Conference Agenda

Social systems often exhibit multilevel structures, such as multiple classrooms, firms, or groups. These structures are assumed to be independent but share a common structure. Within each group, social actors are interconnected through various social relationships, such as friendship and bullying networks. Analyzing repeated observations of these multiplex relations across different groups allows for more generalizable results and addresses group-level research questions.

We propose a hierarchical extension to the multiplex p2 model, a mixed-effects model for cross-sectional binary multiplex network data. This multilevel multiplex p2 model allows for dependency modeling at the actor, dyad, and group levels. At the actor level, ties sent and/or received by the same actors are dependent across different relational dimensions as fixed and random effects. At the dyad level, ties between two actors are dependent across different relational dimensions as fixed effects. At the group level, multiplex relationships in each group share common structures across groups, meaning the fixed effects parameters in each multiplex network are correlated between groups. The model also incorporates group-level covariates, such as class size, in addition to actor and dyad-level covariates.

Compared to fitting each multiplex network separately and aggregating by meta-analysis, our approach estimates parameters more efficiently through pooling. The degree of pooling, which controls how much information is shared between groups, is determined by the data and a prior on the amount of pooling. We demonstrate the utility of the multilevel multiplex p2 model through an original study on gossip, as perceived by gossip senders and targets, and their differing perspectives. The study is based on data from 34 Hungarian elementary school classes.

Network data consists of dyadic observations. In contrast to monadic data, which observes aspects on an individual level, network data have two indices at a minimum. Furthermore, the two sets of indices are self-referent, i.e. they are sets of labels pointing to the same objects. For example, consider a classroom of 10 students. Each individual student receives a unique label, say i\in\left\{1,2,\ldots,10\right\}. Observing ages of the students could be represented as a monadic data variable, A_i. However, the dyadic `Friendship’ relation between all pairs of students is represented in the dyadic variable F_{ij}, where i,j\in\left\{1,2,\ldots,10\right\}. This immediately shows the inherent dependence of observations, as each student is involved in 18 observations (9 sending and 9 receiving), for example, the observations in the subset {F_{1j},\ F_{i1}\ \forall\ i,j\ \lnot\ 1} all are dependent on the friendship behavior of student with the label "1”. Classical statistical tests will lead to underestimation of parameter variance under such conditions. A remedy against such dependence is to use permutation tests, that relabel the network, hence generating a random data set with equal dependence, under the null-hypotheses. This approach is very succesful, but subject to stringent conditions. For example, multicollinearity and skewed distributions require specific adaptations of the permutation approach. Another less studied issue is due to heteroskedasticity which violates the basic assumption of permutation tests, namely the exchangeability assumption. Depending on its source heteroskedasticty can be dealt with through HC-consistent estimators, but also through specific permutaion schemes. A more persistent issue lays in the fact that some non-linear models, such as the logit model inherently induce heteroskedasticity. In this paper we study how different estimators (Maximum Likelihood, GMM) exacerbate the problem of heteroskedasticity with network data. Furthermore, we present a permutation test for the presence of heteroskedasticity, which may prevent overuse of remedies.

Consider for example the determinants of the choice to buy an electric vehicle (EV) or to use modern contraceptives (MC). Your choice of EV will be influenced by your concern for the environment, economic sensibilities, etc, but also the opinions about these things of your friends. Your choice of using MC will depend on whether you think it causes conflict, whether you think others approve, and whether it is important to you that others use MC but, in a small village, the opinion about these things of the people you spend your free time with will also be important. We propose a multivariate autologistic attribute model (MALAAM) for studying the social influence on multiple binary outcomes simultaneously for cross-sectional data. This MALAAM has a regular graphical model for contingency tables as a special case. Furthermore, setting some interactions to zero yields a product ALAAM, where independent ALAAMs are estimated jointly for multiple outcomes. We demonstrate a Bayesian inference procedure for obtaining the posteriors of the model parameters and a Bayesian model selection approach using DIC. Applying this modelling framework to data on MC use in a Kenyan village we find that there are different types of social influence on different outcomes and that the social dependencies confound associations that would be inferred using a regular graphical model.

The preferential attachment model is often suggested to be the underlying mechanism of a network’s growth, largely due to that the degree distribution often follows the power law, albeit approximately and partially. While such attribution can be made in the absence of the network’s evolution history, it is more sensible to directly model the evolution when such data is available. This is the case in this work, where the incremental changes of the dependency network of R packages are available. Not only do we fit a generalised linear model based on preferential attachment, we also incorporate a preference function that is realistic for the tail heaviness of the resulting degree distribution. Results suggest that the influence of packages grows superlinearly initially and linearly above a threshold.

Exponential-Family Random Graph Models (ERGMs) are foundational in social network analysis. More recently, their application has extended beyond traditional static and panel networks to diverse data types. Notable extensions include Exponential Random Network Models (ERNMs), which jointly model networks and outcomes; the Generalized Location System (GLS), used for occupational stratification and residential settlement patterns; and the Autologistic Actor Attribute Model (ALAAM), an influence model that captures outcomes through motif-based structures.

In this paper, we introduce a novel application of the ERGM framework for analyzing complex, interrelated binary outcomes beyond conventional network data. Specifically, we propose modeling jointly-distributed health conditions to examine how multiple diseases may be interdependent. Using an empirical panel dataset, we construct a model that moves beyond assumptions of independence between health outcomes. Looking at the data as a bipartite network where individuals are mapped to various health conditions, our approach conceptualizes diseases as a complex system, where the presence or absence of one condition is characterized by sufficient statistics featuring other conditions.

Our analysis leverages the R package defm, which facilitates the estimation of these models. By providing both a methodological extension and a practical implementation, we demonstrate the potential of the ERGM framework in capturing interdependencies in health and other domains with complex binary data structures.