The dynamics of adolescents’ pubertal maturation, depressive symptoms and friendship networks: stochastic actor-oriented model

This study aimed to examine whether adolescents select friends based on their friends’ levels of depressive symptoms, and to determine whether the potential homophily phenomenon for depressive symptoms is attenuated after considering pubertal maturation and gender. Data were from the first three waves of the Taiwan Youth Project, a longitudinal study that annually surveys 7th graders from 40 junior high schools. Participants were asked at each wave to fill out a survey including depressive symptoms, pubertal maturation, and to name three best friends in school. Stochastic actor-oriented models were built to explore the dynamic changes in friendship networks by estimating the probability of the friendship connections and behavioral changes depending on the individual’s current network position and behavioral status. We used a sample of 2,336 adolescents. From 8 to 9th grade, adolescents tended to select friends who were similar in terms of their levels of depressive symptoms (B = 0.358, SE = 0.131, p < .001), without adjusting for gender and pubertal maturation. This homophily effect based on depressive symptoms became non-significant when pubertal maturation was included. Adolescents’ depressive symptoms did not further influence their friends’ depression levels, after controlling for pubertal maturation and gender. Future studies should further examine the mechanisms and group dynamics within clusters of adolescents who are depressed. Providing a supportive environment and tools is warranted to help adolescents cope with negative emotions within their peer group.


Introduction
Adolescent depressive symptoms are a serious mental health problem worldwide (Thapar et al., 2012). About 7.5%-11.3% of adolescents are clinically diagnosed with major depressive disorders (Avenevoli et al., 2015;Mojtabai et al., 2016), and 28.7% show depressive symptoms (Vancampfort et al., 2018). Depression in adolescence not only increases the likelihood of long-term harm, such as suicide in adulthood and physical health problems (Thapar et al., 2012), but also impairs adolescents' interpersonal relationships (Zlotnick et al., 2000). Genetics, environmental factors, stressful life events, interpersonal problems, and early maturation are also risk factors for depression (Thapar et al., 2012).
Depression in Taiwanese adolescents is an important and commonly discussed health problem. A study that surveyed junior and senior high school students in southern Taiwan found that 12.3% of the students selfreported being depressed (Lin et al., 2008). Another cross-sectional study based on a self-report that surveyed 1 st , 3 rd , 5 th , and 7 th graders in the north and central Taiwan found that 16.8% of the students were depressed (Chiu et al., 2017). Both were higher than a review study, suggesting that the prevalence rate of clinical depression in ages 13-18 years was 5.6% globally (Costello et al., 2006) and 9% in the National Longitudinal Study of Adolescent Health in the US (Rushton et al., 2002). Similar to the US, Taiwanese adolescents with depressive symptoms are provided access to mental health care, including psychiatrists and clinical psychologists in hospitals and clinics covered by universal health care that is affordable for most families. Counselor services in the school system are free of charge. However, the stigma of mental illness is prevalent in Taiwan, and identifying the symptoms of depression is quite difficult among Taiwanese people (Zhuang et al., 2017). They tend to conceal their mental health problems due to the possibility of unacceptance and misunderstanding on the part of their family and friends (Zhuang et al., 2017). This reluctance to disclose health problems highlights the importance of examining depression and associated factors in Taiwanese adolescents.
Adolescence is a critical period during which young adolescents start to emphasize their school friendship networks instead of their family memberships. The scope of adolescent's friendship network might be subjected to community members, family members and peer group. Friendship networks that shape adolescents' attitudes and provide connections to the society could be the foundation for mental health development for adolescents (Sias & Bartoo, 2007). Friendship networks of adolescents can influence their behavior and mental health by viewing others' behavior and interacting with their peers (Mercken et al., 2010;Snijders et al., 2010). The adolescents' search for affiliation with their peers results in the homophily phenomenon (Dijkstra et al., 2013), which means that adolescents tend to choose friends with similar characteristics (McPherson et al., 2001). Homophily contributes largely to how adolescents form their friendship networks (Schaefer et al., 2011;Young, 2011). Some studies have identified a homophily phenomenon among adolescents with similar depression levels (Cheadle & Goosby, 2012;Van Zalk et al., 2010). This homophily phenomenon-based on depression in adolescents' friendship networks-is the result of two mechanisms: peer selection and peer influence.
Peer selection refers to the fact that adolescents tend to select friends with similar traits or behaviors . This can be explained by the Similarity Attraction Theory (Byrne, 1971), which states that similarity in traits or behaviors enables people to share similar beliefs and provides a sense of belonging. Adolescents often affiliate with friends who are similar to them (Dijkstra et al., 2013). Evidence of peer selection is commonly observed in studies that have examined the impact of depression on friendships in various settings, such as in high school samples in the US, Finland, and Sweden (Cheadle & Goosby, 2012;Kiuru et al., 2012;Van Zalk et al., 2010).
Peer influence refers to the process by which traits or behaviors become similar to those of one's friends over time. For example, one's depression may affect another individual's depression at a later time . Contact with a depressed person is a risk factor for depression. Depressed adolescents may repeatedly talk about their problems and dwell on their negative emotions, in turn further increasing the risk of increasing their friends' depression (Stone et al., 2011). Findings on peer influence, however, are equivocal. One study that surveyed 847 8 th graders annually for 5 years in a mediumsized town in Sweden found that friends may increase each other's depressive symptoms (Van Zalk et al., 2010). Another study, which used a US sample of 7 th -12 th graders from three public rural schools and four private schools, suggested that only boys influence their friends' depression levels (Cheadle & Goosby, 2012). However, a peer influence on depression was not supported by a study on a US sample of 299 6 th graders from a public middle school (DeLay et al., 2017). Besides the inconsistent evidence of peer influence as one of the mechanisms of the potential clustering phenomenon among depressed adolescents, further study is needed in various cultural contexts to determine the influence of society and schooling contexts in each country on adolescent development. The acceptability of help-seeking behavior for depression and access to care may be different across countries. In a sample of Taiwanese adolescents ages 15-19 years, the proportion for psychiatric service-seeking was only 10.7% among adolescents with psychiatric morbidities and 5.5% among those with lifetime suicidal ideations (Pan et al., 2021). A much higher number was reported in a US sample of adolescents, where 25.8%-41.1% of adolescents with suicidal ideations received general medical treatment (Nock et al., 2013). When depressed adolescents have difficulty receiving help for mental health problems, such as in Taiwan, the proportion of depression may be high in a friendship network in school, making peer influence more observable.
The possible homophily phenomenon of depression among adolescents occur almost at the same period when a person is going through pubertal changes, which has been found to be associated with the formation of social networks and to play essential roles in adolescent depression (Hamlat et al., 2020;Kaltiala-Heino et al., 2003a, b). Depression is not common in children, but the prevalence of depression increases in adolescence (Costello et al., 2006). At the same period of time, adolescents encounter physiological and psychological changes to achieve sexual maturation and fertility during puberty, and the timing of puberty typically varies (Pinyerd & Zipf, 2005). Pubertal maturation is often observable because of obvious physical changes, such as growing facial hair or breasts. Having different pubertal timing compared to the majority of one's peers may decrease selfesteem and increase the risk of depression (Kaltiala-Heino & Fröjd, 2011). For example, the School Health Promotion Study that surveyed a sample of 36,549 8 th and 9 th graders in Finland suggested that early maturation was correlated with depression (Kaltiala-Heino et al., 2003a, b). A US study using a sample of 603 youth also indicated that early maturation may predict the onset of depressive symptoms (Hamlat et al., 2020). These studies, although demonstrated an association between pubertal timing and depression when adolescents are situated in a school network, have not examined the potential changes in friendship networks under the influence of depression. In consideration of the association between pubertal maturation and depression, how adolescents' networks may evolve along with changes in depression remains unknown.
Gender is one of the essential determinants of adolescents' friendship formation (Poulin & Pedersen, 2007). Gender differences may exist in terms of how depressive symptoms or pubertal maturation affect adolescents' friendship networks. Gender, depression, and pubertal development are connected within friendship networks. One study indicated that depressed girls are more likely to be socially excluded, yet depressed boys tend to select friends with similar levels of depressive symptoms (Cheadle & Goosby, 2012). Earlymaturing girls in a US sample were more likely to be popular but later became more depressed than their normal or late-maturing peers (Reynolds & Juvonen, 2011). Gender is likely to serve an important role in the relationship among adolescents' friendship networks, depressive symptoms, and pubertal maturation. Gender is a particularly important factor not only because studies on pubertal maturation have been stratified by gender (Reynolds & Juvonen, 2011), gender is also associated with adolescent depression. Consistent findings were reported for girls that early maturation is associated with depression (Conley & Rudolph, 2009;Graber et al., 2004;Hamlat et al., 2020;Kaltiala-Heino et al., 2003a, b), but not yet for boys.
The present study focused on the coevolution of friendship networks, depression, and pubertal maturation of adolescents over time. We used a longitudinal follow-up study to explore the complex interplay among 7 th to 9 th graders in Taiwan to examine the following hypotheses: (1) adolescents select friends based on their friends' levels of depressive symptoms; (2) adolescents' level of depressive symptoms influence their friends' levels; (3) the potential homophily phenomenon for depressive symptoms attenuated after considering pubertal maturation and gender.

Participants
Data in this study were obtained from the Taiwan Youth Project (TYP), a longitudinal study conducted by the Institute of Sociology, Academia Sinica, Taiwan (https:// srda. sinica. edu. tw). The TYP started in 2000 and included two cohorts-7 th (J1) and 9 th (J3) graders-among 40 schools in Northern Taiwan. The TYP used multistage stratified cluster random sampling to select public and private schools from three regions: sixteen schools in Taipei City (the largest metropolitan city in Taiwan), nine in Yi-Lan County (a rural county), and fifteen in Taipei County (a county which is a little less urban than Taipei City). The TYP randomly selected two classes in each school and additionally chose a class of students with special physical abilities. All students in the same class were recruited as participants (Yi, 2016). The TYP represents only populations in the north of Taiwan, but not in other regions. However, because the sample included both a metropolitan city and a rural county, it included adolescents from various levels of socioeconomic status. In the current study, data from the first three waves of the J1 database were used, collecting information from 7 to 9 th graders for each year. The participants included 2,691 from the 7 th grade, 2,684 from the 8 th grade, and 2,665 from the 9 th grade; the number of pooled participants was 2,844. Slightly over half of the participants (51%) were male. The mean age of the participants in the 7 th grade was 13.3 (range 13-17), 14.3 (range 14-18) for the 8 th grade, and 15.3 (15-19) for the 9 th grade.

Study design and approach
Among 40 schools, the TYP randomly selected 2-3 classrooms in each school. Participants in each classroom were all asked to fill out a survey that included assessments in each study wave of social networks, depressive symptoms, and pubertal maturation. Each student was asked to nominate three of that student's best friends in school. Only friends who were also participants in the TYP study were kept for the analysis. If participants did not nominate any friend, they were considered as having no friend. Because not every class in each school was selected, we used classes as the boundary for each student's social network. Participants who had missing values for pubertal maturation or depressive symptom scores were excluded (N = 357). Four of 81 classes-consisting of only female or only male students-were also excluded (N = 151) because the friendship networks of same-sex classes may be different from those of mixed-sex classes, and because we were unable to analyze how gender affected the dynamics of friendship networks in same-sex classes. Data for 2,336 students from 77 classes were used in this study (Fig. 1). The participants nominated 6,863, 6,937, and 6,929 friends for the 7 th , 8 th and 9 th grade, respectively, where 1,440, 2,079, and 2,119 nominated friends did not join the TYP. The study was approved by the Institutional Review Board of the National Cheng Kung University Hospital.

Measures
Pubertal maturation (7 th grade) was evaluated by the Pubertal Development Scale (PDS) in the first wave. Detailed descriptions of the scale have been published elsewhere (Carskadon & Acebo, 1993;Petersen et al., 1988). One study suggested that the PDS is an adequate measurement of pubertal maturation compared with a physical examination (Pompéia et al., 2019), and the PDS has also been found to have a moderately high agreement with the Tanner-derived composite stage (Chan et al., 2010).
In the present study's questionnaire, adolescents were asked five items about the change in their growth spurt, body hair, skin changes (especially pimples), and secondary sexual characteristics depending on the gender. For example, participants were asked, "Would you say your growth in height?" The response options were (1) has not yet begun to spurt, (2) has barely started, (3) is definitely underway, (4) seems completed. For secondary sexual characteristics, boys were asked about changes in their voice and facial hair; girls were asked whether they had started to menstruate or had experienced changes in their breasts. All items were rated on a 4-point Likert scale, except for menarche (yes = 4 and no = 1). We added each participants' item scores and used the Z scores to standardize the scores according to gender. The total scores ranged from 5 to 20. A PDS score was created by categorizing the standardization value into five groups according to the percentile, where a higher score represented earlier timing of pubertal maturation. We used the score of pubertal maturation that was measured only in the 7 th grade to analyze the dynamics of friendship networks because pubertal maturation was relatively constant at that stage of physiological development. Pubertal Development Scale (PDS) was used in TYP. The internal consistency reliability of PDS ranged from 0.56 to 0.95 in other Taiwanese studies (Gau & Soong, 2003;Tsai et al., 2011). Depressive symptoms (7 th to 9 th grade) were measured with a short version of the Symptom Checklist-90-Revised (Derogatis, 1992), which consists of 16 items assessing the frequency of psychological distress (Lin & Yi, 2016). Participants were investigated regarding the symptoms that are typically related to adolescent mental health, such as headaches, dizziness, loneliness, nervousness, insomnia, waking up early, light sleeping, and muscle pain. A 5-point Likert scale was used to measure the frequency of the symptoms, and all the scores were added together. The total scores ranged from 16 to 80, where a higher score represented a higher level of depression. We calculated the corresponding cutoff number at the 20 th , 40 th , 60 th , and 80 th percentile in order to divide the participants into five groups the same cutoff was applied for the following waves. Cronbach's alpha values for the 7 th to the 9 th grade were 0.88, 0.86, and 0.87, respectively. The Cronbach's Alpha value of the Symptom Checklist-90-Revised in Chinese language is 0.96 in a China study (Guo et al., 2016). Previous researchers using TYP data have demonstrated that the Cronbach's alpha value of depression is between 0.74 and 0.79 (Sze et al., 2013;Yi et al., 2009).

Analytical strategy
We described the proportion of male participants, depressive symptoms. and pubertal development scores. The network descriptive statistics included the following: the average number of nominated friends (out-degree), the number of friends nominated by the participants (in-degree), the proportion of the tendency to form mutual friendships (reciprocity), and the tendency to select a friend who was the friend of a friend (transitive triplets). To measure the stability of the networks between each of the two waves, we calculated the Jaccard index, which is the fraction of the number of friendship ties maintained among the number of friendship ties dissolved, emerged, and maintained   (Fig. 2). We also calculated the Pearson's correlation coefficient between depressive symptoms and pubertal maturation.
Stochastic actor-oriented models (SAOMs) were built to explore the simultaneous evolution of the friendship networks, depression, and pubertal maturation using the Simulation Investigation for Empirical Network Analysis (SIENA) program in R . SAOMs have been used successfully to examine peer selection and peer influence effects regarding delinquency and mental health status in adolescents (Huang et al., 2014;Mercken et al., 2012). SAOMs were used to analyze the changes in how people select friends (network effects) and how people's behaviors changed due to their friends' behaviors (behavior effect). Participants who proactively nominated friends were called "ego," and those who passively received a nomination were called "alter." The estimation was based on a continuous-time Markov chain Monte Carlo algorithm and tested using the t-ratios with an approximate, standard normal distribution . At any given moment, the SAOMs chose one study participant (also called "ego") to determine the probability of a tie (i.e., a connection between two study participants) and behavioral change depending on this ego's current network position and behavioral status .

In the 7 th grade
In the 8 th grade In the 9 th grade The SAOMs included four functions: the network rate (we refer to it as the "rate of friendship"), the behavior rate (the "rate of depressive symptoms"), the network evaluation, and the behavior evaluation. The "rate of friendship" is defined as the expected frequencies at which actors get the opportunity to change their friendship ties. The "rate of depressive symptoms" is defined as the expected frequencies at which actors get the opportunity to change their levels of depressive symptoms. The network evaluation function for the selected ego i is defined as In this function, net k are parameters, and s net ik (x, v) are network effects based on an ego's attributes ( v ), as defined in  (x, v, z) represents the changes in depressive symptoms ( z ) as the friendship networks ( x ) and other variables ( v, e.g., gender and early maturation) were included (Table 2). We conducted analyses on 77 friendship networks and used the overall maximum convergence ratio to evaluate how well the SAOMs fit each friendship network. The overall maximum convergence ratio needs to be less than 0.25 . We then used a meta-analysis to combine each parameter from the 77 friendship networks Table 1 Description of network dynamic parameters in the SAOMs a When ego i nominated actor j as a friend, we denoted the tie as x ij = 1 . When the friendship tie between ego i and actor j disappeared, we denoted it as x ij = 0 b sim v ij = max ij |vi−vj|−|vi−vj| max ij |vi−vj| c sim v is the mean of all similarity scores d v j represents the level of a nominated friend's (also noted as actor j ) depressive symptoms or early maturation because each friendship network is independent. A parameter that had a standard error larger than five would not be combined with the results of the meta-analysis, resulting in different degrees of freedom in each parameter in the same model . Between-class differences were computed with an approximate chi-square test of parameter variances (Snijders & Baerveldt, 2003). Each parameter within each model was evaluated by a chi-square test.
The SAOM can model changes in social networks longitudinally; however, when changes are not consistent over time, the analysis of the peer selection and influence effect needs to be conducted separately (Mercken et al., 2012). The score for depressive symptoms was significantly higher in the 9 th grade than in the 7 th grade (Strong et al., 2016). Thus, all of the analyses were separated into two periods: 7 th to 8 th grade (period 1) and 8 th to 9 th grade (period 2).

Network effects
We used three effects to capture the friendship network structure : the tendency to select someone as a friend (out-degree), the tendency to form a mutual friendship (reciprocity), and the tendency to select a friend who was the friend of a friend (transitive triplets). To determine the impact of pubertal maturation and depressive symptoms on friendship networks, we estimated peer selection based on three effects: the tendency to select friends based on pubertal maturation or the depressive symptoms of the alter (shortened into early maturation alter or depressed alter), the impact of pubertal maturation and depressive symptoms on the nomination of friends of the ego (shortened into "early maturation ego" or "depressed ego"), and the tendency to select friends with a similar level of pubertal maturation or depressive symptoms (shortened into "early maturation similarity" or "depressive symptoms similarity"). We also controlled for the tendency to select friends of the same gender (shortened into "gender similarity") because gender homophily is an important feature of adolescent networks (Poulin & Pedersen, 2007).

Depressive symptoms effects
We used two effects to describe changes in depressive symptoms: a linear and a quadratic shape effect. The linear shape effect refers to the basic drive toward high values on depressive symptoms . The quadratic shape effect is the effect of depressive symptom on itself and is relevant only when we have three or more categories in depressive symptoms, which was the case in our study . To explore the potential mechanism of depressive symptoms spreading among the adolescents, we estimated the peer influence effect by the adolescents' tendency to change their own level of depressive symptoms in response to the mean of their friends' level of depressive symptoms (shortened into "average alter").
To address the first research question that attempted to determine whether adolescents select friends based on their friends' levels of depressive symptoms, or whether adolescents' level of depressive symptoms influences that of their friends, we estimated the basic network effects (out-degree, reciprocity, and transitive triplets), peer selection effects on depressive symptoms (depressed alter, depressed ego, and depressive symptoms similarity), and the peer influence effect on depressive symptoms (average alter). To answer the second research question that examined whether the Table 2 Description of behavior dynamic parameters in the SAOMs a z i represented the level of an ego's depressive symptoms b When ego i nominated actor j as a friend, we denoted the tie as x ij = 1 . When the friendship tie between ego i and actor j dissolved, we denoted it as x ij = 0 c v j represented the level of a nominated friend's (also noted as actor j ) early maturation or whether this friend is male Effects in the current study Mathematical Formula s beh i (x) =

Description
Linear shape z i The overall shape of the distribution of depressive symptoms Quadratic shape z 2 i The tendency for changes in the level of depressive symptoms depending on initial levels, e.g. the positive parameter "Quadratic shape" represented that changes in the level of depressive symptoms were self-reinforcing, like a U shape Average alter The tendency of participants to have a level of depressive symptoms similar to that of their friends Effect from male z i v i Gender associated with changes in level of depressive symptoms, e.g. the positive parameter "Effect from male" represented that boys were more likely to have higher depression levels Effect from early maturation ego z i v i Early maturation associated with changes in the level of depressive symptoms, e.g. the positive parameter "Effect from early maturation ego" represented that earlymaturing students were more likely to have higher depression levels potential homophily phenomenon for depressive symptoms was attenuated after considering pubertal maturation and gender, we controlled for the male similarity effect in the model, estimating the relationship between depressive symptoms and friendship networks. We further adjusted the peer selection effect on pubertal maturation (early maturation alter, early maturation ego, and early maturation similarity).

Results
Results for the descriptive statistics are listed in Table 3. The average number of nominations and the average number nominated as best friends both decreased slightly from 7 to 9 th grade. The proportion of reciprocity and transitivity increased slightly over time, indicating that students formed friendships with their classmates as the mutual familiarity increased. Overall, 9 th graders were more depressed than 7 th graders. The Jaccard index was 0.14 to 0.49 between 7 to 8 th grade and 0.22 to 0.57 between 8 and 9 th grade. The correlation coefficients between pubertal maturation and depressive symptoms in the 7 th , 8 th , and 9 th grades were 0.08, 0.05, and 0.09, respectively. All of the overall maximum convergence ratios for the friendship networks were less than 0.25. The results of peer selection and the influence effects of depressive symptoms are listed in Table 4 to answer the question as to whether depressive symptoms had an impact on the friendship networks among adolescents. Adolescents tended to select friends with a similar level of depressive symptoms in period 2 (depressive symptoms similarity: B = 0.358, SE = 0.131, p = 0.01), but not in period 1. Also in period 2, the more depressed an adolescent was, the less chance there was that person would be nominated as a friend (depressed alter: B = -0.043, SE = 0.021, p = 0.045). Both effects were found to be significant only in period 2. The adolescents' levels of depressive symptoms were not influenced by their friends' (average alter: period 1: B = 0.112, SE = 0.058, p = 0.063; period 2: B = 0.060, SE = 0.057, p = 0.307). The positive linear shape effect indicated that adolescents' levels of depressive symptoms tended to move toward higher values (linear shape: period 1: B = 0.094, SE = 0.025, p < 0.001; period 2: B = 0.321, SE = 0.028, p < 0.001). The positive quadratic shape effect indicated that changes in the adolescents' levels of depressive symptoms were The chi-square test indicated only one significant betweenclass differences result: the rate of friendship in period 1 ( x 2 = 100, p = 0.034). After identifying the peer selection and influence effects of depressive symptoms, we further estimated the impact of gender on the relationship between depressive symptoms and friendship networks, as shown in Table 5. The results suggest that the impact of gender diminished the tendency to select friends with lower levels of depressive symptoms (depressed alter: B = -0.037, SE = 0.021, p = 0.084), and the similarity of depressive symptoms effect became smaller (depressive symptoms similarity: B = 0.290, SE = 0.13, p = 0.033). As regards the peer influence effect, the adolescents tended to change their level of depressive symptoms in response to their friends' symptoms in period 1 (average alter: B = 0.115, SE = 0.055, p = 0.045). Adolescents tended to nominate friends of the same gender (gender similarity: period 1: B = 1.13, SE = 0.061, p < 0.001; period 2: B = 1.147, SE = 0.06, p < 0.001). Two significant chi-square test results for between-class differences were observed: rate friendship in period 1 ( x 2 = 103, p = 0.021) and out-degree in period 2 ( x 2 = 104, p = 0.018).
Finally, we further controlled for the impact of pubertal maturation on the relationship between depressive symptoms and friendship networks. The results are listed in Table 6. The effect of similarities in depressive symptoms became non-significant. Adolescents with similar levels of pubertal maturation had a higher likelihood of being nominated as a friend in period 2 (early maturation similarity: B = 0.176, SE = 0.064, p = 0.01). Early-maturing adolescents were more likely to be nominated as friends only in period 1 (early maturation alter: B = 0.034, SE = 0.013, p = 0.01), but they nominated fewer friends in period 2 than the normal or late-maturing adolescents (early maturation ego: B = -0.039, SE = 0.015, p = 0.013). Girls were more likely to have a higher level of depressive symptoms than boys over time (effect from male: period 1: B = -0.172, SE = 0.061, p = 0.008; period 2: B = -0.157, SE = 0.063, p = 0.018). Early-maturing adolescents became more depressed in period 2 (effect from early maturation ego: B = 0.062, SE = 0.021, p = 0.005).

Discussion
To our knowledge, this is one of the first studies to examine the complex longitudinal interplay among friendship networks, depressive symptoms, and pubertal maturation in adolescents. The tendency to select friends with similar levels of depressive symptoms was significant only from the 8 th to the 9 th grade, suggesting that a higher level of depressive symptoms may amplify the relationship between depression and friendship networks. Pubertal maturation also influenced the similarity effect of depression. As regards the peer influence effect, after controlling for pubertal maturation and gender, adolescents' depressive symptoms did not further influence their friends in any period.
Adolescents tend to select friends based on their similarity of depressive symptoms, a finding that is in line with previous studies (Cheadle & Goosby, 2012;Kiuru et al., 2012;Van Zalk et al., 2010). Adolescents select friends based not only on observable behaviors such as smoking and drinking (Huang et al., 2014;Mercken et al., 2012), but also based on the similarity of internal mental health states. We also found that depressed adolescents were more likely to be excluded from their peers, suggesting that social exclusion may exacerbate depressive symptoms (Leary, 1990). The stigma of mental illness may be one of the reasons that causes depressed adolescents to be isolated. Thus, improving mental health literacy among the Taiwanese public requires more efforts in the educational system. However, the impact of depressive symptoms on friendship networks was found only from the 8 th to the 9 th grade. One of the possible explanations for this finding is that the association between depression and the friendship networks was more easily observed when the adolescents were more depressed. Adolescents in the 9 th grade in Taiwan are more depressed than adolescents in other grades (Strong et al., 2016). The reason adolescents select friends based on the similarity of levels of depression may be due to the finding that adolescents need to seek social support from friends who are similar to them and who understand their feelings when they are under intense stress (Wilks & Spivey, 2010). The potentially magnifying effect of stress on adolescents' depressive symptoms affects the formation of their social ties. Providing a supportive environment and the tools to help adolescents cope with negative emotions with their peers is warranted. We did not observe the effect of peer influences on depressive symptoms in our study. Peer influences on depression can usually be explained by co-rumination (Van Zalk et al., 2010), meaning that depressed adolescents may rehash their problems and dwell on their negative emotions, thereby further increasing the risk of incurring their friends' depression (Stone et al., 2011). Because the peer influence effect was not observed in our sample, the adolescents may have clustered to give each other social support instead of co-ruminating. Another possible reason that peer influence was not significant in our sample-but significant in other studies (Cheadle & Goosby, 2012;Kiuru et al., 2012;Van Zalk et al., 2010)-could be our relatively younger sample: 9 th graders. Studies that have identified the peer influence effect of depressive symptoms includes mostly adolescents up to 12 th grade or the age of eighteen (Cheadle & Goosby, 2012;Kiuru et al., 2012;Van Zalk et al., 2010). One study that used a younger sample (6 th graders in the Southwest US) did not find a significant peer influence effect of depression (DeLay et al., 2017). Older adolescents have a higher incidence of depression, which may be due to their cognitive maturation and increased response to stress (Thapar et al., 2012). Determining the influencing effects of friendships on depressive symptoms may also require more observation time.
Pubertal maturation attenuated the similarity effect of depressive symptoms in our sample. Pubertal maturation is a key factor in the formation of adolescents' friendship networks because adolescents tend to select friends at similar levels of pubertal maturation. Our finding was in line with a previous study that found that friendship formation is based on pubertal maturation (Franken et al., 2016). Choosing friends based on pubertal maturation may be explained by the Similarity Attraction Theory (Byrne, 1971). The somatic changes that occur due to puberty may be more easily perceived in adolescents than the psychological traits such as depressive symptoms. Thus, adolescents may be attracted to peers with similar levels of pubertal maturation. Another possible reason that the depression similarity effect was attenuated by the puberty similarity effect might be that early-maturing adolescents are more depressed than normal or latematuring adolescents (Benoit et al., 2013;Kaltiala-Heino et al., 2003a, b). Because the adolescents tended to form friendship ties with those at similar levels of pubertal maturation, the clustering of adolescents with a similar level of depressive symptoms may be partly explained by the clustering of similar levels of pubertal maturation.
Gender did not attenuate the similarity effect of depressive symptoms as much as pubertal maturation in our sample. Two previous studies from Finland and Sweden also did not find that gender had an effect on friendship formation among adolescents (Kiuru et al., 2012;Van Zalk et al., 2010), but one study from the US found that gender differences in friendship formation were based on depressive symptoms (Cheadle & Goosby, 2012). Although adolescents of the same gender were more likely to form friendships in our sample, the significance of the similarity effect of depressive symptoms was not influenced by the clustering of adolescents of the same gender. The effect of gender and the interaction with pubertal maturation and social networks warrants more attention. First, we found that the prevalence rate of depression after puberty became higher in girls than in boys. Similarly, several studies have identified a faster slope of increase in depressive symptoms among girls than among boys (Angold & Worthman, 1993;DeRose et al., 2006;Ge et al., 2001;Hayward & Sanborn, 2002;Nolen-Hoeksema & Hilt, 1994;Thapar et al., 2012). This faster slope may be due mainly to the interaction between pubertal development and psychosocial vulnerability factors, the negative emotional arousal elicited by changes in biological systems, and by the different reactions between boys and girls when facing social challenges (DeRose et al., 2006;Thapar et al., 2012). Additionally, the relationship between puberty and depression might differ in boys and girls. Some studies suggest that-although early maturation is associated with elevated depression in girls (Conley & Rudolph, 2009;Graber et al., 2004;Hamlat et al., 2020;Kaltiala-Heino et al., 2003a, b)-the relationship between boys and pubertal timing is diverse. Two studies have suggested that late maturation is associated with depression in boys (Conley & Rudolph, 2009;Graber et al., 2004): one suggested that both early and late maturation is associated with depression in boys (Kaltiala-Heino et al., 2003a, b), and the other study suggested that early maturation is associated with depression in boys (Hamlat et al., 2020). Overall, the independent effect of gender or pubertal maturation on depression is difficult to separate because of the interconnectedness of gender and pubertal maturation.
Our study has several limitations. First, the measurement of pubertal maturation was self-reported and not supported by clinical examinations. Adolescents may have inaccurately reported their pubertal staging since the consistency between child-reported and clinical examinations is not high (kappa value ranges from 0.37 to 0 0.60) (Chan et al., 2010;Shirtcliff et al., 2009). Second, friendships outside of school were not considered in this study because we did not have information regarding students who did not participate in the TYP study. We were unable to determine whether friendships outside of school increased or decreased the levels of depression in our study sample. One study indicated that friendships outside of school can also influence adolescents' depression levels (Van Zalk et al., 2010). Estimating the influence of friendships outside of the entire network would require the development of statistical methods. We might have misclassified some participants who only had friendship relations with people outside of school as having no or few friends. However, not having any friends in school, regardless of having friendships outside of school, might still be a sign of low social integration and may be associated with depression. Thirdly, the nominations of best friends were restricted to only three classmates, which may not have completely captured all of the features of adolescents' networks, but rather captured only the most important friendships. However, some other studies also restricted friend nominations to three (Kiuru et al., 2012;Van Zalk et al., 2010) because three nominations were considered sufficient to display a stable network structure (Yang et al., 2009). Finally, depressive symptoms were assessed using a scale that put more focus on psychosomatic symptoms. Although appropriate for adolescents recruited in Taiwan in year 2000, there might be measurement tools that are developed and validated in recent decades.
In conclusion, our study provides evidence regarding how depressive symptoms affect friendship formation among Asian adolescents. Even though clustering of depressive symptoms was observed in our study, it was affected by pubertal maturation and stress. The impact of pubertal maturation on friendship networks may be stronger than the impact of depressive symptoms. We also found that the clustering of depressed adolescents did not further increase their depression levels. Depressed adolescents may cluster to seek social support from friends who have similar symptoms of depression. Future studies should further examine the mechanisms and group dynamics within clusters of depressed adolescents. Clustering of adolescents based on level of depression is a global and ubiquitous phenomenon, and we added evidence from Asia. This study provides some practical implications. We found that depressed adolescents are less likely to form friendship ties than non-depressed adolescents. Schools and teachers should consider providing programs to help depressed adolescents expand their social networks. Adolescents need programs not only for reducing depression, but also programs that help them learn interpersonal social skills. A universal program in school to reduce mental health-related stigma would also be helpful to improve the connections among adolescents with different levels of depression. Including more mental health literacy in regular classes may help depressed adolescents feel less marginalized in terms of their friendship networks. Interventions such as school-based anti-stigma programs that focused on knowledge acquisition and attitudes about mental illness can effectively empower students and encourage their willingness to interact and seek help (Lanfredi et al., 2019). Data availability statements Publicly available datasets were analyzed in this study. This data can be found here: https:// srda. sinica. edu. tw/ brows ingby datat ype_ result. php? categ ory= surve ymeth od& type= 2& csid=1.

Declarations
Ethical approval The study involving human participants was reviewed and approved by Institutional Review Board at the National Cheng Kung University Hospital in Taiwan (B-ER-107-028). Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.

Conflict of interest All authors declared no conflicts of interest.
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