Research Note: The consequences of different methods for handling missing network data in Stochastic Actor Based Models

Disentangling associations between pubertal development, healthy activity behaviors, and sex in adolescent social networks

With the onset of puberty, youth begin to choose their social environments and develop health-promoting habits, making it a vital period to study social and biological factors contextually. An important question is how pubertal development and behaviors such as physical activity and sleep may be differentially linked with youths' friendships. Cross-sectional statistical network models that account for interpersonal dependence were used to estimate associations between three measures of pubertal development and youth friendships at two large US schools drawn from the National Longitudinal Study of Adolescent to Adult Health. Whole-network models suggest that friendships are more likely between youth with similar levels of pubertal development, physical activity, and sleep. Sex-stratified models suggest that girls' friendships are more likely given a similar age at menarche. Attention to similar pubertal timing within friendship groups may offer inclusive opportunities for tailored developmental puberty education in ways that reduce stigma and improve health behaviors.

Network sampling coverage III: Imputation of missing network data under different network and missing data conditions

Missing data is a common, difficult problem for network studies. Unfortunately, there are few clear guidelines about what a researcher should do when faced with incomplete information. We take up this problem in the third paper of a three-paper series on missing network data. Here, we compare the performance of different imputation methods across a wide range of circumstances characterized in terms of measures, networks and missing data types. We consider a number of imputation methods, going from simple imputation to more complex model- based approaches. Overall, we find that listwise deletion is almost always the worst option, while choosing the best strategy can be difficult, as it depends on the type of missing data, the type of network and the measure of interest. We end the paper by offering a set of practical outputs that researchers can use to identify the best imputation choice for their particular research setting.

International Students’ Cross-Cultural Adjustment: Social Selection or Social Influence?

International education provides students with an opportunity to develop new social networks while they fit in to the new culture. In a three-wave longitudinal study, we investigated how social networks and psychological adjustment coevolve within a group of international students enrolled in a coursework degree at the tertiary level. Using the Stochastic Actor-Oriented Model (SAOM), we identified the occurrences of social selection based on the levels of psychological and sociocultural adjustment. More specifically, students tended to deselect classmates who were dissimilar in their level of psychological adjustment and to befriend those who differed in their levels of sociocultural adjustment. In contrast, little evidence was found to suggest that features of social networks influenced students’ adjustment. Potential applications of this new method to future acculturation research are suggested.

Fixed choice design and augmented fixed choice design for network data with missing observations

The statistical analysis of social networks is increasingly used to understand social processes and patterns. The association between social relationships and individual behaviors is of particular interest to sociologists, psychologists, and public health researchers. Several recent network studies make use of the fixed choice design (FCD), which induces missing edges in the network data. Because of the complex dependence structure inherent in networks, missing data can pose very difficult problems for valid statistical inference. In this article, we introduce novel methods for accounting for the FCD censoring and introduce a new survey design, which we call the augmented fixed choice design (AFCD). The AFCD adds considerable information to analyses without unduly burdening the survey respondent, resulting in improvements over the FCD, and other existing estimators. We demonstrate this new method through simulation studies and an analysis of alcohol use in a network of undergraduate students living in a residence hall.

The interdependence of cigarette, alcohol, and marijuana use in the context of school-based social networks

The concurrent or sequential usage of multiple substances during adolescence is a serious public health problem. Given the importance of understanding interdependence in substance use during adolescence, the purpose of this study is to examine the co-evolution of cigarette smoking, alcohol, and marijuana use within the ever-changing landscape of adolescent friendship networks, which are a primary socialization context for adolescent substance use. Utilizing Stochastic Actor-Based models, we examine how multiple simultaneous social processes co-evolve with adolescent smoking, drinking, and marijuana use within adolescent friendship networks using two school samples from early waves of the National Longitudinal Study of Adolescent to Adult Health (Add Health). We also estimate two separate models examining the effects from using one substance to the initiation and cessation of other substances for each sample. Based on the initial model results, we simulate the model forward in time by turning off one key effect in the estimated model at a time, and observe how the distribution of use of each substance changes. We find evidence of a unilateral causal relationship from marijuana use to subsequent smoking and drinking behaviors, resulting in the initiation of drinking behavior. Marijuana use is also associated with smoking initiation in a school with a low substance use level, and smoking cessation in a school with a high substance use level. In addition, in a simulation model excluding the effect from marijuana use to smoking and drinking behavior, the number of smokers and drinkers decreases precipitously. Overall, our findings indicate some evidence of sequential drug use, as marijuana use increased subsequent smoking and drinking behavior and indicate that an adolescent's level of marijuana use affects the initiation and continuation of smoking and drinking.

Stability of centrality measures in valued networks regarding different actor non-response treatments and macro-network structures

Social network data are prone to errors regardless their source. This paper focuses on missing data due to actor non-response in valued networks. If actors refuse to provide information, all values for outgoing ties are missing. Partially observed incoming ties to non-respondents and all other patterns for ties between members of the network can be used to impute missing outgoing ties. Many centrality measures are used to determine the most prominent actors inside the network. Using treatments for actor non-response enables us to estimate better the centrality scores of all actors regarding their popularity or prominence. Simulations using initial known blockmodel structures based on three most frequently occurring macro-network structures: cohesive subgroups, core-periphery models, and hierarchical structures were used to evaluate the relative merits of the treatments for non-response. The results indicate that the amount of non-respondents, the type of underlying macro-structure, and the employed treatment have an impact on centrality scores. Regardless of the underlying network structure, the median of the 3-nearest neighbors based on incoming ties performs the best. The adequacy (or not) of the other non-response treatments is contingent on the network macro-structure.

Peer Influence, Peer Selection and Adolescent Alcohol Use: a Simulation Study Using a Dynamic Network Model of Friendship Ties and Alcohol Use

While studies suggest that peer influence can in some cases encourage adolescent substance use, recent work demonstrates that peer influence may be on average protective for cigarette smoking, raising questions about whether this effect occurs for other substance use behaviors. Herein, we focus on adolescent drinking, which may follow different social dynamics than smoking. We use a data-calibrated Stochastic Actor-Based (SAB) Model of adolescent friendship tie choice and drinking behavior to explore the impact of manipulating the size of peer influence and selection effects on drinking in two school-based networks. We first fit a SAB Model to data on friendship tie choice and adolescent drinking behavior within two large schools (n = 2178 and n = 976) over three time points using data from the National Longitudinal Study of Adolescent to Adult Health. We then alter the size of the peer influence and selection parameters with all other effects fixed at their estimated values and simulate the social systems forward 1000 times under varying conditions. Whereas peer selection appears to contribute to drinking behavior similarity among adolescents, there is no evidence that it leads to higher levels of drinking at the school level. A stronger peer influence effect lowers the overall level of drinking in both schools. There are many similarities in the patterning of findings between this study of drinking and previous work on smoking, suggesting that peer influence and selection may function similarly with respect to these substances.

Analysing animal social network dynamics: the potential of stochastic actor-oriented models

Animals are embedded in dynamically changing networks of relationships with conspecifics. These dynamic networks are fundamental aspects of their environment, creating selection on behaviours and other traits. However, most social network‐based approaches in ecology are constrained to considering networks as static, despite several calls for such analyses to become more dynamic.

There are a number of statistical analyses developed in the social sciences that are increasingly being applied to animal networks, of which stochastic actor‐oriented models (SAOMs) are a principal example. SAOMs are a class of individual‐based models designed to model transitions in networks between discrete time points, as influenced by network structure and covariates. It is not clear, however, how useful such techniques are to ecologists, and whether they are suited to animal social networks.

We review the recent applications of SAOMs to animal networks, outlining findings and assessing the strengths and weaknesses of SAOMs when applied to animal rather than human networks. We go on to highlight the types of ecological and evolutionary processes that SAOMs can be used to study.

SAOMs can include effects and covariates for individuals, dyads and populations, which can be constant or variable. This allows for the examination of a wide range of questions of interest to ecologists. However, high‐resolution data are required, meaning SAOMs will not be useable in all study systems. It remains unclear how robust SAOMs are to missing data and uncertainty around social relationships.

Ultimately, we encourage the careful application of SAOMs in appropriate systems, with dynamic network analyses likely to prove highly informative. Researchers can then extend the basic method to tackle a range of existing questions in ecology and explore novel lines of questioning.

Network sampling coverage II: The effect of non-random missing data on network measurement

Missing data is an important, but often ignored, aspect of a network study. Measurement validity is affected by missing data, but the level of bias can be difficult to gauge. Here, we describe the effect of missing data on network measurement across widely different circumstances. In Part I of this study (Smith and Moody, 2013), we explored the effect of measurement bias due to randomly missing nodes. Here, we drop the assumption that data are missing at random: what happens to estimates of key network statistics when central nodes are more/less likely to be missing? We answer this question using a wide range of empirical networks and network measures. We find that bias is worse when more central nodes are missing. With respect to network measures, Bonacich centrality is highly sensitive to the loss of central nodes, while closeness centrality is not; distance and bicomponent size are more affected than triad summary measures and behavioral homophily is more robust than degree-homophily. With respect to types of networks, larger, directed networks tend to be more robust, but the relation is weak. We end the paper with a practical application, showing how researchers can use our results (translated into a publically available java application) to gauge the bias in their own data.

Coevolution of adolescent friendship networks and smoking and drinking behaviors with consideration of parental influence

Friendship tie choices in adolescent social networks coevolve simultaneously with youths' cigarette smoking and drinking. We estimate direct and multiplicative relationships between both peer influence and peer selection with salient parental factors affecting both friendship tie choice and the use of these 2 substances. We utilize 1 sample of 12 small schools and a single large school extracted from the National Longitudinal Study of Adolescent to Adult Health. Using a Stochastic Actor-Based modeling approach over 3 waves, we find: (a) a peer selection effect, as adolescents nominated others as friends based on cigarette and alcohol use levels across samples; (b) a peer influence effect, as adolescents adapted their smoking and drinking behaviors to those of their best friends across samples; (c) reciprocal effect between cigarette and alcohol usage in the small school sample; (d) a direct effect of parental support and the home smoking environment on adolescent friendship tie choice in the small school sample; (e) a direct effect of the home smoking environment on smoking across samples; (f) a direct effect of the home drinking environment on alcohol use across samples; and (g) a direct effect of parental monitoring on alcohol use across samples. We observed an interaction between parental support and peer influence in affecting drinking, and an interaction between the home drinking environment and peer influence on drinking, in the small school sample. Our findings suggested the importance of delineating direct and synergistic pathways linking network processes and parental influence as they affect concurrent cigarette and alcohol use. (PsycINFO Database Record

Multiple Imputation for Missing Edge Data: A Predictive Evaluation Method with Application to Add Health

Recent developments have made model-based imputation of network data feasible in principle, but the extant literature provides few practical examples of its use. In this paper we consider 14 schools from the widely used In-School Survey of Add Health (Harris et al., 2009), applying an ERGM-based estimation and simulation approach to impute the network missing data for each school. Add Health's complex study design leads to multiple types of missingness, and we introduce practical techniques for handing each. We also develop a cross-validation based method - Held-Out Predictive Evaluation (HOPE) - for assessing this approach. Our results suggest that ERGM-based imputation of edge variables is a viable approach to the analysis of complex studies such as Add Health, provided that care is used in understanding and accounting for the study design.

Simulating Dynamic Network Models and Adolescent Smoking: The Impact of Varying Peer Influence and Peer Selection

We used a stochastic actor-based approach to examine the effect of peer influence and peer selection--the propensity to choose friends who are similar--on smoking among adolescents. Data were collected from 1994 to 1996 from 2 schools involved in the National Longitudinal Study of Adolescent to Adult Health, with respectively 2178 and 976 students, and different levels of smoking. Our experimental manipulations of the peer influence and selection parameters in a simulation strategy indicated that stronger peer influence decreased school-level smoking. In contrast to the assumption that a smoker may induce a nonsmoker to begin smoking, adherence to antismoking norms may result in an adolescent nonsmoker inducing a smoker to stop smoking and reduce school-level smoking.