Exponential random graph models for management research: A case study of executive recruitment (original) (raw)
Related papers
Quality & Quantity, 2013
Theoretical accounts of network ties between organizations emphasize the interdependence of individual intentions, opportunities, and actions embedded in local configurations of network ties. These accounts are at odds with empirical models based on assumptions of independence between network ties. As a result, the relation between models for network ties and the observed network structure of interorganizational fields is problematic. Using original fieldwork and data that we have collected on collaborative network ties within a regional community of hospital organizations we estimate newly developed specifications of Exponential Random Graph Models (ERGM) that help to narrow the gap between theories and empirical models of interorganizational networks. After controlling for the main factors known to affect partner selection decisions, full models in which local dependencies between network ties are appropriately specified outperform restricted models in which such dependencies are left unspecified and only controlled for statistically. We use computational methods to show that networks based on empirical estimates produced by models accounting for local network dependencies reproduce with accuracy salient features of the global network structure that was actually observed. We show that models based on assumptions of independence between network ties do not. The results of the study suggest that mechanisms behind the formation of network ties between organizations are local, but their specification and identification depends on an accurate characterization of network structure. We discuss the implications of this view for current research on interorganizational networks, communities, and fields.
Explaining the Structure of Inter-Organizational Networks using Exponential Random Graph Models
Industry & Innovation, 2013
A key question raised in recent years is which factors determine the structure of interorganizational networks. While the focus has primarily been on different forms of proximity between organizations, which are determinants at the dyad level, recently determinants at the node and structural level have been highlighted as well. To identify the relative importance of determinants at these three different levels for the structure of networks that are observable at only one point in time, we propose the use of exponential random graph models. Their usefulness is exemplified by an analysis of the structure of the knowledge network in the Dutch aviation industry in 2008 for which we find determinants at all different levels to matter. Out of different forms of proximity, we find that once we control for determinants at the node and structural network level, only social proximity remains significant.
The Social Network within a Management Recruiting Firm: Network Structure and Output
2009
To understand the relationship between information flows and white-collar output, we collected unique data on email communications to study the network connecting individuals in a management recruiting firm. We also gathered data on revenues and contracts at the individual level. Our empirical results suggest that the size of an individual's internal email network is more highly correlated with output than with the number of email messages, the time spent communicating, the external network size, and with all other measures of communication. This result suggests that a more favorable position in the network structure is associated with higher individual output.
Social Networks, 2009
The new higher order specifications for exponential random graph models introduced by Snijders et al. [Snijders, T.A.B., Pattison, P.E., Robins G.L., Handcock, M., 2006. New specifications for exponential random graph models. Sociological Methodology 36, 99-153] exhibit substantial improvements in model fit compared with the commonly used Markov random graph models. Snijders et al., however, concentrated on non-directed graphs, with only limited extensions to directed graphs. In particular, they presented a transitive closure parameter based on path shortening. In this paper, we explain the theoretical and empirical advantages in generalizing to additional closure effects. We propose three new triadic-based parameters to represent different versions of triadic closure: cyclic effects; transitivity based on shared choices of partners; and transitivity based on shared popularity. We interpret the last two effects as forms of structural homophily, where ties emerge because nodes share a form of localized structural equivalence. We show that, for some datasets, the path shortening parameter is insufficient for practical modeling, whereas the structural homophily parameters can produce useful models with distinctive interpretations. We also introduce corresponding lower order effects for multiple two-path connectivity. We show by example that the in-and out-degree distributions may be better modeled when star-based parameters are supplemented with parameters for the number of isolated nodes, sources (nodes with zero in-degrees) and sinks (nodes with zero out-degrees). Inclusion of a Markov mixed star parameter may also help model the correlation between in-and out-degrees. We select some 50 graph features to be investigated in goodness of fit diagnostics, covering a variety of important network properties including density, reciprocity, geodesic distributions, degree distributions, and various forms of closure. As empirical illustrations, we develop models for two sets of organizational network data: a trust network within a training group, and a work difficulty network within a government instrumentality.
The Problem of Scaling in Exponential Random Graph Models
Sociological Methods & Research, 2021
This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model-even those uncor-related with other predictors-or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot be interpreted as effect sizes or compared between models and homophily coefficients, as well as other interaction coefficients, cannot be interpreted as substantive effects in most ERGM applications. We conduct a series of simulations considering the substantive impact of these issues, revealing that realistic levels of residual variation can have large consequences for ERGM inference. A flexible methodological framework is introduced to overcome these problems. Formal tests of mediation and moderation are also proposed. These methods are applied to revisit the relationship between selective mixing and triadic closure in a large AddHealth school friendship network. Extensions to other classes of statistical work models are discussed.
An introduction to exponential random graph ( p *) models for social networks
Social Networks, 2007
This article provides an introductory summary to the formulation and application of exponential random graph models for social networks. The possible ties among nodes of a network are regarded as random variables, and assumptions about dependencies among these random tie variables determine the general form of the exponential random graph model for the network. Examples of different dependence assumptions and their associated models are given, including Bernoulli, dyad-independent and Markov random graph models. The incorporation of actor attributes in social selection models is also reviewed. Newer, more complex dependence assumptions are briefly outlined. Estimation procedures are discussed, including new methods for Monte Carlo maximum likelihood estimation. We foreshadow the discussion taken up in other papers in this special edition: that the homogeneous Markov random graph models of Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association 81, 832-842] are not appropriate for many observed networks, whereas the new model specifications of Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handock, M. New specifications for exponential random graph models. Sociological Methodology, in press] offer substantial improvement.
2018
This work aims to explain how firms behave and select their suppliers and customers in the Japanese production network. We study a supplier-customer network of listed firms in Japan (3,198 firms with 20,417 links). In order to specify how firms choose their partners, the so-called exponential random graph model is applied to estimate the ties formation process. For the estimation of such a large-scale network, we employ a recent technique of sampling called the improved fixed density Markov Chain Monte Carlo (MCMC). Our main result shows that all of the effects (social and economic effects) are statistically significant in explaining the ties formation between firms. Social effects such as mutuality and transitivity with common partners in different directional links between suppliers and customers are shown. Moreover, homophily with the same industrial sectors and geographical locations, and disassortative mixing between low-profit firms and high-profit ones are also found. We argu...
On Job Contact Networks and Labor Market Mobility
2007
In this paper we adopt the probabilistic framework of Calvo-Armengol and Jack- son (2004), in which social networks facilitate the transmission of information on job vacancies among workers, in order to study the effects of social connections on mobility (in terms of transition out of unemployment) in labor markets. Fur- thermore, we assume that probabilities to access information on job vacancies can change according to individuals' employment status. This also aims at capturing firms' different recruitment strategies. We find that social connections and networks topology can play an important role in explaining labor market mobility. At the same time, we also show that results may strongly depend on different hypothe- ses concerning individuals' access to information about job opportunities (or firms' recruitment strategies) and on network's dimension.