13 An Introduction to Stochastic Actor-Oriented Models (aka SIENA)

An Introduc+on to
Stochas+c Actor-Oriented Models
(aka SIENA)
Dr. David R. Schaefer
Arizona State University
Social Networks & Health Training Workshop
Duke University
June 20, 2016

1 Dyad independent models
2 R (sna) = lnam

Outcome
Figure adapted from jimi adams
Modeled Interdependencies
None w/in Dyad1 Dyad+
A;ribute
General Linear
Model
Actor-Partner
Interdependence
(APIM)
Network
Autoregressive2 Stochas+c
Actor-
Oriented
Model
(SAOM) Network Erdös-Renyi (MR)QAP
Exponen+al
Random Graph
(ERGM/TERGM),
Rela+onal Event
May 20, 2016 Duke Social Networks & Health Workshop 2
Sta?s?cal Modeling & SNA

When to use a SAOM
•  Ques+ons about changes in network structure over +me
–  Including mul+ple networks
–  Including two-mode networks (selec+ng into foci)
•  Ques+ons about how networks affect individual “behaviors,”
such as through peer influence
–  Including mul+ple behaviors and possible reciprocal
effects
•  Ques+ons about the endogenous associa+on between
networks and behavior

Stochas?c Actor-Oriented Model
•  Also called Stochas+c Actor-Based Model (SABM), or “SIENA”
based on the sobware used to es+mate the model
–  Simula'on Inves'ga'on for Empirical Network Analysis
–  Currently es+mable in R (RSiena)
•  Recogni+on that networks and behavior are interdependent
–  Behaviors can affect network structure
–  Network structure can affect behavior
–  Thus, both “outcomes” are endogenous
–  Complicates adempts to answer important theore+cal
ques+ons (e.g., peer influence)

Network Homogeneity on Smoking
Peer
Influence
or
Friend
Selection
time t
time t-1
A
C D
B
A
C D
B
A
C D
B

Smoking-Related Popularity
Popularity
leads to
smoking
or
Smoking
enhances
popularity
time t
time t-1
C D
BA
C D
BA
C D
BA

Inferring Network → Behavior
Requires controlling for network selec?on based on:
1.  Pre-exis+ng similarity in the behavior
2.  Similarity on adributes correlated with the behavior
3.  Network processes, such as triad closure
•  Can amplify network-behavior paderns (see below)
C D
BA
I ♥
Homophily!
C D
BA
C D
BA
Homophily
through
Reciprocity
Homophily
through
Transi?vity

Overview of Model Presenta?on
1.  The general form of the model
–  Network func+on for rela+onship change
–  Behavior func+on for “behavior” change
–  Rate func+ons
2.  Model es+ma+on procedure
–  Model assump+ons
–  MCMC es+ma+on algorithm
–  Goodness of Fit
3.  Empirical example
4.  Extensions & Miscellany

1. General SAOM Form

•  Discrete change is modeled as occurring in con+nuous +me
(between observa+ons) through a sequence of micro steps
•  Actors control their outgoing +es and behavior
–  Func+ons specify when and how they change

SAOM Components
Decision Timing
(when changes occur)
Decision Rules
(how changes occur)
Network Evolu+on
Network rate
func+on
Network objec+ve
func+on
Behavior Evolu+on
Behavior rate
func+on
Behavior objec+ve
func+on

Network Objec?ve Func?on
•  Network change is modeled by allowing actors to select +es (by adding or
dropping them) based upon:
fi(β,x) is the value of the network objec+ve func+on for actor i, given:
•  the current set of parameter es+mates (β)
•  state of the network (x)
•  For k eﬀects, represented as ski, which may be based on
–  the network (x), or individual adributes (z)
•  Es+mated with random disturbance (ε) associated with x, z, t and j
•  Goal of model ﬁmng is to es+mate each βk
fi (β, x) = βkski
k
∑ (x)+ε(x, z,t, j)

j3
ego
j4
j2
j1
Network Decision
€
fego(β,x) = -2
€
xij
j
∑ + 1.8
€
xij x ji
j
∑
outdegree reciprocity
€
fego(β,x) = -2
€
xij
j
∑ + 1.8
€
xij x ji
j
∑fego(β,x) = -2
€
xij
j
∑ + 1.8
€
xij x ji
j
∑
During a micro step, an actor evaluates how changing its outgoing
+e in each dyad would aﬀect the value of the objec+ve func+on
(goal is to maximize the value of the func+on)
ego j1 j2 j3 j4
ego - 1 1 0 0
j1 1 - 0 0 0
j2 0 0 - 0 0
j3 1 0 0 - 0
j4 0 0 0 0 -
If… outdegree reciprocity sum
No change -2 * 2 = -4 1.8 * 1 = 1.8 -2.2
Drop j1 -2 * 1 = -2 1.8 * 0 = 0 -2
Drop j2 -2 * 1 = -2 1.8 * 1 = 1.8 -.2
Add j3 -2 * 3 = -6 1.8 * 3 = 3.6 -2.4
Add j4 -2 * 3 = -6 1.8 * 1 = 1.8 -4.2
Given the current state of the network, ego is
most likely to drop the ?e to j2, because that
decision maximizes the objec+ve func+on

•  Outdegree always present
•  Network processes (e.g., reciprocity, transi+vity)
•  Adribute based:
–  Sociality: effect of adribute on outgoing +es
–  Popularity: effect of behavior on incoming +es
–  Homophily: ego-alter similarity
–  Note: adributes may be stable or +me-changing
(exogenous or endogenously modeled)
•  Dyadic adributes (e.g., co-membership)
Network Objec?ve Func?on Effects

•  Predict change in “behavior,” which is the generic term for an
individual adribute
–  Refers to any amtude, belief, health factor, etc.
•  Op+onal: SAOMs don’t require one and they’re not relevant
for many ques+ons
•  Ordinal measurement required (~2-10 levels best)
•  Goal is to es+mate eﬀect of network on behavior change
Behavior Objec?ve Func?on

Behavior Objec?ve Func?on
•  Choice probabili+es take the form of a mul+nomial logit
model instan+ated by the objec+ve func+on
where z represents the behavior
•  The func+on dictates which level of the behavior actors adopt
–  Actors evaluate all possible changes
•  Increase/decrease by one unit, or no change
–  Op+on with highest evalua+on most likely
fi
z
(β, x, z) = βk
z
ski
z
k
∑ (x, z)+ε(x, z,t,δ)
Figure adapted from C. Steglich

•  Linear term to control for distribu+on (quadra+c term if the
behavior has 3+ levels)
•  Predictors of peer influence
–  Alters’ value on the behavior, or another adribute or
behavior
•  Mul+ple specifica+ons, including mean, minimum, maximum…
•  Ego’s other behaviors or adributes (e.g., gender, age)
–  Ego’s network posi+on (e.g., degree)
–  Interac+ons with reciprocity
Behavior Objec?ve Func?on Effects

Behavior Decision
Linear effect
Quadra+c effect
Adribute effect
(e.g. age)
Similarity effect
How adrac+ve is each level of the behavior based on these effects?

Ego, j1 1 - | 1 - 1 | / 2 = .5 1 (.5 - .05) = .45
Ego, j2 1 - | 1 - 1 | / 2 = .5 1 (.5 - .05) = .45
Ego, j3 1 - | 1 - 0 | / 2 = 0 1 (0 - .05) = .05
Ego, j4 1 - | 1 - 2 | / 2 = 0 0 (0 - .05) = 0
Similarity sta?s?c = .95
Behavior Decision*
J3(0)
Ego (1)
J4(2)
J1(1)
€
xij (simij
Z
− simZ
)
j
∑
€
simij
Z
=1−|
€
zi−z j|
€
/ΔZ
€
ΔZ = maxij |
€
zi−z j| = 2where =
€
simZ
= similarity expected by chance= similarity expected by chance = .05
simij
Z
xij (simij
Z
− simZ
)
j2(1)
Maintain z=1
First, calculate similarity for each
of ego’s possible decisions
* Assume covariates uncentered

Behavior Decision*
If… linear quad age similarity sum
Drop to 0 -.5 * 0 = 0 .25 * 0 = 0 .1 * 10 * 0 = 0 1 * .35 = .35 .35
Stay at 1 -.5 * 1 = -.5 .25 * 1 = .25 .1 * 10 * 1 = 1 1 * .95 = .95 1.7
Up to 2 -.5 * 2 = -1 .25 * 4 = 1 .1 * 10 * 2 = 2 1 * -.55 = -.55 1.45
Second, calculate the contribu+ons for
each of the other eﬀects

Behavior Decision*
If… linear quad age similarity sum
Drop to 0 -.5 * 0 = 0 .25 * 0 = 0 .1 * 10 * 0 = 0 1 * .35 = .35 .35
Stay at 1 -.5 * 1 = -.5 .25 * 1 = .25 .1 * 10 * 1 = 1 1 * .95 = .95 1.7
Up to 2 -.5 * 2 = -1 .25 * 4 = 1 .1 * 10 * 2 = 2 1 * -.55 = -.55 1.45
These eﬀects pull
ego toward the
extremes
The posi+ve age b
pushes ego’s
behavior upward
Similarity pushes
ego to stay the
same
Altogether, the greatest contribu+on to the behavior func+on comes
from ego choosing to maintain the same behavior level

•  Necessary for both network and behavior
•  Determine the wai+ng +me un+l actor’s chance to make decisions
•  Func+on of observed changes
–  But not the same as the number of changes observed
–  Separate rate parameter for each period between observa+ons
•  Wai+ng +me distributed uniformly by default, but diﬀerences can
be modeled based on:
•  Actor adributes: do some types of actors experience more or
less change
•  Degree: do actors with more/fewer +es experience a diﬀerent
volume of change
Rate Func?ons

2. SAOM Es+ma+on

SAOM Es?ma?on
•  Goal during es+ma+on is to iden+fy parameter values (i.e., a model) that
produce networks whose sta+s+cs are centered on target sta+s+cs
–  Same as modeled eﬀects measured at t1+
•  Robbins-Monro algorithm in three phases
1.  Ini+alize parameter star+ng values
2.  Use simula+ons to reﬁne parameter es+mates (next slide)
•  A large number of simula+on itera+ons, nested in 4+ subphases
•  Actor decisions and +ming based on objec+ve and rate func+ons
•  Update parameter es+mates aber each simula+on itera+on
–  Adempt to minimize devia+on of ending state from target
3.  Addi+onal simula+ons (2,000+) to calculate standard errors based on
parameter es+mates from phase 2

Markov Chain Algorithm
Ini+alize at ﬁrst observa+on
Actors draw:
1)  Wai+ng +me for network
2)  Wai+ng +me for behavior
Determined by rate func+ons
Shortest wai+ng +me/type iden+ﬁed
Time up?
Actor changes +e|behavior
Determined by
objec+ve func+ons
Update +me
(next micro step)
“STOP”
Yes No
For each step in a
Markov chain:
Max
itera+ons?
No
Yes
If Phase 2,
update
parameters
Store ending network
& behavior

Post-Es?ma?on 1
•  Check for Convergence
•  Convergence achieved when model is able to reproduce
observed network & behavior at +me 2+
–  For each eﬀect, t-ra+o to compare target sta+s+cs with
distribu+on (t should be < .10)
–  Maximum t-ra+o for convergence (tconv.max) should be
less than .25
–  If convergence not reached, rerun with using es+mates as
new star+ng values; may need to respecify model

Post-Es?ma?on 2
•  Goodness of Fit
•  Use simula+ons to compare networks generated by model to
sta+s+cs NOT explicitly in the model
–  Typical candidates:
•  In- & Out-degree distribu+ons
•  Triad Census
•  Geodesic distribu+on
•  Behavior distribu+on
•  Behavior network associa+ons

3. SAOM Example

An Empirical Example with Adolescent Smoking
•  Na+onal Longitudinal Study of Adolescent Health (Add Health)
•  In-home surveys conducted 1994-1995 (2 waves)
–  Earlier in-school survey has network data but limited
behavior data
•  Students nominated up to 5 male and 5 female friends
(directed network)
–  Friendships coded present (1) or absent (0) for each dyad

30-day smoking
None (0)
1-11 days (1)
12+ days (2)
Jeﬀerson High (Add Health, 1995)

•  Helpful to imagine the network func+on as a logis+c regression
–  Unit of analysis: dyad
–  Outcome: +e presence (keeping or adding) vs. absence
(dissolving or failing to add)
–  Each effect represents how a one-unit change in the effect
sta+s+c affects the log-odds of a +e, all else being equal
•  Some effects interpretable using odds ra+os, but
– One-unit changes may not be meaningful
– All else is never equal (any change also affects the
outdegree count, at a minimum)
•  Behavior func+on specifies how a one-unit change in the effect
sta+s+c affects the odds of increasing behavior one unit
Interpre?ng Results

Network func?on b SE
Rate 10.26 *** .49
Outdegree -3.91 *** .08
Reciprocity 1.91 *** .09
Transi+ve triplets .52 *** .04
Popularity .29 *** .04
Extracurric. act. overlap .28 *** .06
Smoke similarity .68 *** .12
Smoke alter .14 ** .05
Smoke ego -.04 .05
Female similarity .24 *** .04
Female alter -.11 * .05
Female ego -.04 .05
Age similarity 1.00 *** .13
Age alter -.01 .03
Age ego -.04 .03
Delinquency similarity .15 .08
Delinquency alter -.04 .04
Delinquency ego .02 .04
Alcohol similarity .27 ** .10
Alcohol alter -.03 .03
Alcohol ego -.03 .04
GPA similarity .70 *** .13
GPA alter -.05 .04
GPA ego -.02 .04
From Schaefer, D.R. S.A. Haas, and N. Bishop. 2012. “A Dynamic
Model of US Adolescents’ Smoking and Friendship Networks.”
American Journal of Public Health, 102:e12-e18.
Rate: Each actor is given ~10
micro steps in which to make a
change to its network
•  Add a +e, drop a +e, or make
no change
Rate

Rate 10.26 *** .49
Outdegree -3.91 *** .08
Smoke ego -.04 .05
Female ego -.04 .05
Age alter -.01 .03
Age ego -.04 .03
GPA alter -.05 .04
GPA ego -.02 .04
Outdegree: The nega+ve sign is
typical. It means that +es are
unlikely, unless other eﬀects in
the model make a posi+ve
contribu+on to the network
func+on.
density

Rate 10.26 *** .49
Outdegree -3.91 *** .08
Smoke ego -.04 .05
Female ego -.04 .05
Age alter -.01 .03
Age ego -.04 .03
GPA alter -.05 .04
GPA ego -.02 .04
Reciprocity: Ties that create a
reciprocated +e are more likely
to be added or maintained. This
eﬀect hovers around 2 in
friendship-type network.
recip

Rate 10.26 *** .49
Outdegree -3.91 *** .08
Smoke ego -.04 .05
Female ego -.04 .05
Age alter -.01 .03
Age ego -.04 .03
GPA alter -.05 .04
GPA ego -.02 .04
Transi?ve triplets: Ties that
create more transi+ve triads
have a greater likelihood.
•  Should also test interac+on
with Reciprocity (usually
nega+ve)
transTrip

Rate 10.26 *** .49
Outdegree -3.91 *** .08
Smoke ego -.04 .05
Female ego -.04 .05
Age alter -.01 .03
Age ego -.04 .03
GPA alter -.05 .04
GPA ego -.02 .04
Indegree Popularity: Actors with
more incoming +es have a
greater likelihood of receiving
future +es
inPop

Rate 10.26 *** .49
Outdegree -3.91 *** .08
Smoke ego -.04 .05
Female ego -.04 .05
Age alter -.01 .03
Age ego -.04 .03
GPA alter -.05 .04
GPA ego -.02 .04
Dyadic Covariate: Actors who
share an extracurricular ac+vity
(coded 1) are more likely to have
a friendship +e
X

Rate 10.26 *** .49
Outdegree -3.91 *** .08
Smoke ego -.04 .05
Female ego -.04 .05
Age alter -.01 .03
Age ego -.04 .03
GPA alter -.05 .04
GPA ego -.02 .04
Ties driven by similarity on:
Gender (could use “same” eﬀect)
Age
Alcohol use
GPA
Females less adrac+ve as friends
than males.
altX
egoX
simX

Rate 10.26 *** .49
Outdegree -3.91 *** .08
Smoke ego -.04 .05
Female ego -.04 .05
Age alter -.01 .03
Age ego -.04 .03
GPA alter -.05 .04
GPA ego -.02 .04
Ties driven by similarity on
smoking behavior.
Smokers more adrac+ve as
friends than non-smokers.
Alter
Nonsmoker Smoker
Ego
Nonsmoker .25 -.19
Smoker -.51 .41
Similarity is an “interac+on” between
ego and alter, thus interpreta+on
requires considering the main eﬀects

Ego-alter selec+on: Contribu+ons to
network objec+ve func+on by dyad type

Smoking func?on b SE
Rate 2.06 *** .26
Linear shape -.11 .22
Quadra+c shape 1.17 *** .16
Female .16 .19
Age -.00 .10
Parent Smoking .01 .23
Delinquency .44 ** .16
Alcohol -.10 .14
GPA -.09 .13
Average similarity 2.89 *** .91
In-degree -.04 .11
In-degree squared .00 .01
Rate: Students have around 2
chances on average (micro steps)
to change their smoking
behavior
Rate

Rate 2.06 *** .26
Female .16 .19
Age -.00 .10
Alcohol -.10 .14
GPA -.09 .13
In-degree -.04 .11
linear
quad

Rate 2.06 *** .26
Female .16 .19
Age -.00 .10
Alcohol -.10 .14
GPA -.09 .13
In-degree -.04 .11
Smoking (z, M=.9) Linear Quad
Raw Centered b = -.11 b = 1.17 Sum
0 -.90 .099 .948 1.047
1 .10 -.011 .012 .001
2 1.10 -.121 1.416 1.295
Smoking Level
Summed Eﬀects
In combina+on, the linear and
quad eﬀects represent the U-
shaped smoking distribu+on.
•  Kids either don’t smoke or
smoke 12+ days/month.
.0
.2
.4
.6
.8
1.0
1.2
1.4
0 1 2
Contribu?on to Behavior Func?on
+ =
+ =
+ =

Rate 2.06 *** .26
Female .16 .19
Age -.00 .10
Alcohol -.10 .14
GPA -.09 .13
In-degree -.04 .11
Ego Covariate: Delinquency
leads to higher levels of smoking
effFrom

Rate 2.06 *** .26
Female .16 .19
Age -.00 .10
Alcohol -.10 .14
GPA -.09 .13
In-degree -.04 .11
Average Similarity: Students
adopt smoking levels that bring
them closer to the average of
their friends
xi+
−1
xijj
∑ (simij
z
− simz
)
Δ
−−Δ
=
ji
ij
zz
sim
jiij zz −=Δ max
avSim

•  How well is the es+mated model able to reproduce features
of the observed data that were not explicitly modeled?
–  Network
•  Degree distribu+on
•  Geodesic distribu+on
•  Triad census
–  Behavior distribu?on
Lots of room to improve GOF measures, especially behavior
Goodness of Fit (GOF)

Cumula?ve Indegree Distribu?on
Goodness of Fit of IndegreeDistribution
p: 0
Statistic
0 1 2 3 4 5 6 7 8
139
193
282
343
401
437
459
483
491

Geodesic Distribu?on
Goodness of Fit of GeodesicDistribution
p: 0.001
Statistic
1 2 3 4 5 6 7
1381
2795
5014
7772
10598
12081 11892

Triad Census Goodness of Fit of TriadCensus
p: 0.114
Statistic(centeredandscaled)
003 012 102 021D 021U 021C 111D 111U 030T 030C 201 120D 120U 120C 210 300
21286492
428358
129429
693
1141
1052
923
625
108
4 171
114
58
39
91
36

Smoking Distribu?on
Goodness of Fit of BehaviorDistribution
p: 1
Statistic
0 1 2
222
98
182

4. Extensions & Miscellany

Extensions to Basic Model
•  interac+ons
•  event history outcomes
•  mul+ple behaviors
•  mul+ple network op+ons
•  valued +es
•  mul+level networks
•  two mode networks
•  increase vs. decrease in +es and/or behavior
•  +me heterogeneity
•  simula+ons (test interven+ons)
•  ML, Bayes es+ma+on

Asymmetric Peer Inﬂuence
•  Implicit assump+on that eﬀects work the same for:
–  Tie forma+on vs. dissolu+on
–  Behavior increase vs. decrease
•  Unrealis+c for smoking
–  Physical/psychological dependence, social learning
•  Easy to relax this assump+on
–  Separate behavior objec+ve func+on into:
•  Crea?on func?on: only considers increases
•  Maintenance func?on: only considers decreases
–  Could make similar dis+nc+on in the network func+on

Contribu?ons to the Smoking Func?on
Contribu+on
Prospec+ve
Smoking
Nonsmoking Alters
J = Jeﬀerson High School
S = Sunshine High School
From Haas, Steven A. and David R. Schaefer. 2014. “With a Lidle Help from My Friends? Asymmetrical Social Inﬂuence on
Adolescent Smoking Ini+a+on and Cessa+on.” Journal of Health and Social Behavior, 55:126-143.
Smoking level with
greatest contribu+on
most likely to be
adopted (with caveat
that actors can only
move behavior one
level during a given
micro step)
-3-113
Current Smoking
Util.
0 1 2
J
J
J
S
S
S
A
-3-113
Current Smoking
Util.
0 1 2
J
J
J
S
S
S
B
-3-113
Current Smoking
Util.
0 1 2
J
J
J
S
S
S
C
-3-113
Util.
J
J
J
S
S
S
D
-3-113
Util.
J
J
J
S
S
S
E
-3-113
Util.
J
J
J
S
S
S
F
Contribu+on
Prospec+ve
Smoking
Smoking Alters
-3-11
Current Smoking
Util.
0 1 2
J
J
J
S
S
S
-3-11
Current Smoking
Util.
0 1 2
J
J
J
S
S
S
-3-11
Util.
-3-113
Util.
0 1 2
J
J
J
S
S
S
G
-3-113
Util.
0 1 2
J
J
J
S
S
S
H
-3-113
Util.
Ego is currently a moderate smoker (1)

SIENA as an ABM
•  Useful to evaluate goodness-of-ﬁt, decompose network-
behavior associa+ons, evaluate interven+ons
•  Uses the same algorithm as model ﬁmng
1.  Fit model to empirical data (op+onal)
2.  Simulate network evolu+on using es+mated parameters or
manipula+ons of them
•  Can also manipulate ini+al condi+ons (e.g., network
structure, behavior distribu+on, etc.)
3.  Measure simulated network/behavior proper+es of interest

Decomposing Network Homogeneity
Source Selec?on (%) Influence (%) Sample
Schaefer et al. 2012 40 34 U.S.
Mercken et al. 2009 17-47 6-23 Europe (6 countries)
Mercken et al. 2010 31-46 15-22 Finland
Steglich et al. 2010 25-34 20-37 Scotland
•  How much network homogeneity on smoking is due to
selec?on vs. influence?
–  Systema+cally set selec+on and influence parameters to
zero and simulate network-behavior co-evolu+on (see
Steglich et al. 2010)

Evalua?ng Interven?ons
How do smoking/friendship dynamics affect smoking
prevalence?
•  Manipulate model parameters related to key “interven+on
levers”
–  Peer influence (absent…strong)
–  Smoker popularity (unpopular…absent…popular)
•  Remaining model parameters from fided model
•  Ini+al condi+ons = observed wave 1 data

Results of Manipula?ng Peer Influence (PI) and
Smoking-based Popularity (smoke alter)
Schaefer DR, adams j, Haas SA. 2013. Social Networks
and Smoking: Exploring the Effects of Peer Influence
and Smoker Popularity through Simula+ons.
Health Educa'on & Behavior, 40(S1):24-32.
Independent Manipula+ons
Joint Manipula+on
Stronger peer influence increases smoking
prevalence, but only when smokers are
popular (nega+ve effects when smokers
unpopular)

Context Effects
How do these effects depend upon context?
•  Randomly manipulate ini+al smoking prevalence
–  25% ini+al smokers up to 75%
•  Randomly distribute smokers and nonsmokers across the
network
–  Similar results with empirical and model-based
manipula+ons
•  Full results in adams, jimi & David R. Schaefer. 2016. “How
Ini+al Prevalence Moderates Network-Based Smoking
Change: Es+ma+ng Contextual Effects with Stochas+c Actor
Based Models.” Journal of Health & Social Behavior 57(1):
22-38.

Smoking Distribu+on: Empirically-Based, Model-Based, Random

PI Parameter0
1
2
3
4
5
6
SmokeAlterParameter
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
ChangeinSmokers
-0.2
-0.1
0.0
0.1
0.2
25% Ini+al Smokers 75% Ini+al Smokers
PI Parameter0
1
2
3
4
5
6
SmokeAlterParameter
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
ChangeinSmokers
-0.2
-0.1
0.0
0.1
0.2
Contras?ng Contexts

•  Ties are more or less enduring states
–  Plausible for friendship or collabora+ons
–  Not useful for “event” data (e.g. phone calls)
•  Change occurs in con+nuous +me
•  Markov process: future state only a func+on of current state
–  No lagged eﬀects, “grudges”
•  Actors control outgoing +es and behavior
•  One change at a +me
–  No coordinated or simultaneous changes
Assump?ons

•  Up to 10% probably ok, more than 20% likely a problem
•  Endogenous network & behavior imputa+on
–  Missing values at t0 set to 0 (network) or mode (behavior)
–  Missing values at t1+ imputed with last valid value if
possible, otherwise 0
•  Covariates imputed with the mean
–  Other values can be speciﬁed
•  Imputed values are treated as non-informa+ve, thus not used
in calcula+ng target sta+s+cs
–  Convergence and ﬁt are determined based only upon
observed cases
Missing Data

Good Sources of Informa?on
•  RSiena manual
•  Snijders, van de Bunt & Steglich, 2010
•  Steglich, Snijders & Pearson, 2010
•  Tom Snijders’ SIENA website
www.stats.ox.ac.uk/siena/
–  Workshops
–  Scripts
–  Applica+ons in the literature
–  Latest version of RSiena
–  Link to stocnet listserv – important updates announced here
–  “Siena_algorithms.pdf”

End of Lecture

SAOM Lab
If you haven’t done so already:

•  Download the “RSiena lab.R” script from dropbox
•  Install the RSiena library
– See “RSiena lab.R” sec+on 1
or
– Type: install.packages("RSiena”)

•  One mode or two mode network with at least two
observa+ons, each represented as a matrix
–  Ties coded 0, 1, 10 (structural 0), 11 (structural 1), or NA
•  For each “period” between adjacent waves, stability measured
by the Jaccard coeﬃcient should be at least .25
–  Ties persisted / (+es formed + +es dissolved + +es persisted)
•  “Complete network data” all actors w/in bounded semng
–  Some turnover in set of actors allowed but same actors in
the data for each wave (even if not observed during wave)
–  See manual for how to deal with composi+on change
•  Recommended N: 30-2000
Data Structure: Network

•  Dependent behaviors
–  Time-varying adributes used as dependent variable(s)
–  Coded as integer (e.g., 1-10)
–  Last +me point is used
•  Changing actor covariates
–  Time-varying adributes used as independent variables
–  Last +me point not used (only applicable for 3+ waves)
•  Constant covariates
–  Ex: age, sex, race/ethnicity, behavior
•  Dyadic covariates
–  Ex: semngs that drive contact
NOTE: Covariates are centered by default
Addi?onal Data Structures

13 An Introduction to Stochastic Actor-Oriented Models (aka SIENA)

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