p₂: a random effects model with covariates for directed graphs

Abstract

A random effects model is proposed for the analysis of binary dyadic data that represent a social network or directed graph, using nodal and/or dyadic attributes as covariates. The network structure is reflected by modeling the dependence between the relations to and from the same actor or node. Parameter estimates are proposed that are based on an iterated generalized least‐squares procedure. An application is presented to a data set on friendship relations between American lawyers.

Factors Affecting Influential Discussions Among Physicians: A Social Network Analysis of a Primary Care Practice

“…To analyze statistical patterns in the data, we used a P2 logistic regression model to examine the 1,056 (33*32) binary variables indicating whether 1 physician cited another as a partner in influential discussions about women's health. 17,18 These analyses distinguished only between reports of no discussions and 1 or more discussions. Predictors included characteristics of the citing physician, characteristics of the cited physician, and variables describing the pair of physicians.…”

Bayesian inference for exponential random graph models

“…Many probability models have been proposed in order to summarise the general structure of graphs by utilising their local properties. Each of these models take different assumptions into account: the Bernoulli random graph model (Erdös and Rényi, 1959) in which edges are considered independent of each other; the p 1 model (Holland and Leinhardt, 1981) where dyads are assumed independent, and its random effects variant the p 2 model (van Duijn et al, 2004); and the Markov random graph model (Frank and Strauss, 1986) where each pair of edges is conditionally dependent given the rest of the graph. The family of exponential random graph models (Wasserman and Pattison (1996), see also Robins et al (2007b) for a recent review) is a generalisation of the latter model and has been thought to be a flexible way to model the complex dependence structure of network graphs.…”

Why So Difficult? Exploring Negative Relationships between Educational Leaders: The Role of Trust, Climate, and Efficacy

“…Therefore, we conducted p2 modeling to test the effect of individual and dyadic characteristics on having difficult professional relationships (van Duijn et al 2004). We used the p2 program within the StOCNET software suite to run the multilevel p2 models (van Duijn et al 2004;Zijlstra 2008;Zijlstra et al 2006). …”