The most promising class of statistical models for expressing structural properties of social networks observed at one moment in time is the class of exponential random graph models (ERGMs), also known as p * models. The strong point of these models is that they can represent a variety of structural tendencies, such as transitivity, that define complicated dependence patterns not easily modeled by more basic probability models. Recently, Markov chain Monte Carlo (MCMC) algorithms have been developed that produce approximate maximum likelihood estimators. Applying these models in their traditional specification to observed network data often has led to problems, however, which can be traced back to the fact that important parts of the parameter space correspond to nearly degenerate distributions, which may lead to convergence problems of estimation algorithms, and a poor fit to empirical data. This paper proposes new specifications of exponential random graph models. These specifications represent structural propertiesWe thank Emmanuel Lazega for permission to use data collected by him. A portion of this paper was written in part while the first author was an honorary senior fellow at 99 100 SNIJDERS, PATTISON, ROBINS, AND HANDCOCK such as transitivity and heterogeneity of degrees by more complicated graph statistics than the traditional star and triangle counts. Three kinds of statistics are proposed: geometrically weighted degree distributions, alternating k-triangles, and alternating independent two-paths. Examples are presented both of modeling graphs and digraphs, in which the new specifications lead to much better results than the earlier existing specifications of the ERGM. It is concluded that the new specifications increase the range and applicability of the ERGM as a tool for the statistical analysis of social networks.

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categorical data analysis, social network analysis, random graphs,

This article reviews new specifications for exponential random graph models proposed by Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handcock, M., 2006. New specifications for exponential random graph models. Sociological Methodology] and demonstrates their improvement over homogeneous Markov random graph models in fitting empirical network data. Not only do the new specifications show improvements in goodness of fit for various data sets, but they also help to avoid the problem of neardegeneracy that often afflicts the fitting of Markov random graph models in practice, particularly to network data exhibiting high levels of transitivity. The inclusion of a new higher order transitivity statistic allows estimation of parameters of exponential graph models for many (but not all) cases where it is impossible to estimate parameters of homogeneous Markov graph models. The new specifications were used to model a large number of classical small-scale network data sets and showed a dramatically better performance than Markov graph models. We also review three current programs for obtaining maximum likelihood estimates of model parameters and we compare these Monte Carlo maximum likelihood estimates with less accurate pseudo-likelihood estimates. Finally, we discuss whether homogeneous Markov random graph models may be superseded by the new specifications, and how additional elaborations may further improve model performance.

While PTSD and comorbid PTSD/depression are indistinguishable, the findings support the existence of depression as a separate construct in the acute, but not the chronic, aftermath of trauma.

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We integrated existing cognitive processing models of posttrauma reactions into a longitudinal model. Data were obtained after a multiple shooting in a city office block. The subject group comprised 158 office workers who were in the building at the time of the shootings. The methodology of this research was a repeated measures survey, with data collection at 4, 8, and 14 months posttrauma. Measures included the Impact of Events Scale (IES) and the Symptom Checklist-90-Revised. A path analysis was performed with the IES as an indication of cognitive processing. Intrusion and avoidance were shown to mediate between exposure to trauma and symptom development. Intrusion was also found to be negatively related to subsequent symptom levels. The findings provide provisional support for a cognitive processing model.

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