Introduction to
Stochastic Actor-oriented Models
Estimation
András VörösNursing Physical Assessment
Department of Social Statistics, University of Manchester
SOST71032 Social Network Analysis
* Thanks to Christoph Stadtfeld for many nice figures and examples.
How to infer a continuous-time model from
discrete panel data?
Discrete data
Continuous-time
model
Estimation through simulations
The rate function
 Actors consider changing their network at discrete time
points following a Poisson process
 the timespans between two subsequent change
considerations are exponentially distributed
 the time model can be specified with parameters (like the
choice model / objective function)
The objective function
The multinomial choice
The multinomial choice function has a value in [0,1]
How does the estimation work in RSiena?
 Phase 1: the sensitivity of the statistics of the simulated
networks to the parameters is determined
 Phase 2: parameters are estimated by iterative
updating; aim is roughly to minimize abs(target
statistics – simulated statistics)
 Phase 3: check convergence (target stats. – sim stats.
really close to 0?) and calculate standard errors
 Implemented estimation methods:
 Method of Moments (MoM; default)
 Generalized Method of Moments (GMoM)
 Maximum Likelihood (ML) estimation
 Bayesian estimation
 the last two have higher precision but more comp. intensive
This is actually Phase 2 of the estimation!
Checking the convergence of the model
 Very important – models that did not converge shall
not be interpreted!
 t-ratios for convergence:
 “t-ratios for deviations from targets”
 They quantify how much the simulated statistics deviate from
the target statistics on average
 calculated as: average deviation / s.d. of deviation
 the smaller the better – smaller deviation; rule of thumb: <0.1
 Overall maximum convergence t-ratio
 similar to the above but for any linear combination of the
target statistics
 rule of thumb: <0.25
 If a model did not converge
 rerun with “prevAns”: continue from last values, skip phase 1
Please continue with the next topic.