Introduction to
Stochastic Actor-oriented ModelsEvidence for communication with assessors
The objective function
András Vörös
Department of Social Statistics, University of Manchester
SOST71032 Social Network Analysis
Formulation of effects
 An effect is expressed in the SAOM by a so-called
effect statistic (or target statistic) – sk
 describes an aspect of the network state at a given moment
 e.g. how many female friends do actors have?
 this can be used technically as explanatory variable in the
model
 Each effect has a weight – β
 a parameter that tells if actors prefer higher (+) or lower (–)
values of the effect statistic
 e.g. do actors prefer to have more or fewer female friends?
Formulation of effects
 We want to estimate an appropriate effect weight
 search for the parameter value which brings the simulations
closest to the second observed network
 e.g. find the parameter for the number of female friends effect
that will best predict the observed number of female friends
(Method of Moments Estimation; default strategy in RSiena)
 The optimal weight/parameter for this effect may vary
given the other effects that are included in the model
– multivariate model specifications
(= results sensitive to omitted variables, as in the case
of “standard” regressions)
Examples for structural effects
Examples for attribute-related effects
E.g. the tendency of girls to send ties, receive ties, and
the tendency of actors to have same-sex ties
Overview: the objective function
Overview: the objective function
Of course, the choice is probabilistic
The multinomial choice function has a value in [0,1]
An example
A considers three options:
create a tie to B, dissolve a tie to C, or do nothing
A
C B
A
C B
A
C B
A
C B
Option 1 Option 2 Option 3
???
An example
A cares about not having too many friends
(outdegree=-1), reciprocity (2), and sex homophily* (1.5)
A
C B
A
C B
A
C B
Option 1 Option 2 Option 3

* assume that A and C are female, B is male
An example
A cares about not having too many friends
(outdegree=-1), reciprocity (2), and sex homophily* (1.5)
A
C B
A
C B
A
C B
Option 1 Option 2 Option 3

f = 1.5 f = 0 f = 1
P = 55% P = 12% P = 33%
Summary: Stochastic Actor-oriented Models
 At certain points in time, actors consider changing the
set of their outgoing network ties
 Each possible choice is described by an objective
function that takes different effects into account
 outdegree (number of ties)
 reciprocity
 transitivity
 homophily
 …
 The probability to change a specific tie is modeled by a
multinomial choice probability model which is based
on the comparison of the objective functions
 Add a tie? Drop a tie? Do nothing?
 How attractive is each outcome relative to the others?
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