Conference Agenda

The new R-package MrQAP allows more flexible estimation of Multiple Regression Quadratic Assignment Procedure models in R. In this talk I will introduce the package, how to use it, and give some example applications on Cognitive Social Structure data. It is the first package that allows analyzing Cognitive Social Structures within a permutation regression framework, that is, network data where every participant not only reports about their ties but also about the ties they perceive others have. This forms a three dimensional data cube of senders, receivers, and perceivers, which can now be properly permuted.

The package comes with a variety of quality of life features: parallel processing, handling of many model families (OLS, logistic, Poisson, multinomial choice, etc.), heteroskedastic consistent estimators, random intercepts, within-group permutations, and handling of multiple networks at the same time. Naturally, the package is freely available on Github and hopefully soon on CRAN.

The statistical treatment of social network panel data often presupposes that micro-level network mechanisms generate observed macro-level outcomes, without fully accounting for the emergent meso-level network structures and the feedback mechanisms they may instantiate. To address this gap, we introduce a novel form of dependence in stochastic actor-oriented models (SAOMs), where actors’ network choices are influenced by their latent memberships in cohesive subgroups. These groups correspond to dense subgraphs in which actors are embedded and, as the network evolves over time, reflect shifting cohesive patterns. Formally, this is represented as the co-evolution of a one-mode network and a two-mode latent membership structure. The model requires prior ideas about the expected number of groups per actor and the number of actors per group, along with their variances. As application, we model school friendships, where cohesive subgroups represent unobserved peer groups formed among friends. We compare different specifications of friendship closure and find evidence that the social context of peer groups stabilizes and balances friendships, as students prefer to have more ties with their new groupmates. Furthermore, our results indicate that endogenous friendship dynamics induced by latent memberships better reproduces cohesive subgraphs observed at the network meso-level.

Exponential-family Random Graph Models (ERGMs) are vital for network analysis, yet parameter estimation remains challenging due to normalizing constant intractability. A popular approach, Stochastic Approximation (SA), works by repeatedly conducting a short simulation for the current parameter guess to obtain an estimate for the gradient of the log-likelihood, then making an update in the direction of the gradient whose magnitude is gradually reduced. A number of variants have been proposed, including Robbins-Monro and Equilibrium Expectations. Variants of SA are also found in machine learning, with the ADAptive Moments (ADAM) algorithm particularly popular for fitting neural network models. Each of these variants in turn involves further decisions such as how quickly the update size is reduced, and when the algorithm is determined to have converged.

We introduce a general framework that has these three variants as special cases. We conduct a series of simulation studies evaluating the impact of these settings on rate and reliability of convergence for difficult ERGM problems found in the literature. Through heuristic arguments and empirical study, we synthesise a variant of SA for ERGMs that seeks to draw on the best aspects of each of the existing.

For nearly two decades, Relational Event Models (REMs) have provided the framework for analyzing streams of time-stamped interactions. These models explain the governing dynamics of related relational phenomena based on statistics of previously observed events. However, as the size and complexity of temporal networks increase, REMs face computational bottlenecks. While several inference techniques have been proposed to reduce the computational costs of estimation procedures, improvements have been modest in optimizing the computation of history-based statistics.

We propose a series of estimators of explanatory statistics obtained from a sampled history of events. By deriving their theoretical properties, we can quantify and estimate their measurement errors, allowing us to make appropriate corrections during the estimation phase. Specifically, we fit REMs using error-in-variable techniques, including simulation-extrapolation methods. We assess the validity of our approach through both synthetic and real-world analyses designed to show the impact of history sampling and to compare our method to existing baseline techniques.

Our methodology enables the fitting of REMs to very large datasets, greatly expanding the practical applicability of these models.

This paper presents effects in Stochastic Actor-oriented Models for selection and influence in co-evolution of two two-mode networks with a common first node set which may be called 'actors'; the second node sets differ between the two networks; the first network serves to represent (by the one-mode projection) connections between the actors, who make choices of items in the second node set of the second network.

'Selection' refers to the impact of the item choices on the connections between actors in the first network, while 'influence' refers to the impact of the connections on the item choices in the second network.

Distinct specifications are proposed for selection and influence which are item-specific, and which refer to the number of items chosen (actor degrees in the second network). Descriptive statistics are proposed to represent the cross-sectional association between the two-mode networks, the explanation of which is the target of the selection and influence effects.

This is illustrated by an empirical example.