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Sicheng Xiong Department of Psychology, Hunan University of Chinese Medicine, Hunan, China

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Yi Xu Department of Rehabilitation, Hunan Children's Hospital, Hunan, China

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Yun Chen Department of Psychology, Hunan University of Chinese Medicine, Hunan, China

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Bin Zhang Department of Psychology, Hunan University of Chinese Medicine, Hunan, China

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Abstract

Background and aims

Researchers have suggested that subtypes of problematic social media use (PSMU) should be identified for purposes of prevention and intervention. However, most studies have overlooked the heterogeneous characteristics of PSMU trajectories, and no research has systematically examined which interpersonal factors could predict these trajectories. In the present study, we identified classes of developmental trajectories of PSMU and examined differences across classes in adolescents' interpersonal functioning in family, school, and peer contexts.

Methods

Participants were 357 Chinese adolescents enrolled in two middle schools in China (52.1% girls, aged 12–15 years). The students completed questionnaires in their classrooms over the course of one year in a three-wave longitudinal study.

Results

Latent growth mixture modeling (LGMM) revealed three developmental trajectory classes of PSMU based on the intercepts and slopes of PSMU scores over time: high risk-gradual increase group (37%), low risk-sharp increase group (39%), and low risk-stable group (24%). Parent-adolescent attachment (family context), teacher-student relationships (school context), and deviant peer affiliation (peer context) were associated with variations in developmental trajectories.

Conclusions

The findings can inform the design of prevention and intervention programs for specific subgroups of adolescents who show problematic social media use.

Abstract

Background and aims

Researchers have suggested that subtypes of problematic social media use (PSMU) should be identified for purposes of prevention and intervention. However, most studies have overlooked the heterogeneous characteristics of PSMU trajectories, and no research has systematically examined which interpersonal factors could predict these trajectories. In the present study, we identified classes of developmental trajectories of PSMU and examined differences across classes in adolescents' interpersonal functioning in family, school, and peer contexts.

Methods

Participants were 357 Chinese adolescents enrolled in two middle schools in China (52.1% girls, aged 12–15 years). The students completed questionnaires in their classrooms over the course of one year in a three-wave longitudinal study.

Results

Latent growth mixture modeling (LGMM) revealed three developmental trajectory classes of PSMU based on the intercepts and slopes of PSMU scores over time: high risk-gradual increase group (37%), low risk-sharp increase group (39%), and low risk-stable group (24%). Parent-adolescent attachment (family context), teacher-student relationships (school context), and deviant peer affiliation (peer context) were associated with variations in developmental trajectories.

Conclusions

The findings can inform the design of prevention and intervention programs for specific subgroups of adolescents who show problematic social media use.

Introduction

In our increasingly digitalized society, social media have evolved into a versatile tool that fulfills a wide range of social needs. A recent global survey revealed that by the end of January 2024, China had 1.06 billion social media users, the highest number in the world (DataReportal, 2024). Of these, 15.9% were between the ages of 5 and 17. Adolescence is an important period for identity formation, autonomy development, and future orientation (Kaplan & Flum, 2010). Social media offer adolescents a space to explore their identities, express their autonomy, and connect with peers, facilitating their journey towards independence (Akbari et al., 2023). However, excessive social media use can be problematic for some adolescents (Akbari et al., 2023; Cheng, Lau, Chan, & Luk, 2021; Homaid, 2022). A meta-analysis involving 34,798 respondents from 32 countries estimated that the prevalence of problematic social media use (PSMU) was 24% worldwide, with an even higher rate of 31% in Asian countries such as China. Among adolescents worldwide, the rate was estimated to be 35% (Cheng et al., 2021). PSMU has been shown to be directly or indirectly associated with various problems, including wrist pain, blurred vision (Huang, 2022), poor academic performance (Homaid, 2022), and insomnia (Brailovskaia, Balcerowska, Precht, & Margraf, 2023) in adolescents. Given the high prevalence of PSMU among adolescents and the problems associated with it, there has been increased research attention on identifying subgroups of individuals with different expressions of PSMU (Akbari et al., 2023; Boer, Stevens, Finkenauer, & Van den Eijnden, 2022; Li et al., 2020). This information could be helpful for understanding the heterogeneity in PSMU and for designing prevention and intervention programs. Thus, the purpose of this study was to identify distinct developmental trajectories of PSMU and to test whether these trajectories could be predicted by adolescents' interpersonal functioning in family, school, and peer contexts.

Developmental trajectories of PSMU

In recent years, as research into behavioral addictions has deepened, many scholars have concluded that digital-related addictions are not fundamentally about an obsession with computers or mobile devices themselves. Instead, they involve an individual's dependence on specific core functionalities provided by these devices, such as social media (Nawaz, 2023; Panova & Carbonell, 2018; Sun & Zhang, 2021). Consequently, the focus of academic research is gradually shifting from a general concern with internet or mobile dependency to a more specific focus on individual dependencies on particular online functionalities (Sun & Zhang, 2021). This trend provides a broad research space for deeper exploration of the characteristics of PSMU. PSMU is an umbrella term covering problematic use of a variety of social websites and applications (Marino, Canale, Melodia, Spada, & Vieno, 2021), including digital content platforms (e.g., YouTube), traditional social networking sites (e.g., Facebook), and instant messaging apps (e.g., WhatsApp messenger). Although there is a lack of direct neurobiological evidence supporting the idea of PSMU as a behavioral addiction, several researchers have described it as such. These researchers maintain that PSMU's core symptoms are an inability to control social media use and negative consequences of overuse, such as academic and occupational failures (Cataldo, Billieux, Esposito, & Corazza, 2022; Cheng et al., 2021; Marino et al., 2021). We assert that whether or not PSMU is an addiction, the severity of expression and changes in severity over time can be used to identify subgroups of individuals who show problems due to social media use.

One way that researchers have identified subgroups is by assessing severity, and adolescents indeed show a range of severity in their expression of PSMU. For example, Akbari et al. (2023) examined the heterogeneity of PSMU in a sample of 3,375 Iranian adolescents aged 13–18 years. They identified five profiles: low-risk (24.4%), low-to-moderate-risk (24.7%), moderate-risk (18.7%), moderate-to-high-risk (17.3%), and high-risk (14.9%). In a study of 4,951 Chinese adolescents with a mean age of 13.9 years (Li et al., 2020), three PSMU profiles were empirically derived: low-risk (36.4%), average-risk (50.4%), and high-risk (13.2%) groups. The results of these studies advanced the understanding of the heterogeneity of PSMU. However, the studies were cross-sectional and it is not clear how adolescents' PSMU evolves over time.

Another option is to assess increases and decreases in severity over time. For example, among a group of early adolescents who show few problems with social media use, some will maintain a low level of problems into middle adolescence and others will show an increase in problems over the same period. Without information about prognosis, students who could benefit from prevention efforts may be overlooked. A handful of longitudinal studies on PSMU assessed the average trend of PSMU over time in a group of adolescents, and found a linear increase as adolescents aged (Raudsepp, 2019; Raudsepp & Kais, 2019). However, these studies fail to distinguish between the initial levels and growth rates of PSMU in different individuals and struggle to scientifically explain potential developmental differences and their causes. Based on a review of the literature, Cataldo et al. (2022) concluded that the occurrence and development of PSMU might exhibit group differences. To identify these differences, it is necessary to assess individual characteristics (i.e., individual trajectories based on initial levels and growth rates) and their heterogeneity (i.e., differences across classes of trajectories). This approach could offer insights into prognosis, serving as both a conceptual and empirical foundation for developing personalized prevention and intervention strategies for PSMU in adolescents (Boer et al., 2022).

Latent growth mixture modeling (LGMM) can be used to reveal the heterogeneity in the developmental trajectories of PSMU. LGMM is a person-centered classification approach that assesses heterogeneity in the intercepts and slopes of individuals' PMSU scores (Grimm, Ram, & Estabrook, 2016). In this approach, the intercept represents the initial level of the variable at the start of the study, while the slope indicates the rate and direction of growth of the variable over time. Through probability-based mixture modeling, LGMM helps researchers to identify groups of people with similar developmental patterns and to determine how many distinct groups are present in the sample (Nylund, Asparouhov, & Muthén, 2007). Over the past few years, LGMM has been widely used to explore heterogeneity in the developmental trajectories of behavioral addictions (Kim, Jo, & Song, 2023; Zhou, Zhen, & Wu, 2018). For instance, Kim et al. (2023) found that children's developmental trajectories for smartphone dependency over a three-year period were heterogeneous and could be classified into three classes: low-stable (low initial level, non-significant growth rate), medium-increasing (medium initial level, significant increasing growth rate), and high-increasing (high initial level, significant increasing growth rate). Similarly, Zhou et al. (2018) focused on problematic internet use over the course of two and a half years, and identified four developmental trajectories among 391 Chinese adolescents aged 12–19 years: slower-increasing (relatively lower initial level, significant increasing growth rate), medium-stable (medium initial level, non-significant growth rate), high-decreasing (highest initial level, significant decreasing growth rate), and quick-increasing (lowest initial level, significant increasing growth rate).

To our knowledge, only one study has explored heterogeneity in the developmental trajectories of PSMU among adolescents using LGMM. Boer et al. (2022) studied 1,419 Dutch adolescents, with an average age of 12.5 years, and identified three trajectory classes: variably high PSMU (24.7%), characterized by a significantly higher initial level compared to the other classes and a significant nonlinear growth rate; persistently high PSMU (15.8%), marked by a relatively high initial level and a non-significant growth rate; and persistently low PSMU (59.5%), with a significantly lower initial level compared to the other classes and a non-significant growth rate. There are two important differences between the Boer et al. (2022) study and our own. First, Boer et al. (2022) examined the developmental trajectories of PSMU in Dutch adolescents, whereas our study was conducted in China. Given the significant variation in social media use and the development of PSMU across different cultures (Alshakhsi, Babiker, Montag, & Ali, 2023; Marino et al., 2021), it is valuable to have information about PSMU trajectories in more than one cultural context. This is particularly important in the case of China, due to its very high prevalence of PSMU (Cheng et al., 2021). Second, Boer et al. (2022) tested personal characteristics (subjective well-being and self-control) as predictors of developmental trajectories of PSMU, whereas we focused on interpersonal factors as predictors. Compared to relatively stable personal factors, interpersonal factors are more amenable to change through interventions during adolescence (Xiong, Zhang, Zhang, & Xu, 2023). Therefore, it is practically important to examine the relationships between interpersonal factors and the developmental trajectories of PSMU in adolescents.

Interpersonal factors associated with PSMU

The social-compensation hypothesis posits that when individuals lack supportive resources from their primary life contexts over an extended period, they may develop pathological compensatory motivations, specifically a desire to use the virtual online world to compensate for disappointments in reality (Lee, 2009). Based on this theory, researchers have found that family, school, and peer contexts are all important interpersonal contexts of youth development and may play a direct or indirect role in the formation of PSMU (Lin, Mastrokoukou, & Longobardi, 2023; Vossen, van den Eijnden, Visser, & Koning, 2024). First, parent-adolescent attachment, a key component of the family context, is closely related to adolescents' PSMU. Previous research on parent-adolescent attachment has demonstrated that adolescents who have negative relationships with their parents tend to adopt problematic ways to cope with stress, increasing the likelihood of PSMU (Ballarotto, Volpi, & Tambelli, 2021; Vossen et al., 2024; White-Gosselin & Poulin, 2022). Second, teacher-student relationships within the school context may also serve as significant predictors of PSMU. Adolescents who have a weak relationship with their primary teacher have been shown to feel neglected and to be more likely to show excessive use of smartphones (Xiong et al., 2023) and social media (Hamedinasab, Gholami, & Azizi, 2020; Lin et al., 2023) as a means to gain attention. Finally, deviant peer affiliation within the peer context has also been found to be associated with PSMU in adolescents. Deviant peer affiliation, which refers to associating with peers who engage in deviant behaviors such as truancy, smoking, and fighting, is a robust predictor of various behavioral addictions, including PSMU (Sarour & El Keshky, 2023; Toyin & Nkecchi, 2020; Xie, Chen, Zhu, & He, 2019).

Despite the above studies indicating that family, school, and peer contexts may play an important role in PSMU among adolescents, significant gaps remain. A primary limitation is that the majority of studies only focus on the isolated effects of single interpersonal factor within the same context, without sufficiently considering the synergistic effects of multiple interpersonal factors across various contexts on PSMU. The ecological systems theory posits that family, school, and peer contexts are the most immediate and persistent proximal environmental contexts affecting adolescents, with factors from these contexts collaboratively shaping adolescents' behavioral development (Bronfenbrenner & Morris, 1998). If only a single context is assessed, this may lead to the overestimation of the contribution of certain interpersonal contexts to adolescents' development (Xiong, Xu, Zhang, Zhu, & Xie, 2022). Consequently, it is essential to incorporate data from these three critical interpersonal contexts into a unified PSMU research framework. More importantly, previous investigations mainly employed cross-sectional designs and explored the relationship between interpersonal factors and PSMU as a whole. This approach assumes that the relationships between variables apply uniformly to all adolescents, thereby overlooking the heterogeneity in the developmental process of PSMU (Grimm et al., 2016). This fails to accurately investigate the connections between multiple interpersonal factors and distinct developmental trajectories of PSMU. Therefore, a deeper understanding of the predictive roles of parent-adolescent attachment (family context), teacher-student relationships (school context), and deviant peer affiliation (peer context) on the initial levels and growth rates of PSMU developmental trajectories is warranted.

The present study

Researchers are interested in identifying subgroups of people with PSMU to inform prevention and treatment programs. We conducted a three-wave longitudinal study over the course of one year to identify subgroups of Chinese adolescents with similar developmental trajectories of PSMU. We then tested multiple interpersonal factors as predictors of these trajectory classes. The social-compensation hypothesis and the ecological systems theory provided the conceptual framework for the research. We tested the following hypotheses: (1) there will be distinct classes of developmental trajectories of PSMU based on the intercepts and slopes of PSMU scores at T1, T2, and T3; (2) parent-adolescent attachment (family context), teacher-student relationships (school context), and deviant peer affiliation (peer context) will predict the intercepts and slopes of these developmental trajectories to varying degrees.

Method

Participants and procedure

Five middle schools in Changsha, a developed city in south-central China, were invited to participate in the study, and two of those that consented were chosen. Participants were recruited using random cluster sampling. Specifically, this approach involved the random selection of two classes, each containing 30 to 40 students, from each grade within each school. Data were collected in four waves, each six months apart, May 2022 and November 2023. The initial wave in May 2022 included 410 Chinese adolescents (52.2% girls, Mage = 12.87 years, SD = 0.96). However, because the initial wave of the larger study did not incorporate the PSMU variable, we only used data from the second (T1; November 2022), third (T2; May 2023), and fourth (T3; November 2023) waves. Forty-one participants were lost to attrition due to class reassignments, and twelve were excluded due to a lack of experience with social media use during the second wave (T1). From the second (T1) to the fourth wave (T3), there was no attrition, and no samples were excluded since less than 5% of the data was missing for all variables. The final sample included 357 Chinese adolescents (52.1% girls, age range = 12–15 years, Mage = 13.10 years, SD = 0.74).

The questionnaires were administered in the classroom by experienced researchers in psychology and with the attendance of a teacher. Data collection did not occur during the two weeks preceding or following major examinations, such as midterms and finals, to ensure that participants maintained a consistent state across all administrations. The participants spent approximately 20 min completing the questionnaires and then received a small gift, such as a mechanical pen or marker, as a token of appreciation for their assistance.

Measures

Problematic Social Media Use

Problematic Social Media Use (PSMU) was measured using the Instagram Addiction Scale (Kircaburun & Griffiths, 2018), which is widely utilized for assessing PSMU globally and was developed relatively recently to reflect the latest changes in social media (Cataldo et al., 2022). The three psychology researchers translated the Instagram Addiction Scale to fit the Chinese cultural context and deleted and revised items to align with the study's objectives (e.g., changing “Instagram” to “social media” in each item). This adapted version includes 10 items, such as “How often do you fear that life without social media (e.g., WeChat, QQ, and TikTok) would be boring, empty, and joyless?” Adolescents respond on a 6-point Likert scale from 1 (never) to 6 (always), with higher scores indicating a greater tendency toward PSMU. In the present study, McDonald's omega, ω was 0.94, 0.94, 0.96 at T1, T2, and T3, respectively.

Parent-adolescent attachment

The Parent-Adolescent Attachment Scale (Li et al., 2009) is a 13-item Chinese-language measure designed to assess the adolescents' attachment to parents (e.g., “For matters of personal importance, I prefer to seek advice from my parents.”). Adolescents respond on a 5-point Likert scale ranging from 1 (not at all true) to 5 (always true), with higher scores indicating a more positive parent-adolescent relationship. In the present study, McDonald's omega, ω at T1 was 0.93.

Teacher-student relationships

The Teacher-Student Relationship Questionnaire (Jiang, 2004) is an eight-item Chinese-language measure designed to assess the quality of the teacher-student relationship (e.g., “I can trust my class teacher”). A 5-point Likert scale is used ranging from 1 (not at all true) to 5 (always true), with higher scores indicating more positive relationships between teachers and students. In the present study, McDonald's omega, ω at T1 was 0.96.

Deviant peer affiliation

The Deviant Peer Affiliation Scale (Li, Zhou, Zhao, Wang, & Sun, 2016) is an eight-item Chinese-language measure to assess the extent to which adolescents associate with peers who exhibit tendencies toward delinquent behavior, engagement in illegal activities, and other negative behaviors (e.g., “How many of your close friends cheat in exams?”). Adolescents rated each item on a 5-point Likert scale from 1 (none) to 5 (almost all), with higher scores indicating a stronger association of the individual with deviant peers. In the present study, McDonald's omega, ω at T1 was 0.73. All the measures employed in this study are provided in the Appendix.

Statistical analyses

The analyses were conducted in three steps. In the first step, the unconditional latent growth curve model was estimated using Mplus 8.2 to capture the overall developmental trajectory of PSMU in the sample. In the unconditional latent growth curve model analysis, the intercept and slope each possess two parameters: mean and variance (Grimm et al., 2016). The mean of the intercept factor describes the average initial level of PSMU, while the variance of the intercept factor reflects the degree of differences among individuals regarding the initial level of PSMU. The mean of the slope factor represents the average growth rate of PSMU across various time points, and the variance of the slope factor reflects the differences in growth rate among individuals' PSMU. Furthermore, model fit was evaluated using the following indices (Hu & Bentler, 1999): the comparative fit index (CFI; acceptable >0.90), Tucker–Lewis index (TLI; acceptable >0.90), root mean square error of approximation (RMSEA; acceptable <0.08), and standardized root mean square residual (SMRM; acceptable <0.08). Given that the rates of missing data for all variables in the current study were less than the recommended cut-off of 5% (Moon, 1996), Expectation-Maximization (EM) was applied to address the missing data.

In the second step, LGMM using Mplus 8.2 was employed to identify latent trajectory classes of PSMU. To determine the number of latent trajectory classes (ranging from a 1-class to 6- class solution), the Akaike information criterion (AIC), Bayesian information criterion (BIC), adjusted BIC, Entropy, Lo-Mendell-Rubin Test (LMR) and Bootstrap Likelihood Ratio Test (BLRT) were reviewed. Specifically, smaller AIC, BIC, and adjusted BIC values provide a better model fit (Nylund et al., 2007); an entropy value of 0.80 or higher indicates acceptable classification precision, with values closer to 1.0 signifying even greater precision; significant LMR and BLRT results indicate that the model with k-classes was a significant improvement over the model with k-1 classes (Nylund et al., 2007). Additionally, it is important to highlight that the developmental trajectory classes identified by the LGMM should be both logically meaningful and distinctly different. Thus, developmental trajectory classes representing less than 5% of the sample were omitted, as they often represent spurious classes (Masyn, 2013).

In the third step, the conditional latent growth curve models using Mplus 8.2 were applied to each class of developmental trajectories of PSMU. This analysis tested parent-adolescent attachment, teacher-student relationships, and deviant peer affiliation as predictors of initial levels and changes over time for each trajectory class. Additionally, given that there may be gender and age differences in PSMU (Cataldo et al., 2022; Marino et al., 2023; Wartberg, Kriston, & Thomasius, 2020), we used gender and age as control variables.

Ethics

The research project was reviewed and approved by the Ethics Committee affiliated with the University of the first author. Participants were briefly informed about the procedures and purpose of the current study, and then written informed consent was obtained from the adolescents and their parents. Thus, the study is in accordance with the principles of the Declaration of Helsinki.

Results

Overall developmental trajectory of PSMU

To examine the overall developmental trajectory of PSMU, an unconditional latent growth curve model was constructed for PSMU. The analysis suggested that the measurement model fit the data well: χ2/df = 2.179, CFI = 0.998, TLI = 0.994, RMSEA = 0.057, SRMR = 0.012. The average intercept factor (M = 24.72, p < 0.001) and average slope factor (M = 5.45, p < 0.001) indicated a significant increase in PSMU over time in the sample as a whole. The variances for PSMU included the intercept factor (var = 106.32, p < 0.001) and slope factor (var = 20.84, p = 0.001), suggesting individual differences in initial level and growth rate of PSMU. Details are depicted in Fig. 1.

Fig. 1.
Fig. 1.

Unconditional latent growth curve model of PSMU

Note: In accordance with the requirements of LGMM, the factor loadings for the intercept were fixed at 1, and the factor loadings for the slope were fixed at 0, 1, and 2. M represents the mean, var denotes the variance, and the numbers under the PSMU boxes indicate the residual variances. ***p < 0.001.

Citation: Journal of Behavioral Addictions 2025; 10.1556/2006.2025.00032

Developmental trajectory classes of PSMU

Given the observed heterogeneity in the initial level and growth rate of PSMU, an exploration of latent trajectory classes using LGMM was warranted. Table 1 presents the model fit indices for models with one to six latent trajectory classes of PSMU. With the addition of more classes, a consistent decline was observed in the AIC, BIC, and adjusted-BIC values, indicating an enhancement of the model's fit. The entropy values for all six solutions fell within an acceptable range and displayed minimal variability. Despite the six-class solution presenting the lowest AIC, BIC, and adjusted-BIC (Nylund et al., 2007), the LMR test failed to reach statistical significance. Moreover, the smallest classes in both the four-class and five-profile solutions each constituted less 5% of the full sample, failing to meet the meaningfulness threshold (Masyn, 2013). As a result, the three-class solution of PSMU was chosen as the best fitting model.

Table 1.

Model fit indices for one-to six-class solutions of PSMU

ClassAICBICadjusted-BICEntropyLMR (p)BLRT (p)Percent of participants in each class
18,079.418,110.438,085.05
27,905.687,948.347,913.440.940.05<0.0010.28/0.72
37,812.467,866.757,822.330.930.01<0.0010.37/0.24/0.39
47,748.847,814.767,760.830.930.10<0.0010.33/0.03/0.25/0.39
57,713.457,791.017,727.550.950.01<0.0010.33/0.02/0.38/0.24/0.03
67,679.927,769.117,696.140.920.29<0.0010.27/0.08/0.24/0.02/0.14/0.25

Note: Bold indicates best fit.

We named the three classes based on comparisons of the mean intercept and slope factors between each pair of developmental trajectory classes, as detailed in Table 2. The first group (n = 132, 37%), termed high risk-gradual increase, exhibited the highest initial levels of PSMU (M intercept = 39.28, p < 0.001) and a steadily increasing growth rate (M slope = 3.22, p < 0.001). The second group (n = 140, 39%), termed low risk-sharp increase, exhibited significantly lower initial levels of PSMU (M intercept = 17.98, p < 0.001) and a sharper increase in their growth rate (M slope = 11.43, p < 0.001) compared to the first group. The third group (n = 85, 24%), termed low risk-stable, exhibited low initial levels of PSMU (M intercept = 12.86, p < 0.001) that were similar to those in the second group, and maintained a stable growth rate without significant changes (M slope = −0.42, p = 0.104). Figure 2 visually illustrates the characteristics of different developmental trajectory classes of PSMU.

Table 2.

Mean intercept and slope factors for each developmental trajectory class of PSMU

ClassClass nameFactorMS.E.pWald test
χ2p
1High risk-gradual increaseIntercept39.280.69<0.001C1 vs C26.860.009
Slope3.220.60<0.001C1 vs C216.55<0.001
2Low risk-sharp increaseIntercept17.980.65<0.001C2 vs C31.920.166
Slope11.430.53<0.001C2 vs C321.25<0.001
3Low risk-stableIntercept12.860.36<0.001C3 vs C110.580.001
Slope−0.420.260.104C3 vs C113.09<0.001

Note: C1 = High risk-gradual increase, C2 = Low risk-sharp increase, C1 = Low risk-stable.

Fig. 2.
Fig. 2.

Developmental trajectory classes of PSMU across three time points

Citation: Journal of Behavioral Addictions 2025; 10.1556/2006.2025.00032

Predictors of PSMU developmental trajectories

Conditional latent growth curve models were generated to test parent-adolescent attachment, teacher-student relationships, and deviant peer affiliation as predictors of the mean intercept and slope for each of the developmental trajectory classes of PSMU. A summary of these analyses is provided in Table 3. In the high risk-gradual increase group, T1 parent-adolescent attachment significantly negatively predicted the slope of PSMU (B = −0.113, S.E. = 0.047, p = 0.016), and T1 deviant peer affiliation significantly positively predicted the slope of PSMU (B = 0.298, S.E. = 0.134, p = 0.026).

Table 3.

Interpersonal factors predicting intercept and slope of each of three trajectory classes

PredictorInterceptSlope
BS.E.pBS.E.p
High risk-gradual increase
Gender0.9050.5920.126−1.7400.5400.001
Age0.5430.2370.022−0.6310.2160.003
T1 Parent-adolescent attachment0.0480.0510.352−0.1130.0470.016
T1 Teacher-student relationships−0.0300.0640.641−0.0120.0590.832
T1 Deviant peer affiliation−0.2180.1470.1380.2980.1340.026
Low risk-sharp increase
Gender0.4530.3850.240−1.2230.4300.004
Age0.5720.126<0.001−1.0240.141<0.001
T1 Parent-adolescent attachment−0.0570.0280.040−0.0650.0310.036
T1 Teacher-student relationships−0.1100.0450.0140.0640.0500.199
T1 Deviant peer affiliation0.2000.0910.0290.2150.1020.035
Low risk-stable
Gender−0.2320.2610.374−0.1490.2570.561
Age−0.0190.0960.841−0.1050.0950.269
T1 Parent-adolescent attachment−0.0720.020<0.0010.0280.0200.160
T1 Teacher-student relationships−0.0630.0270.0220.0450.0270.096
T1 Deviant peer affiliation0.1690.0670.011−0.1070.0660.105

Note: Gender (1 = boy, 2 = girl).

In the low risk-sharp increase group, T1 parent-adolescent attachment and T1 teacher-student relationships significantly negatively predicted the intercept of PSMU (B = −0.057, S.E. = 0.028, p = 0.040; B = −0.110, S.E. = 0.045, p = 0.014), and T1 deviant peer affiliation significantly positively predicted the intercept of PSMU (B = 0.200, S.E. = 0.091, p = 0.029). Additionally, T1 parent-adolescent attachment significantly negatively predicted the slope of PSMU (B = −0.065, S.E. = 0.031, p = 0.036), and T1 deviant peer affiliation significantly positively predicted the slope of PSMU (B = 0.215, S.E. = 0.102, p = 0.035).

In the low risk-stable group, T1 parent-adolescent attachment and T1 teacher-student relationships significantly negatively predicted the intercept of PSMU (B = −0.072, S.E. = 0.020, p < 0.001; B = −0.063, S.E. = 0.027, p = 0.022), and T1 deviant peer affiliation significantly positively predicted the intercept of PSMU (B = 0.169, S.E. = 0.067, p = 0.011).

Discussion

Although the heterogeneity has been acknowledged, there is little knowledge about whether and for whom PSMU persists, increases, or decreases over time. This study is the first to examine developmental trajectories of PSMU in relation to adolescents' interpersonal functioning, which was assessed in multiple interpersonal contexts. In the sample, only 3% (12 participants) had no prior experience with social media, which to some extent reflects the widespread use of social media among Chinese adolescents. Over the course of one year, Chinese adolescents showed an overall increase in PSMU. LGMM revealed that there were three developmental trajectory classes with distinct characteristics: high risk-gradual increase group (37%), low risk-sharp increase group (39%), and low risk-stable group (24%). Parent-adolescent attachment (family context), teacher-student relationships (school context), and deviant peer affiliation (peer context) were associated with variations in different developmental trajectories. The results have potential applications in designing prevention and intervention programs that can be tailored to specific developmental trajectories of PSMU.

Characteristics of developmental trajectories of PSMU

Overall, the Chinese adolescents showed a linear increase in PSMU over the course of one year, consistent with existing longitudinal research (Raudsepp, 2019; Raudsepp & Kais, 2019). This trend can primarily be attributed to two factors. First, as adolescents age, they face increasing academic pressures and societal expectations. These stresses may prompt them to spend more time on social media, seeking escapism and emotional support, which in turn can lead to an increase in PSMU (Akbari et al., 2023; Wolfers & Utz, 2022). Second, in China, the prevalent “421” family structure (one couple supporting four elderly parents and one child) results in many Chinese adolescents growing up without sibling interaction and competition. This only-child environment may limit Chinese children's agreeableness and interpersonal abilities (Yang et al., 2017). As adolescents grow older, they increasingly seek to spend more time and energy on various social activities to fulfill their expanding emotional and social needs. However, due to the lack of early social skills caused by the only-child environment, these adolescents tend to compensate for their real-world social deficiencies through social media features such as “likes” and “comments” (Lee, 2009). This compensation behavior can contribute to an increase in PSMU.

The more significant contribution of this study lies in identifying the heterogeneity of PSMU development, supporting hypothesis 1. Based on each student's initial level of problems and changes in level of problems from T1 to T3 (i.e., the intercept and slope of PSMU scores), we classified the PSMU developmental trajectories of Chinese adolescents into three groups: high risk-gradual increase group, low risk-sharp increase group, and low risk-stable group. This result differs from previous research on Dutch adolescents, which identified trajectory classes of variably high PSMU, persistently high PSMU, and persistently low PSMU (Boer et al., 2022).

A point worth discussing is that the growth rates of the developmental trajectories identified in Boer et al. (2022)'s Dutch sample were generally stable, whereas about two-thirds of our sample (i.e., high risk-gradual increase group and low risk-sharp increase group) showed an increase from T1 to T3. This can be explained by the differences in the increase of academic pressure in different cultural contexts. In China, middle schoolers must prepare for the high-stakes high school entrance exam, which determines the 50% of students who can attend a regular high school and thus attend a public university later. This makes middle school a period of surging academic pressure for Chinese adolescents (Jiang, Ren, Jiang, & Wang, 2021), which may lead students to use social media more frequently for video entertainment and emotional release as a way to alleviate these mounting pressures (Wolfers & Utz, 2022). Consequently, this behavior contributes to the growth of PSMU. By comparison, the Dutch secondary education system is relatively more relaxed, with academic pressures being more evenly distributed across different stages (Bogt et al., 2024). This might explain the lack of significant fluctuation in PSMU scores among Dutch adolescents. This discrepancy demonstrates the potential impact of cultural context on the developmental patterns of PSMU, further emphasizing the necessity of conducting research across different cultural backgrounds.

In this study, the high risk-gradual increase group accounted for 37% of the sample. This group exhibited the highest PSMU at the beginning of the study compared to the other classes, and PSMU gradually worsened over time, making this group the most severely affected by PSMU. This observation underscores the urgent need for sustained measures to prevent or mitigate persistently high levels of PSMU among these adolescents. It is noteworthy that the low risk-sharp increase group accounted for 39% of the sample, making it the largest subgroup. This group exhibited a low initial level of PSMU that was similar to that in the low risk-stable group, but it followed a sharper increase in growth rate. This result strongly indicated the critical importance of distinguishing between different developmental trajectories of PSMU. Focusing solely on current (cross-sectional) PSMU levels can easily overlook the low risk-sharp increase group, leading to missed opportunities for timely intervention. Therefore, precise identification of this developmental trajectory through predictive factors is a crucial first step for effective subsequent interventions (Boer, Stevens, Finkenauer, de Looze, & van den Eijnden, 2021). However, the results suggest that prevention and intervention are not necessary for all students. Chinese adolescents in the low risk-stable group accounted for 24% of the sample, exhibited the lowest PSMU, and maintained a stable growth rate without significant changes.

Associations between developmental trajectories of PSMU and interpersonal factors

The present study, based on the social-compensation hypothesis (Lee, 2009) and the ecological systems theory (Bronfenbrenner & Morris, 1998), integrated family, peer and school factors into the same research framework to predict PSMU. We found that parent-adolescent attachment (family context), teacher-student relationships (school context), and deviant peer affiliation (peer context) predicted the initial levels and growth rates of some classes of developmental trajectories of PSMU, supporting hypothesis 2. Specifically, in the high risk-gradual increase group, none of interpersonal factors included in the study was associated with the initial level of PSMU. One potential explanation for this finding is that when certain behavior patterns are deeply entrenched, external factors may not have an immediate effect but instead require more time to take effect (Kwasnicka, Dombrowski, White, & Sniehotta, 2016; Lally, Van Jaarsveld, Potts, & Wardle, 2010). In other words, when Chinese adolescents showed very high initial PSMU, they might have been less susceptible to immediate changes from external interpersonal influences due to the dominance of already established patterns of social media use. However, we found that lower parent-adolescent attachment scores and higher deviant peer affiliation scores were related to a faster increasing growth rate of PSMU in this group. This delayed effect can be described as a snowball effect in which specific external factors may not have a significant impact initially, but in the long term, through sustained infiltration and accumulation, they gradually change the development of adolescents' behavioral patterns (Bukowski, Laursen, & Hoza, 2010). In the high risk-gradual increase group, negative parent-adolescent attachment may reduce the emotional and supervisory support available to the adolescent. Over time, this lack of support may undermine the adolescent's ability to develop healthy coping strategies, leading to a gradual increase in PSMU (Vossen et al., 2024). Concurrently, higher affiliation with deviant peers may introduce and reinforce negative behavior patterns (Toyin & Nkecchi, 2020). As these affiliations persist, the influence of peers who model and encourage PSMU grows stronger, further accelerating the developmental trend of PSMU as a form of conformity to group norms (Xiong et al., 2023).

In the low risk-sharp increase group, we found that all three measures of interpersonal functioning predicted the initial low level of PSMU. These findings align with the assertion that interpersonal functioning in the family, school, and peer contexts can have a more significant impact on adolescent problem behaviors before these patterns become entrenched and severe (Antonishak, Sutfin, & Reppucci, 2005). In the low risk-sharp increase group, low initial levels of PSMU indicate that adolescents' social media usage habits are not yet entrenched and are thus immediately susceptible to the influence of interpersonal contexts. The immediate feedback from social media networks can quickly offer virtual emotional support, making adolescents with poorer parent-adolescent attachment and teacher-student relationships more likely to seek a sense of belonging and self-worth by using social media (Ballarotto et al., 2021; Lin et al., 2023). Meanwhile, adolescents with higher deviant peer affiliation are prone to encounter and imitate their peers' negative behaviors and attitudes via social media, potentially increasing their initial level of PSMU (Toyin & Nkecchi, 2020). Finally, lower parent-adolescent attachment scores and higher deviant peer affiliation scores were related to a sharply increasing growth rate of PSMU. This indicates that the PSMU of the low risk-sharp increase group responds significantly to interpersonal functioning in the family and peer contexts, not only showing prominent immediate effects but also continuously driving the increase in PSMU over the long term.

It is important to note that lower teacher-student relationship scores were not significantly associated with the increase in growth rates of PSMU in either the low risk-sharp increase group or in the high risk-gradual increase group described earlier. This may be related to China's exam-driven education system, where teacher-student relationships are often maintained through students' academic performance (Lei, Wang, Chiu, Du, & Xie, 2023). While poor teacher-student relationships may immediately prompt students to engage in PSMU in the short term to compensate for a lack of external attention (Lin et al., 2023), in the long term, fluctuations in students' academic performance could cause instability in teacher-student relationships (Wubbels, Brekelmans, Mainhard, den Brok, & van Tartwijk, 2016). This instability makes it difficult for researchers to effectively predict the sustained impact of teacher-student relationships on the development of PSMU.

In terms of the low risk-stable group, we observed that the results concerning the initial level of PSMU were similar to those found in the low risk-sharp increase group. Specifically, lower parent-adolescent attachment scores, lower teacher-student relationship scores, and higher deviant peer affiliation scores were positively associated with the initial level of PSMU. This finding further supports the idea that before PSMU becomes entrenched and severe, interpersonal relations in these three contexts may significantly influence adolescents' current PSMU (Antonishak et al., 2005), regardless of subsequent development. Furthermore, we found that none of the interpersonal factors included in the study were associated with the growth rate of PSMU in this group. This may be related to certain personal traits in this group of adolescents that help them resist the negative impacts of interpersonal contexts and maintain a stable, low level of PSMU development. Although we did not directly measure personal traits, there is indirect evidence suggesting that adolescents with high gratitude in low risk contexts can mitigate the adverse effects of such contexts on the development of smartphone addiction (Zhang, Xu, Zhang, Chen, & Xiong, 2024). Therefore, even with early negative interpersonal influences, adolescents in the low risk-stable group may benefit from personal traits like gratitude (Zhang et al., 2024), psychological resilience (Hou et al., 2017), and extraversion (Dalvi-Esfahani et al., 2021). These traits may help them adjust and cope with these adverse influences in a timely manner during their growth, thereby maintaining a relatively low level of PSMU over the long term. Future research can further explore which specific personal traits in the low risk-stable group play a crucial role in protecting against the negative influence of interpersonal factors on the growth rate of PSMU.

As with all research, our findings come with a few caveats. First, this study revealed three developmental trajectory classes of PSMU among Chinese adolescents. This finding provides a significant foundation for research on the heterogeneity of PSMU development but requires further validation. Future studies should be conducted over longer time spans, include larger sample sizes, and examine diverse cultural backgrounds to provide more comprehensive evidence. Second, it would be beneficial to include a broad range of interpersonal factors in the measurements. However, given the feasibility constraints of achieving this within a single study and to ensure data quality in longitudinal research, only one representative variable from the family, school, and peer contexts was included in the study. Future research can further explore a wider array of interpersonal factors to enhance the ecological validity of the findings. Third, we included only interpersonal factors at T1 as baseline predictors. Future research should consider alternative modeling approaches, such as multilevel residual dynamic structural equation modeling, and incorporate multiple waves to elucidate the complex influence of interpersonal factors at different time points on the PSMU developmental trajectories. Finally, given that the diagnostic criteria for PSMU have not yet been standardized, we are unable to definitively establish the absolute criteria for the developmental trajectory classes. We look forward to the future establishment of a diagnostic “gold standard” for PSMU, which would further strengthen the validation of the robustness of our conclusions.

Conclusions

To the best of our knowledge, the current study is the first to explore interpersonal relations in multiple social contexts as predictors of developmental trajectories of PSMU among adolescents. This is an important extension of previous research on the development of PSMU and enriches the evidence for the social-compensation hypothesis and ecological systems theory. We identified three developmental trajectories of PSMU among Chinese adolescents with distinct characteristics: high risk-gradual increase group (37%), low risk-sharp increase group (39%), and low risk-stable group (24%). Interpersonal functioning in family, school, and peer contexts was associated with variations in these trajectories. The findings have applied value for developing and testing prevention and intervention strategies tailored to specific groups of adolescents who exhibit similar developmental trajectories of PSMU and similar patterns of interpersonal functioning in multiple social contexts.

Funding sources

This study was supported by the Humanity and Social Science Youth Fund of Ministry of Education of China [Project No. 24YJC880151], the Natural Science Foundation of Hunan Province [Project No. 2025JJ50413], the Department of Education of Hunan Province, Outstanding Youth Project [Project No. 23B0363], the Hunan Province Higher Education Teaching Reform Research Project [Project No. 202401000763], and the Hunan University of Chinese Medicine University-Level Research Project [Project No. Z2023YYJJ12].

Authors' contribution

SX started the original study conceptualization. YX and YC conducted data collection and quality assessment. BZ conducted the data analysis and made a draft for the results and methodology section. YX drafted the introduction and discussion sections. All authors read and approved the manuscript.

Conflict of interest

No conflict of interest exits in the submission of this manuscript.

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  • Zhou, X., Zhen, R., & Wu, X. (2018). Trajectories of problematic internet use among adolescents over time since Wenchuan earthquake. Computers in Human Behavior, 84, 8692. https://doi.org/10.1016/j.chb.2018.02.030.

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Appendix

Instagram Addiction Scale (Revised Version)

ItemNeverRarelyOccasionallySometimesOftenAlways
How often do you prefer the excitement of social media (e.g., WeChat, QQ, and TikTok) instead of being with your close friends?123456
How often do you form new relationships with fellow social media (e.g., WeChat, QQ, and TikTok) users?123456
How often do you try to hide how long you've been on social media (e.g., WeChat, QQ, and TikTok)?123456
How often do you try to cut down the amount of time you spend on social media (e.g., WeChat, QQ, and TikTok) and fail?123456
How often do your grades or school work suffer because of the amount of time you spend on social media (e.g., WeChat, QQ, and TikTok)?123456
How often do you check your social media (e.g., WeChat, QQ, and TikTok) before something else that you need to do?123456
How often do you turn to social media (e.g., WeChat, QQ, and TikTok) to distract yourself from troubling thoughts about your life?123456
How often do you find yourself anticipating when you will go on social media (e.g., WeChat, QQ, and TikTok) again?123456
How often do you fear that life without social media (e.g., WeChat, QQ, and TikTok) would be boring, empty, and joyless?123456
How often do you find yourself saying “just a few more minutes” when on social media (e.g., WeChat, QQ, and TikTok)?123456

Parent-Adolescent Attachment Scale

ItemNot at all trueSlightly untrueUncertainMostly trueAlways true
For matters of personal importance, I prefer to seek advice from my parents.12345
My parents help me better understand myself.12345
I share my difficulties and worries with my parents.12345
My parents assist me in discussing my problems.12345
My parents respect my feelings.12345
I believe my parents are competent caregivers.12345
When discussing issues with my parents, they care about my perspective.12345
My parents understand me.12345
I trust my parents.12345
*I feel uncomfortable when interacting with my parents.12345
*My parents make me feel angry.12345
*I do not receive much attention from my parents.12345
*My parents do not understand my current situation.12345

Note: * indicates that the item is reverse-scored.

Teacher-Student Relationship Questionnaire

ItemNot at all trueSlightly untrueUncertainMostly trueAlways true
My class teacher is kind and friendly.12345
My class teacher cares about me.12345
My class teacher is approachable.12345
I can trust my class teacher.12345
My classmates like my class teacher.12345
My class teacher is fair and understanding.12345
My class teacher encourages me.12345
My class teacher respects my self-esteem.12345

Deviant Peer Affiliation Scale

ItemNoneRarelySomewhatFairlyAlmost all
How many of your close friends smoke?12345
How many of your close friends drink alcohol?12345
How many of your close friends cheat in exams?12345
How many of your close friends steal?12345
How many of your close friends are addicted to the internet?12345
How many of your close friends skip school or play truant?12345
How many of your close friends have been disciplined by the school?12345
How many of your close friends bully others verbally or physically?12345

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Dr. Zsolt Demetrovics
Institute of Psychology, ELTE Eötvös Loránd University
Address: Izabella u. 46. H-1064 Budapest, Hungary
Phone: +36-1-461-2681
E-mail: jba@ppk.elte.hu

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Journal of Behavioral Addictions
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Subscription Information Gold Open Access

Journal of Behavioral Addictions
Language English
Size A4
Year of
Foundation
2011
Volumes
per Year
1
Issues
per Year
4
Founder Eötvös Loránd Tudományegyetem
Founder's
Address
H-1053 Budapest, Hungary Egyetem tér 1-3.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
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Publisher
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ISSN 2062-5871 (Print)
ISSN 2063-5303 (Online)

Senior editors

Editor(s)-in-Chief: Zsolt DEMETROVICS

Assistant Editor(s): 

Csilla ÁGOSTON

Dana KATZ

Associate Editors

  • Stephanie ANTONS (Universitat Duisburg-Essen, Germany)
  • Joel BILLIEUX (University of Lausanne, Switzerland)
  • Beáta BŐTHE (University of Montreal, Canada)
  • Matthias BRAND (University of Duisburg-Essen, Germany)
  • Daniel KING (Flinders University, Australia)
  • Gyöngyi KÖKÖNYEI (ELTE Eötvös Loránd University, Hungary)
  • Ludwig KRAUS (IFT Institute for Therapy Research, Germany)
  • Marc N. POTENZA (Yale University, USA)
  • Hans-Jurgen RUMPF (University of Lübeck, Germany)
  • Ruth J. VAN HOLST (Amsterdam UMC, The Netherlands)

Editorial Board

  • Sophia ACHAB (Faculty of Medicine, University of Geneva, Switzerland)
  • Alex BALDACCHINO (St Andrews University, United Kingdom)
  • Judit BALÁZS (ELTE Eötvös Loránd University, Hungary)
  • Maria BELLRINGER (Auckland University of Technology, Auckland, New Zealand)
  • Henrietta BOWDEN-JONES (Imperial College, United Kingdom)
  • Damien BREVERS (University of Luxembourg, Luxembourg)
  • Julius BURKAUSKAS (Lithuanian University of Health Sciences, Lithuania)
  • Gerhard BÜHRINGER (Technische Universität Dresden, Germany)
  • Silvia CASALE (University of Florence, Florence, Italy)
  • Luke CLARK (University of British Columbia, Vancouver, B.C., Canada)
  • Jeffrey L. DEREVENSKY (McGill University, Canada)
  • Geert DOM (University of Antwerp, Belgium)
  • Nicki DOWLING (Deakin University, Geelong, Australia)
  • Hamed EKHTIARI (University of Minnesota, United States)
  • Jon ELHAI (University of Toledo, Toledo, Ohio, USA)
  • Ana ESTEVEZ (University of Deusto, Spain)
  • Fernando FERNANDEZ-ARANDA (Bellvitge University Hospital, Barcelona, Spain)
  • Naomi FINEBERG (University of Hertfordshire, United Kingdom)
  • Sally GAINSBURY (The University of Sydney, Camperdown, NSW, Australia)
  • Belle GAVRIEL-FRIED (The Bob Shapell School of Social Work, Tel Aviv University, Israel)
  • Biljana GJONESKA (Macedonian Academy of Sciences and Arts, Republic of North Macedonia)
  • Marie GRALL-BRONNEC (University Hospital of Nantes, France)
  • Jon E. GRANT (University of Minnesota, USA)
  • Mark GRIFFITHS (Nottingham Trent University, United Kingdom)
  • Joshua GRUBBS (University of New Mexico, Albuquerque, NM, USA)
  • Anneke GOUDRIAAN (University of Amsterdam, The Netherlands)
  • Susumu HIGUCHI (National Hospital Organization Kurihama Medical and Addiction Center, Japan)
  • David HODGINS (University of Calgary, Canada)
  • Eric HOLLANDER (Albert Einstein College of Medicine, USA)
  • Zsolt HORVÁTH (Eötvös Loránd University, Hungary)
  • Susana JIMÉNEZ-MURCIA (Clinical Psychology Unit, Bellvitge University Hospital, Barcelona, Spain)
  • Yasser KHAZAAL (Geneva University Hospital, Switzerland)
  • Orsolya KIRÁLY (Eötvös Loránd University, Hungary)
  • Chih-Hung KO (Faculty of Medicine, College of Medicine, Kaohsiung Medical University, Taiwan)
  • Shane KRAUS (University of Nevada, Las Vegas, NV, USA)
  • Hae Kook LEE (The Catholic University of Korea, Republic of Korea)
  • Bernadette KUN (Eötvös Loránd University, Hungary)
  • Katerina LUKAVSKA (Charles University, Prague, Czech Republic)
  • Giovanni MARTINOTTI (‘Gabriele d’Annunzio’ University of Chieti-Pescara, Italy)
  • Gemma MESTRE-BACH (Universidad Internacional de la Rioja, La Rioja, Spain)
  • Astrid MÜLLER (Hannover Medical School, Germany)
  • Daniel Thor OLASON (University of Iceland, Iceland)
  • Ståle PALLESEN (University of Bergen, Norway)
  • Afarin RAHIMI-MOVAGHAR (Teheran University of Medical Sciences, Iran)
  • József RÁCZ (Hungarian Academy of Sciences, Hungary)
  • Michael SCHAUB (University of Zurich, Switzerland)
  • Marcantanio M. SPADA (London South Bank University, United Kingdom)
  • Daniel SPRITZER (Study Group on Technological Addictions, Brazil)
  • Dan J. STEIN (University of Cape Town, South Africa)
  • Sherry H. STEWART (Dalhousie University, Canada)
  • Attila SZABÓ (Eötvös Loránd University, Hungary)
  • Hermano TAVARES (Instituto de Psiquiatria do Hospital das Clínicas da Faculdade de Medicina, Universidade de São Paulo, São Paulo, Brazil)
  • Wim VAN DEN BRINK (University of Amsterdam, The Netherlands)
  • Alexander E. VOISKOUNSKY (Moscow State University, Russia)
  • Aviv M. WEINSTEIN (Ariel University, Israel)
  • Anise WU (University of Macau, Macao, China)
  • Ágnes ZSILA (ELTE Eötvös Loránd University, Hungary)

 

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