Statistical models for social networks as dependent variables must represent the typical network dependencies between tie variables such as reciprocity, homophily, transitivity, etc. This review ...first treats models for single (cross-sectionally observed) networks and then for network dynamics. For single networks, the older literature concentrated on conditionally uniform models. Various types of latent space models have been developed: for discrete, general metric, ultrametric, Euclidean, and partially ordered spaces. Exponential random graph models were proposed long ago but now are applied more and more thanks to the non-Markovian social circuit specifications that were recently proposed. Modeling network dynamics is less complicated than modeling single network observations because dependencies are spread out in time. For modeling network dynamics, continuous-time models are more fruitful. Actor-oriented models here provide a model that can represent many dependencies in a flexible way. Strong model development is now going on to combine the features of these models and to extend them to more complicated outcome spaces.
Multiple regression quadratic assignment procedures (MRQAP) tests are permutation tests for multiple linear regression model coefficients for data organized in square matrices of relatedness among ..."n" objects. Such a data structure is typical in social network studies, where variables indicate some type of relation between a given set of actors. We present a new permutation method (called "double semi-partialing", or DSP) that complements the family of extant approaches to MRQAP tests. We assess the statistical bias (type I error rate) and statistical power of the set of five methods, including DSP, across a variety of conditions of network autocorrelation, of spuriousness (size of confounder effect), and of skewness in the data. These conditions are explored across three assumed data distributions: normal, gamma, and negative binomial. We find that the Freedman-Lane method and the DSP method are the most robust against a wide array of these conditions. We also find that all five methods perform better if the test statistic is pivotal. Finally, we find limitations of usefulness for MRQAP tests: All tests degrade under simultaneous conditions of extreme skewness and high spuriousness for gamma and negative binomial distributions.
The co-evolution of adolescents' friendship networks and their smoking behavior is examined in a large sample across six European countries. Selection and influence processes are disentangled using ...new methods of social network analysis that enable alternative selection mechanisms to be controlled for. The sample consisted of 7704 adolescents participating in the control group of the ESFA (European Smoking prevention Framework Approach) study. The design was longitudinal with four observations. The main measurements were friendship ties, adolescents smoking behavior, parental smoking behavior, and sibling smoking behavior. Results indicated that in each country adolescents preferred selecting friends based on similar smoking behavior. Support for the influence of friends was found in only two countries. A similarity in smoking behavior between friends was explained more strongly by smoking-based selection processes than by the influence of friends in each of the six countries. Prevention programs need to address aspects that drive peer selection, and reinforce non-smoking attitudes in adolescents.
Two approaches for the statistical analysis of social network generation are widely used; the tie-oriented exponential random graph model (ERGM) and the stochastic actor-oriented model (SAOM) or ...Siena model. While the choice for either model by empirical researchers often seems arbitrary, there are important differences between these models that current literature tends to miss. First, the ERGM is defined on the graph level, while the SAOM is defined on the transition level. This allows the SAOM to model asymmetric or one-sided tie transition dependence. Second, network statistics in the ERGM are defined globally but are nested in actors in the SAOM. Consequently, dependence assumptions in the SAOM are generally stronger than in the ERGM. Resulting from both, meso- and macro-level properties of networks that can be represented by either model differ substantively and analyzing the same network employing ERGMs and SAOMs can lead to distinct results. Guidelines for theoretically founded model choice are suggested.
Stochastic actor-based models for network dynamics have the primary aim of statistical inference about processes of network change, but may be regarded as a kind of agent-based models. Similar to ...many other agent-based models, they are based on local rules for actor behavior. Different from many other agent-based models, by including elements of generalized linear statistical models they aim to be realistic detailed representations of network dynamics in empirical data sets. Statistical parallels to micro–macro considerations can be found in the estimation of parameters determining local actor behavior from empirical data, and the assessment of goodness of fit from the correspondence with network-level descriptives. This article studies several network-level consequences of dynamic actor-based models applied to represent cross-sectional network data. Two examples illustrate how network-level characteristics can be obtained as emergent features implied by microspecifications of actor-based models.
Statistical Power in Longitudinal Network Studies Stadtfeld, Christoph; Snijders, Tom A. B.; Steglich, Christian ...
Sociological methods & research,
11/2020, Letnik:
49, Številka:
4
Journal Article
Recenzirano
Odprti dostop
Longitudinal social network studies can easily suffer from insufficient statistical power. Studies that simultaneously investigate change of network ties and change of nodal attributes (selection and ...influence studies) are particularly at risk because the number of nodal observations is typically much lower than the number of observed tie variables. This article presents a simulation-based procedure to evaluate statistical power of longitudinal social network studies in which stochastic actor-oriented models are to be applied. Two detailed case studies illustrate how statistical power is strongly affected by network size, number of data collection waves, effect sizes, missing data, and participant turnover. These issues should thus be explored in the design phase of longitudinal social network studies.
A recurrent problem in the analysis of behavioral dynamics, given a simultaneously evolving social network, is the difficulty of separating the effects of partner selection from the effects of social ...influence. Because misattribution of selection effects to social influence, or vice versa, suggests wrong conclusions about the social mechanisms underlying the observed dynamics, special diligence in data analysis is advisable. While a dependable and valid method would benefit several research areas, according to the best of our knowledge, it has been lacking in the extant literature. In this paper, we present a recently developed family of statistical models that enables researchers to separate the two effects in a statistically adequate manner. To illustrate our method, we investigate the roles of homophile selection and peer influence mechanisms in the joint dynamics of friendship formation and substance use among adolescents. Making use of a three-wave panel measured in the years 1995-1997 at a school in Scotland, we are able to assess the strength of selection and influence mechanisms and quantify the relative contributions of homophile selection, assimilation to peers, and control mechanisms to observed similarity of substance use among friends.
A statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed. The probability model assumes that the vertices of the digraph are partitioned into several ...unobserved (latent) classes and that the probability distribution of the relation between two vertices depends only on the classes to which they belong. A Bayesian estimator based on Gibbs sampling is proposed. The basic model is not identified, because class labels are arbitrary. The resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant functions of the parameters and the vertex class membership. In addition, models are considered where class labels are identified by prior distributions for the class membership of some of the vertices. The model is illustrated by an example from the social networks literature (Kapferer's tailor shop).
The complex interplay between bullying/victimization and defending was examined using a longitudinal social network approach (stochastic actor-based models). The (co)evolution of these relations ...within three elementary schools (Grades 2-5 at Time 1, ages 8-11, N = 354 children) was investigated across three time points within a year. Most bullies and defenders were in the same grade as the victims, although a substantial number of bullies and defenders were in other grades (most often one grade higher). Defenders were usually of the same gender as the victims, whereas most bullies were boys, with boys bullying both boys and girls. In line with goal-framing theory, multiplex network analyses provided evidence for the social support hypothesis (victims with the same bullies defended each other over time) as well as the retaliation hypothesis (defenders run the risk of becoming victimized by the bullies of the victims they defend). In addition, the analysis revealed that bullies with the same victims defended each other over time and that defenders of bullies initiated harassment of those bullies' victims. This study can be seen as a starting point in unraveling the relationship dynamics among bullying, victimization, and defending networks in schools.
► Analysis of peer effects in educational settings. ► Longitudinal data on academic performance, friendship, and advice relations among MBA students. ► Process of peer selection modelled by ...actor-oriented models. ► Social influence operates similarly for friendship and advice networks. ► High performers are less likely to initiating ties, to be chosen as friends but are sought after as advisors.
Studies of peer effects in educational settings confront two main problems. The first is the presence of endogenous sorting which confounds the effects of social influence and social selection on individual attainment. The second is how to account for the local network dependencies through which peer effects influence individual behavior. We empirically address these problems using longitudinal data on academic performance, friendship, and advice seeking relations among students in a full-time graduate academic program. We specify stochastic agent-based models that permit estimation of the interdependent contribution of social selection and social influence to individual performance. We report evidence of peer effects. Students tend to assimilate the average performance of their friends and of their advisors. At the same time, students attaining similar levels of academic performance are more likely to develop friendship and advice ties. Together, these results imply that processes of social influence and social selection are sub-components of a more general a co-evolutionary process linking network structure and individual behavior. We discuss possible points of contact between our findings and current research in the economics and sociology of education.
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