# SOST71032 Social Network Analysis Assessment II

**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:

- Visualize and describe the co-work network in terms of number of nodes, number of edges and density. Interpret the results. (10%)
- 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%) - You are interested in running an ERGM with the following statistics
- nodecov(“practice”)
- nodematch(“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

- 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. (10%)

- 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%)

- 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%)