thereby exploiting within-school between-class variation. This approach automatically adjusts for all school-level confounding factors (resources, policies, neighborhood characteristics), thereby addressing correlated effects operating at the school level. Selection into classes may also be less problematic than selection into schools, as class assignments are typically determined by administrators. However, school FE does not control for individual-level time-invariant confounding or within-school selection, and does not resolve simultaneity bias as individual and classmates’ stress are measured concurrently. Moreover, if contagion effects are heterogenous across school size, the school-FE estimates may diverge from the average treatment effect since only students in schools with at least two classes will contribute to the estimates. School-FE models have been extensively used to study social contagion in economics [33,42].

The school-FE model was specified as follows:

Where is the school fixed effects. The school-FE model was fitted as a cross-sectional model on the grade 6 students since the participants in ETF are dispersed into more schools after the transition to the upper stage of compulsory school in grade 9. School fixed effects can in principle be incorporated in a longitudinal model, but a cross-sectional analysis was chosen here since school fixed effects is among the most important tools used for drawing causal conclusions concerning contagion from cross-sectional data [43].

Table 1 summarizes the model types.

Download:

• PNG
  larger image
• TIFF
  original image

Table 1. Summary of model types.

https://doi.org/10.1371/journal.pone.0348437.t001

Sample restrictions and conditions

Operationalization of stress and choice of link function

Control variables

The last set of analytical decisions considered in this study is the choice of control variables (the “X” in the above-described statistical models). Control variables should block the influence of confounders, but not block mediating pathways through which the treatment exerts its influence. Socio-demographic variables may influence, but are not influenced by, classmates’ stress, and were therefore included in all models. These included student grade level, sex, immigration status, parental education, age, and birth cohort, as well as the class average share of girls, foreign-born students, and students with university-educated parents. We also consistently controlled for school ownership (independent vs. public).

The status of other potential control variables available in ETF is less straight-forward, since they may both influence and be influenced by classmates’ stress. These included teaching practices (teacher-centered, student-centered, or student dominated [49]); the class average cognitive ability, grade point average, and share of students with special educational support (as measures of class achievement); as well as class-average indicators of self-reported social exclusion in school, self-reported academic demands, and achievement goal orientations (performance and mastery goals). We measured these as class averages or shares to align them with the measurement of the focal treatment variable. For the additional control variables, we included every possible combination of four of these variables. We restricted the number of additional variables to four per model, since the number of unique combinations increases exponentially with the number of control variables.

The exact measurement of all covariates, along with summary statistics, is described in S1 Table and S2 Table.

Summary of the multiverse analysis

In a multiverse analysis, the results are primarily summarized using descriptive statistics, such as the mean, median or range of the estimates, or the share of the estimates that are positive, negative and statistically significant. In addition, Young & Holsteen [18] propose a measure called the robustness ratio:

Where is the average regression coefficient (or odds ratio), is the average standard error of the regression coefficients, and is the standard deviation of the combined regression coefficients. A higher mean estimate, combined with a lower sampling uncertainty (as captured by ) or model uncertainty (as captured by ), generates a greater robustness ratio and hence indicate more robust results. The robustness ratio is designed to be analogous to a t-statistic in conventional regression analysis, and Young & Holsteen (2017) suggest as a rule of thumb that robustness ratios larger than 2 can be interpreted as indicating robust results.

Table 2 summarizes the different model specifications. In total, 9,240 different models were estimated. Cognitive ability was only available in grade 6, and grade point average in grade 9, meaning that the number of additional control variables varied between different types of models.

Download:

• PNG
  larger image
• TIFF
  original image

Table 2. Summary of analytical decisions.

https://doi.org/10.1371/journal.pone.0348437.t002

All analyses were conducted using Stata v 18. Multiverse analysis used the multivrs-program for Stata [18]. Ethical approval for use of ETF data was granted by the Swedish Ethical Review Authority on December 16 2024 (reference number: 2024-07679-01). Data were accessed from 15.09.2025 to 24.02.2026. The authors did not have access to information that could identify individual participants during or after data collection. All participants and their guardians provided written informed consent to the use of their data for research purposes. The study was conducted in accordance with the principles of the Declaration of Helsinki.

Limitations

There are data limitations that restrict the veracity and generalizability of our results. First, stress was measured using a single item, restricting reliability and content validity and increasing measurement error. The importance of measurement error may be compounded when aggregating responses to the class level. Second, there were missing data on classmates, especially in grade 9, which could further compound measurement error. Third, we did not have sociometric data. If students are influenced more by close friends than by the overall class, contagion effects will likely be underestimated. Moreover, lack of sociometric data precludes the use of social network models used to disentangle selection from influence effects. Fourth, the three-year gap between measurements is substantial relative to the likely timescale of stress contagion. In the LDV models, using lagged stress measured three years prior to the outcome may inadequately capture time-varying confounding or selection, although the direction of this form of bias cannot be ascertained á priori. The estimates of the prospective models may be attenuated if the true effects weaken over time, while the long interval may introduce noise from intervening factors in the unit FE models; in both cases likely drawing the estimates towards the null. The modest effect sizes we observe may, thus, partly reflect attenuation due to temporal distance. More, or more proximately spaced, measurements may have provided greater power to detect contagion effects. Lastly, for practical purposes, we did not cover the full space of plausible models. For instance, apart from the LDV and prospective models, the four types of models included in our multiverse analysis can be combined in almost any way, and the number of combinations of potentially relevant confounders is practically infinite.