SOST71032 Social Network Analysis
Assessment II Submission Deadline: 30 April at 14:00
Part A: Lazega’s Lawyers
For part A of this assessment, you will be using a network observed on lawyers at a lawfirm. You
can read about this data set here. The network and attribute file called lazegacowork.txt and
lazpractice.txt are available on Blackboard. The first file is the adjacency matrix for co-work
(symmetrical, that is an undirected network) and the second one is a node attribute; the type of
law that each lawyer practices (0 = litigation, 1 = corporate). Below you will find the R syntax for
importing the network and attribute file:
LazNet <- read.table('lazcowork.txt')
LazAtt <- read.table('lazpractice.txt')
Your tasks for Part A are the following:
a) Visualize and describe the co-work network in terms of number of nodes, number of edges
and density. Interpret the results. (10%)
b) Assume we want to test for homophily based on the attribute "practice". We want to use
the null model U|L, that is uniform graph distribution given number of edges. State the
hypotheses and describe how you would perform this test. (15%)
c) You are interested in running an ERGM with the following statistics
– nodecov("practice")
– match("practice")
– gwesp(decay = 0.693)
Describe what these statistics represent and why they might be of interest to include in
an ERGM. Fit the mentioned ERGM and interpret the parameter estimates. What can you
conclude? Briefly explain how you would assess the goodness of fit of this model. (50%)
Part B: SAOM
a) We obtained network data from a workplace of 34 employees. At two time points a few
months apart, we measured who trusted whom (binary, directed trust network) and the sex
of employees (binary sex covariate). To explain how the network evolved between the two
observations, we fitted a Stochastic Actor-oriented Model (SAOM) to the data using RSiena.
The results from the model are presented in the table below.
Effect par. (s.e.)
Rate 1 8.96 (1.61)
outdegree (density) –2.32∗∗∗ (0.40)
reciprocity 1.39∗∗∗ (0.29)
transitive triplets 0.16∗ (0.08)
indegree - popularity –0.04 (0.07)
sex alter 0.06 (0.31)
sex ego 0.60 (0.40)
same sex 0.91∗∗ (0.28)
∗ p < 0.05; ∗∗ p < 0.01; ∗∗∗ p < 0.001;
convergence t ratios all < 0.03.
Overall maximum convergence ratio 0.1.
Interpret the results. Assess the convergence of the model and discuss each effect in the table.
b) Let’s assume that we are modelling changes in a network of four actors (named A, B, C, D)
using SAOMs. In one of the simulation chains, we consider a ‘ministep’ when actor A is
prompted to make a change to the network. The state of the network at this moment is shown
in the figure below.
The shape of nodes represents their sex (circle – female, square – male). Actor A is coloured
differently to highlight that we are considering the choice to be made by this actor.
The following parameter values are used in the simulation:
– outdegree: -2.5;
– reciprocity: +1.5;
– transitive triplets: +0.5;
– same sex: +1.0;
– all other parameters: 0.
What is the probability that A will create a tie to D in this ministep? Present the details of
your calculation, including: the four options for the multinomial choice, the effect statistics in
each option, the value of the objective function in each option, and the probability of the AD
tie to be created. (10%)
c) We are interested in the goodness of fit of the SAOM presented in point a). We run the
sienaGOF function and get the result shown in the figure below.
Discuss the goodness of fit of the model with regard to the indegree distribution. (5%)