Neighbourhood-based models for social networks: model specification issues

Outline

1. Random graph models
Why is it important to model networks?

Approach to modelling networks

What do we model?

A simplified multi-layered framework

Local interactivity

Some assumptions about proximity

Models for interactive systems of variables
(Besag, 1974)

Exponential random graph (p*) models
 (Frank & Strauss, 1986)

What is a neighbourhood?

Neighbourhoods depend on
proximity assumptions

Homogeneous network models

Homogeneous Markov random graphs
(Frank & Strauss, 1986)

Model specification:
edge and dyad parameters

Homogeneous Markov models
with sp = 0, for p > p0

3. New specifications
 I: the alternating k-star hypothesis

Properties of alternating k-star models

Other functions of degree

Alternating k-star models

Realisation-dependent models

Generalised exchange: 4-cycles in networks
(Pattison & Robins, 2002)

New specifications II. Realisation-dependent models for higher-order clustering effects

Some neighbourhoods for 4-cycle model:
independent 2-paths

Independent 2-path statistics

Change statistic for U[l](x)

More neighbourhoods for 4-cycle model

Triangle and k-triangle statistics

Change statistic for T[l](x)

MCMC parameter estimates for mutual collaborations among partners of a law firm (Lazega, 1999; SIENA, conditioning on total ties)

Features of model fit

5.  Model specification: what have we learnt?

Next steps