2.1 Developing a social network typology

A personal network is a set of individuals who are linked to each other in ways specified by social roles (Hall and Wellman, Reference Hall, Wellman, Cohen and Syme1985). Traditional studies focusing on a single network aspect, nevertheless, ignore the multidimensional nature of social networks, and their findings would be confounded by the remaining aspects due to mutual interdependence (Li and Zhang, Reference Li and Zhang2015). To address these methodological caveats, inductive network typology turns out to be an economic, comprehensive, and useful way to encapsulate the main characteristics of networks. Previous network-health studies consistently report four common networks that have cross-cultural validity, namely Restricted, Friend, Family, and Diverse (Li and Zhang, Reference Li and Zhang2015). Besides, other distinct types have been identified among non-Western populations. For instance, the Congregant network, deeply involved in religious activities, has been reported in Korea and Israel (Litwin and Shiovitz-Ezra, Reference Litwin and Shiovitz-Ezra2011; Sohn et al., Reference Sohn, Joo, Kim, Kim, Youm, Kim and Lee2017), and a Distant Family network focusing on extended kin has been found in a sample of older Chinese adults (Cheng et al., Reference Cheng, Lee, Chan, Leung and Lee2009).

These inconsistencies may, on one hand, stem from cultural heterogeneity across countries, and on the other hand, from different sets of network variables selected to train the clustering algorithm and different algorithms employed. In terms of criterion variable selections, two lines of research exist that differ in variable choice and the resulting typology, namely support classification and structural classification (Maya-Jariego, Reference Maya-Jariego2021). The former emphasizes support-related information, such as the number of supportive network members and composition of help providers, while the latter further includes structural indicators such as network size, homogeneity, and density. Most network typology-health research to date follows the support classification tradition that considers the location and resource feature yet ignores structural elements. Consequently, the typology obtained fails to comprehensively represent social networks, and subsequent analysis may suffer from omitted variable bias. To overcome these potential drawbacks, the current study selects criterion variables that cover both support and structural dimensions so that the typology “captures the holistic nature of networks” (Perry et al., Reference Perry, Pescosolido and Borgatti2018).

In terms of the algorithm, K-means clustering and the more recently developed latent variable modeling techniques are commonly employed to detect network typology (Park et al., Reference Park, Jang, Lee, Chiriboga, Chang and Kim2018). Nevertheless, K-means clustering hinders researchers from including more criterion variables due to “the curse of high dimensionality” (Kouiroukidis and Evangelidis, Reference Kouiroukidis and Evangelidis2011). Further, K-means and latent analysis are also sensitive to noise, outliers, and variable scales, which may obscure the discovery of robust network types (Giannella and Fischer, Reference Giannella and Fischer2016). To overcome these obstacles, G&F use the random forest to construct network types because it can capture the most useful variables in characterizing distinctive network types. Also, it outperforms traditional clustering methods because of its compatibility with both continuous and categorical variables with different scales, robustness to outliers, incorporation of extraneous features, and adaptation to multicollinearity (Cutler et al., Reference Cutler, Cutler and Stevens2012). Hence, we build on G&F’s method to identify network typology in this sample.

2.2 Pandemic and social network dynamics

The vast literature on network dynamics suggests personal networks are likely to change as pandemic-induced social distancing policies, such as public space closures, become more stringent. First, social networks are shaped by structural contexts. According to Feld (Reference Feld1981), personal networks evolve around foci, namely social entities, contexts, or organizations, such as the workplace, school, home, or voluntary clubs. They are also referred to as context or spatial composition, without which social interactions and joint activities are unlikely to take place, and social ties cannot be formed or sustained (Blau, Reference Blau1977; Small and Adler, Reference Small and Adler2019). Social distancing policies change the accessibility of these foci by closing schools, restaurants, and other public spaces, but at the same time encourage staying-at-home behaviors, which make individuals switch network types. For instance, networks between Cornell University students became less dense, less connected, and more fragmented during the pandemic when on-campus teaching was replaced by a hybrid instruction mode (Weeden et al., Reference Weeden, Cornwell and Park2021).

Second, personal networks change because they “adapt to the dynamic and uncertain environment” (Perry, Reference Perry, Pescosolido, Perry, Smith and Small2021), which is exactly the case of the pandemic, and especially during lockdowns. Previous research found that individuals endeavor to activate their network ties for help in times of crises, and rely heavily on kinship ties for resources in contexts such as Hurricane Katrina (Hurlbert et al., Reference Hurlbert, Haines and Beggs2000) or the Gulf War (Shavit et al., Reference Shavit, Fischer and Koresh1994). Friendship networks among students have also proved to be robust in the context of COVID-19, as nominations for informational and emotional assistance increased modestly (Elmer et al., Reference Elmer, Mepham and Stadtfeld2020). Changes in network types also occur as the ego’s needs evolve or when alters self-activate to offer help upon perceiving the ego’s difficulties (Perry and Pescosolido, Reference Perry and Pescosolido2012; Small, Reference Small, Pescosolido, Perry, Smith and Small2021). In the case of Wuhan, a large number of volunteers from local neighborhoods formed non-kin networks during the lockdown to meet local residents’ needs of grocery deliveries, medicine purchases, basic health services, and so on (Miao et al., Reference Miao, Zeng and Shi2021). Therefore, we have the following hypotheses about network turnover that contextualize social inequality in mental health during the pandemic.

2.3 Network types, health, and SES

Among commonly reported network types, Restricted networks are characterized as being limited in every supportive aspect of networks and thus associated with the worst mental health profile (Cheng et al., Reference Cheng, Lee, Chan, Leung and Lee2009; Litwin, Reference Litwin2001; Litwin and Shiovitz-Ezra, Reference Litwin and Shiovitz-Ezra2011). On the contrary, Diverse networks are considered a more beneficial type for health (Moore et al., Reference Moore, Daniel, Paquet, Dubé and Gauvin2009). The superiority of Friend vis-à-vis Family networks remains debated. Some studies suggest that Friend networks yield better mental health (see, Antonucci et al., Reference Antonucci, Fiori, Birditt, Jackey, Lerner, Overton, Lamb and Freund2010), whereas other research, especially those conducted in East Asian contexts, finds that Family networks are either among the healthiest types or similar to friend-focused types (Cheng et al., Reference Cheng, Lee, Chan, Leung and Lee2009; Fiori et al., Reference Fiori, Antonucci and Akiyama2008, Reference Fiori, Smith and Antonucci2007).

Although individuals’ network types are strong predictors of health outcomes (Litwin, Reference Litwin2001), estimated effects in previous research may be confounded by personal- and macro-level background factors. First, according to the social convoy theory, personal background factors including age, personality, life and family history (e.g., divorce, unemployment, imprisonment), all affect individuals’ network types (see, Antonucci et al., Reference Antonucci, Fiori, Birditt, Jackey, Lerner, Overton, Lamb and Freund2010; Kahn and Antonucci, Reference Kahn, Antonucci, Baltes and Brim1980), and yet they are also important social determinants of health (Phelan et al., Reference Phelan, Link and Tehranifar2010). Second, the macro-level context that individuals are embedded in, such as cultural background and level of regional economic development, shapes both their social network types and mental health simultaneously (Li et al., Reference Li, Yang and Zhang2018). Therefore, the current study uses fixed-effect models to rule out these observed and unobserved confounders and examines the health effect of network types.

More importantly, the impact of network type on life outcomes may not be universal or constant. Instead, it tends to be contingent on the SES of the ego according to the strand of study on social capital and network inequality (Shepherd and Garip, Reference Shepherd, Garip, Pescosolido, Perry, Smith and Small2021). On the one hand, high-SES individuals have more resource-enriching personal networks. For instance, Campbell et al. (Reference Campbell, Marsden and Hurlbert1986) demonstrated that network members’ educational level, job prestige, and family income are positively related to the SES of the ego. These network deficits make low SES groups less likely to have the resources they need in their networks (Lai et al., Reference Lai, Lin and Leung1998), which has been used to explain why poverty is self-perpetuating (Granovetter, Reference Granovetter1983). On the other hand, higher-SES individuals are more capable of accessing the resources in personal networks than their low-SES counterparts, even if the resources embedded in their networks are similar. For example, research in social capital activation has found that weak ties are beneficial for job status only for high SES individuals (Lin et al., Reference Lin, Ensel and Vaughn1981). By contrast, low-status individuals are often denied assistance even though they already have alters in their networks who wield the resources needed. They also have difficulties mobilizing social ties for resources due to the “functional deficit” of personal networks, especially in low SES neighborhoods and among low-wage occupations (Smith, Reference Smith2005). This leads to our central hypothesis on the heterogeneous protective effect of networks across SES groups.

In terms of why personal networks impact health, previous literature proposed three mechanisms, namely, social support, social capital, and behavioral diffusion (McCarty et al., Reference McCarty, Lubbers, Vacca and Molina2019). Most network typology-health studies rely on the first framework that highlights the benefit of embedded social support on buffering life stressors and facilitating resilient coping strategies (Cohen et al., Reference Cohen, Underwood and Gottlieb2000; Song et al., Reference Song, Son, Lin, Scott and Carrington2011), which the present study follows to explain the network health disparities. Though scholars have long articulated the multidimensional nature of social support, which consists of actual support and perceived support according to the degree of subjectivity, only a few empirical studies take both aspects into consideration (Lin and Peek, Reference Lin, Peek, Horwitz and Scheid1999; Song et al., Reference Song, Son, Lin, Scott and Carrington2011). Even if individuals are embedded in networks with abundant resources, they could still feel lonely, disconnected, and unsatisfied with the current network conditions (de Jong Gierveld et al., Reference de Jong Gierveld, Van Groenou, Hoogendoorn and Smit2009). Hence, the paper also examines different levels of social support embedded in each network type to help make sense of our central hypothesis on the network effect heterogeneity across SES groups.

3.1 Data

The data for this study are the Wuhan subsample of COVID-19 and the Social Network Panel Study (CovNetps-Wuhan), a web-based survey with a representative sample of the college population in Wuhan city. Respondents are drawn proportionately according to the five-tier system developed by the Ministry of Education (MOE), a classification system that ranks the higher educational institutions (HEI) from the most selective national universities to local vocational colleges (see Section A1, Supplementary Material). The first wave of CovNetps-Wuhan was collected between March and May 2020, at the end of the first wave outbreak in China, to fully capture the network consequences of pandemic exposure. A total of 2,047 respondents participated in the study, who were then residing in all provincial-level administrative regions of China during the pandemic. The second wave was conducted from January to February 2021, three months after the reopening of the campus following MOE’s administrative order. In total, 524 respondents participated in the follow-up survey. All qualified participants in Cov-Netps study meet the following screening criteria: (1) currently being enrolled in one of Wuhan’s HEI; (2) aged 17 or above; (3) choose the “I agree to participate in this study” option; (4) manage to pass two filtering questions; and (5) spend an average of at least 3 s on each item. In this research, we further employ list-wise deletion on less than 5% of the respondents who reported missing or unmatched information. CovNetps-Wuhan applies egocentric network study methods to capture an individual’s core networks through a two-step process similar to Fischer (Reference Fischer1982). First, a name generator asked respondents to recall “people you typically do these sorts of things with, or other social things as well, such as going shopping, out for sports, studying together, chatting, or people who are important to you (both online and offline)”, and then the survey recorded up to six names reported. Next, in the following name-interpreting stage, respondents were requested to describe their relationship with alters, the characteristics of each alter, and the connections among alters. These items offer detailed knowledge on personal networks, paving the way for our network typology development.

3.2 Measures

Social network types. Social network typology is derived from the 43 network indicators listed in Table S1, Supplementary Material. These variables are selected or constructed to cover different network aspects to obtain a comprehensive typology (Moren-Cross and Lin, Reference Moren-Cross, Lin, Binstock and George2006).

Depressive symptoms. As a dependent variable, we use the nine-item version of the Center for Epidemiologic Studies-Depression Scale (CES-D) to measure depressive symptoms and represent respondents’ mental health status (Santor and Coyne, Reference Santor and Coyne1997). The depression scale asks respondents the number of days in the past week that they experience certain emotions (e.g., sad, depressed, happy), and we recoded the scale so that a higher score indicates a higher level of depressive symptoms.

The pandemic and social distancing. We use the data from the Oxford Covid-19 Government Response Tracker that captures government policies related to space closure and social distancing (Hale et al., Reference Hale, Angrist, Goldszmidt, Kira, Petherick, Phillips, Webster, Cameron-Blake, Hallas and Majumdar2021). The database includes seven indicators of social distancing policies, which can be used as proxies to capture the disruptions caused by the pandemic. These include the closure of schools, closure of workplaces, cancellation of public events, limits on gatherings, closure of public transport, stay-at-home requirements, and restrictions on travels between cities/regions (0 = no measures, 1 = recommend closing, 2 = require closing only some levels, 3 = require closing all levels), and we use the factor score of these items to measure the strength of local social distancing policies.

Actual and perceived support. Social support is considered in both actual support and perceived support dimensions, which are considered equally important (Moren-Cross and Lin, Reference Moren-Cross, Lin, Binstock and George2006; Wethington and Kessler, Reference Wethington and Kessler1986). Actual support is measured by the number of alters with whom respondents confide personal matters, exchange pandemic-related information, discuss entertainment topics, and from whom they receive substantial help. The second dimension, perceived support, reflects the self-rated quality of social support or how satisfied respondents are with their current networks. It is measured by three dichotomous questions asking whether they hope to meet more friends to confide, hang out, and provide practical help (0 = Hope to know more, 1 = Enough for now). A higher score indicates the respondent is more satisfied and has a higher level of perceived social support. In alignment with the literature, Confirmatory Factor Analysis demonstrates that our two-factor model of social support fits the data well ( $\chi ^{2}$ = 59.196, df = 13, RMSEA = 0.037, CFI = 0.990, TLI = 0.983), which is superior to a traditional single-dimension construct ( $\Delta \chi ^{2}$ = 2312.827, $p \lt 0.001$ ).

SES and other control variables. The MacArthur scale of subjective socioeconomic status (SES) is used to measure SES. Sociodemographic covariates are age, gender, single or not, educational status, and college type in the five-tier system. In terms of the pandemic’s impact, we also control the cumulative confirmed cases (log-transformed) and respondents’ COVID experience. For subsequent analysis, the fixed-effect model has already held all time-invariant confounders constant. The descriptive statistics of all variables are presented in Table 1, and the sociodemographic profile of different network types is reported in Table 2.

Table 1.

Descriptive statistics of wave one and wave two data

Table 2.

Background characteristics, socioeconomic status, and depressive symptoms by seven network types

Notes: Only 1,881 of 2,047 Wave One respondents embedded in coherent network types (prediction accuracy $\gt$ 80%) are included. $M$ = mean; SD = standard deviation. ^*** $p \lt 0.001$ , ^** $p \lt 0.01$ .

3.3 Analytical strategy

Developing a network typology. We build on the network typology methodology developed by G&F and further adopt the streamlined version as demonstrated by Laier et al. (Reference Laier, Hennig and Hundsdorfer2022). The original G&F methodology is a multi-stage iterative process: it begins with an unsupervised random forest model on 43 raw network indicators to create a similarity matrix, then uses agglomerative clustering to partition observations into groups, followed by a supervised random forest model to assess prediction accuracy and filter out clusters with high prediction errors ( $\gt 20$ – $25\%$ ). Next, it creates composite variables through principal component analysis using only observations from these “coherent” clusters, reducing the 43 indicators to approximately 10 composite dimensions. Finally, the entire process—unsupervised random forest, clustering, and validation—is repeated using these composite variables to arrive at the final network types. This approach involves two complete clustering cycles with an intermediate filtering and dimensionality reduction step.

Following Laier et al. (Reference Laier, Hennig and Hundsdorfer2022), we tested whether skipping the intermediate steps (initial clustering, filtering, and PCA on filtered data) would affect results. Our analysis reveals that directly creating composite variables from all observations and clustering once on these composites yielded very similar cluster assignments. Therefore, we adopt this streamlined methodology: (1) reduce 43 network indicators to 10 composite variables using principal component analysis on all Wave 1 observations, (2) apply unsupervised random forest on these composite variables to generate a similarity matrix, (3) perform spectral clustering to partition observations into groups, and (4) use supervised random forest to validate prediction accuracy, retaining only clusters with prediction errors below 20%. This simplified approach produces seven network types substantively identical to those from the original method while significantly improving computational efficiency, reducing processing time to one-sixth of that of the original approach. For Wave 2 observations, we use the algorithm trained on Wave 1 data to perform out-of-sample prediction (for methodology details, see Section A2, Supplementary Material).

Moreover, we improve G&F’s method by applying the spectral clustering method in step two instead of hierarchical agglomerative clustering (HAC), which is used by previous research. Spectral clustering does not make a priori assumptions about the shape of the clusters (Von Luxburg, Reference Von Luxburg2007). It also performs better in this case and meets our research goal to obtain several distinctive, small, intuitive, and robust clusters. By contrast, HAC fails to fulfill our goal because the size of the resulting clusters tends to vary greatly in size (i.e., a few extremely large clusters and many small clusters), and this algorithm cannot revoke previously made decisions (Cheng et al., Reference Cheng, Qiao, Bian and Tao2011; Maimon and Rokach, Reference Maimon and Rokach2010; Smoliński et al., Reference Smoliński, Walczak and Einax2002). Figure 2 highlights how these two methods differ and how spectral clustering’s flexibility enables it to learn the data’s internal patterns more effectively. While HAC tends to maintain fixed clustering membership before the next split, the spectral clustering method allows making a “regret decision” that could change the individual’s cluster membership in the future split. Therefore, spectral clustering has the advantage of balancing the size of different clusters and thus generates a more desirable result for the task of clustering.

Fixed effect models. The fixed effect model takes all time-invariant variables into account (e.g., personality, family history, regional development), which are likely to correlate with both social network type and depressive symptoms. Since every respondent was treated as his/her own control in this model, fixed effect regression makes use of within-person variation observed in repeated measures, and the estimated effect reports the depressive symptoms outcome that would ensue should an “average” individual’s network type change (Boone-Heinonen et al., Reference Boone-Heinonen, Roux, Kiefe, Lewis, Guilkey and Gordon-Larsen2011; Rabe-Hesketh and Skrondal, Reference Rabe-Hesketh and Skrondal2008). To confirm our model selection, the Breusch–Pagan Lagrange multiplier test indicates pooled regression is biased for panel data analysis ( $\chi ^{2}$ = 76.41, df = 1, $p \lt 0.001$ ), and the Hausman test result ( $\chi ^{2}$ = 30.89, df = 14, $p \lt 0.001$ ) suggests that fixed effect model is more favorable over random effect model in the current study (Greene, Reference Greene2008). Last but not least, we implement inverse probability weighting (IPW) in all panel fixed-effects analyses to address potential bias arising from selective attrition between the two survey waves. Specifically, we first estimate each respondent’s probability of being observed in Wave 2 as a function of Wave-1 characteristics. We then weight the fixed-effects models by the inverse of this predicted retention probability, so that individuals who were under-represented among Wave-2 respondents receive greater weight in the estimation. This procedure rebalances the analytic sample to more closely resemble the original Wave-1 population and mitigates bias due to differential attrition that is correlated with observed characteristics. Importantly, IPW corrects for selection on observables rather than assuming random attrition, while preserving the within-individual identification afforded by the fixed-effects design.Footnote ¹