We study the cohesion within and the coalitions between political groups in the Eighth European Parliament (2014–2019) by analyzing two entirely different aspects of the behavior of the Members of the European Parliament (MEPs) in the policy-making processes. On one hand, we analyze their co-voting patterns and, on the other, their retweeting behavior. We make use of two diverse datasets in the analysis. The first one is the roll-call vote dataset, where cohesion is regarded as the tendency to co-vote within a group, and a coalition is formed when the members of several groups exhibit a high degree of co-voting agreement on a subject. The second dataset comes from Twitter; it captures the retweeting (i.e., endorsing) behavior of the MEPs and implies cohesion (retweets within the same group) and coalitions (retweets between groups) from a completely different perspective. We employ two different methodologies to analyze the cohesion and coalitions. The first one is based on Krippendorff’s Alpha reliability, used to measure the agreement between raters in data-analysis scenarios, and the second one is based on Exponential Random Graph Models, often used in social-network analysis. We give general insights into the cohesion of political groups in the European Parliament, explore whether coalitions are formed in the same way for different policy areas, and examine to what degree the retweeting behavior of MEPs corresponds to their co-voting patterns. A novel and interesting aspect of our work is the relationship between the co-voting and retweeting patterns.
We employ two statistically sound methodologies developed in two different fields of science. The first one is based on Krippendorff's @cite_27 . , is a measure of the agreement among observers, coders, or measuring instruments that assign values to items or phenomena. It compares the observed agreement to the agreement expected by chance. , is used to measure the inter- and self-annotator agreement of human experts when labeling data, and the performance of classification models in machine learning scenarios @cite_7 . In addition to , we employ Exponential Random Graph Models (ERGM) @cite_4 . In contrast to the former, ERGM is a network-based approach, often used in social-network analyses. ERGM can be employed to investigate how different network statistics (e.g., number of edges and triangles) or external factors (e.g., political group membership) govern the network-formation process.
@cite_27 @cite_4 @cite_7
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Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through choice of model terms (sufficient statistics). However, those ERGMs modeling the more complex features have, to date, been limited to binary data: presence or absence of ties. Thus, analysis of valued networks, such as those where counts, measurements, or ranks are observed, has necessitated dichotomizing them, losing information and introducing biases. In this work, we generalize ERGMs to valued networks. Focusing on modeling counts, we formulate an ERGM for networks whose ties are counts and discuss issues that arise when moving beyond the binary case. We introduce model terms that generalize and model common social network features for such data and apply these methods to a network dataset whose values are counts of interactions. The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM’s expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses. We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in 3 kinds of psychological datasets: datasets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered datasets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means---the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials. We describe some of the capabilities of the ergm package and the statistical theory underlying it. This package contains tools for accomplishing three important, and inter-related, tasks involving exponential-family random graph models (ERGMs): estimation, simulation, and goodness of fit. More precisely, ergm has the capability of approximating a maximum likelihood estimator for an ERGM given a network data set; simulating new network data sets from a fitted ERGM using Markov chain Monte Carlo; and assessing how well a fitted ERGM does at capturing characteristics of a particular network data set.