Longitudinal Network
Analysis
Content
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Basic model assumptions in SIENA
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Exercise
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Interpretation of results
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Improvement of model
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Further relevant topics
Basic model assumptions in
SIENA
What are the assumptions SIENA makes
and can you apply SIENA to test your
hypotheses?
Let‘s start with a small movie……
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Communication in a class room with
two teachers
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All communication was observed.
Model assumptions 1 / 2
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Most observed networks in social sciences are censored data. They
desribe the current state of a network but this state is the outcome
of unobserved processes and subject to further change
– Plausible for many networks: friendship, trust, exchange.
– Plausible for your network?
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Networks change in micro steps. Micro steps of actors in the
network account for large changes in the observed networks (t1,
t2, t3, ….. tn).
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Markov process: For any point in time, the current state of the
network determines probabilistically its further evolution, and there
are no additional effects of the earlier past. All relevant information
is therefore assumed to be included in the current state.
– Social network change as endogeneous process: social network
is the social context that influences the probabilties of ist own
change
– But: one can include exogeneous effects: constant covariates
or changing covariates
Model assumptions 2 / 2
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Actors control their outgoing ties = Actor-based model: Actors
change their outgoing ties on basis of their and others‘ attributes,
their position in the network, and their perceptions about the rest
of the network
– This is more plausible for directed graphs. In undirected graphs
one actor will take the iniatiative.
– Options for actors are to create a tie, withdraw a tie, or do
nothing
– Theoretical problem of limited information: Can you justify that
actors are aware of others‘ attributes or even the wider
network (e.g., actors at distance two)?
• Bringing the individual back in (Kilduff & Krackhardt, 1994).
• Structural individualism (Udehn, 2002; Hedström, 2005)
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No more than one tie can change at a time:
– Sequential change. Denies the possibility of coordinated action.
The stochastic estimation processes
1. Estimation of frequency of opportunities a actor can make to
change a tie (not doing anything is also a choice an actor can
make)
– How many micro steps does the model require to arrive at the
observed network?
2. Estimation of user-specified effects on the probabilities of tie
change
– E.g., Does and actor‘s attribute or the tendency to reciprocate
contribute to explain the observed model?
– Parameter estimates are based on a simulation that uses t1 as
starting point to predict the subsequent observed network ->
conditional method of moments estimation.
–
t1 is not modeled but only used as input.
3. The estimation process takes time! Depending on your network
size and the amount of parameters it can take several hours to run
one estimation.
– Use fast computers
– Use multiple computers
– Define your models well
Defining a model
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Check if the basic assumptions of SIENA are in agreement with
your model!!! If not, try to use another mehtod. Social network
analysis is (should be) theory driven not driven by the method!
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The objective function is the part of SIENA that allows you to
define how you expect actors form ties in a network
– It is the rule of network behavior we assume in our theory
– Like in linear statistical models the probability to change a tie is
the linear combination of effects specified by the user accoding
to a theoretical model
– If a effect is estimated to be positive an actor will make a
choice that leads to a network state where the corresponding
effect is higher. The converse applies when the effect is
negative. If the parameter is estimated to be zero, the effect is
irrelevant for actors‘ choices.
Example:
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Objective function: 0.8 * reciprocity + 0.5 homophily
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Imagine the given function and that it is the middle actor‘s turn to
make a choice. What will the choice be?
Time for an example:
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Objective function: 0.8 * reciprocity + (- 0.5 )homophily
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Imagine the given function and that it is the middle actor‘s turn to
make a choice. What will the choice be?
Basic effects: Effects you should consider to control for
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Outdegree effect: Actors‘ basic tendency to form ties. If negative
(usually the case), it indicates that actors are generally reluctant to
form ties. If positive, it indicates that actors form ties no matter
what.
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Reciprocity effect: Seems to be a basic feature of social structure
(Gouldner, 1960; Wasserman & Faust, 1994)
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Transitivity: Also seems to be a basic feature of social networks
(Davis, 1970; Holland & Leinhardt, 1970) (….but might not be well
understood???)
In general, however, the choice of effects should be
theoretically driven
A typology of effects
Degree related
effects
e.g. indegree popuarity
endogenous effects
Triadic effects
e.g. transitivity
Covariate
effects
e.g. alter/ receiver effect
can be both, endogenous and exogenous
effects
Getting SIENA started
A guideline for applying SIENA
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Data requirements
Panel waves >= 2; preferably > 3.
– When number gets high (let‘s say > 5) check if effects are homogeneous
or if they change with time. See SIENA manual section 6.6.1
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Advisable to have at least 20 actors. Technically, the amount of actors is
only restricted by your computer‘s working memory and it‘s speed – and the
time you have to finish your thesis.
– The larger the network the more difficult it is to assume that each actor
is a potential partner for any other actor in the network. Can you assume
that for your data?
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Design your data collection in a way that you capture enough changes
between ties.
– Minimum of 40 changes cumulated over all successive panel waves is
desired.
– But you also don’t want to have too many changes because that could
imply that your observations were too far away and that you lost
valuable information along the way.
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No less that 80% response. But actors may enter and leave the network ->
See “composition change” in SIENA manual section 5.7 for an elegant
solution
Running SIENA
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This is done in 5 steps:
1. Data
2. Transformation
3. Selection
4. Model
5. Results
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Example here: van den Bunt friendship Data. Available at SIENA
homepage
0. Getting started
•For starting a new project choose “Start with new project”
(who would have not guessed that?)
0. Getting started
When running SIENA for the first time you need to define directories where you store your file –
after a first time installation StocNet might ask you to do this right away.
1. Data
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Network and covariate data have to be entered in .txt or .DAT files and
have to be tab separated (consult SIENA manual section 5 for other
options).
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There cannot be blanks
– Network files are adjacency matrices.
– Covariates are rows with as many rows as actors. Actors have the
same order as in the network.
• Changing covariates: When number of observations is m then you
need to include m-1 columns.
– Example: First column contains covariate at T1, which is then
used to predict T2. Second column contains covariate at T2,
which is used to predict T3, etc,….
• Constant covariate : File can contain multiple constant covariates
(e.g., demographics of an actor). E.g, first column age; second
column gender, etc.
– Dyadic variables: Enter in same format as network variables
(adjacency matrix). Values between 0 – 255. Only integers.
• for changing dyadic variables you need m -1 variables.
1. Data
– Usually, you can copy/ paste from Ucinet/Excel into .txt files
and it is automatically tab seperated.
– When using large data sets (several hundreds of actors) you
might run into trouble when using Microsoft Notepad to
manage .txt files. Use some other software (e.g., EditPad Lite ;
its for free).
1. Data
1.
Click “Add” to add network files in successive order
2.
Choose the file (which you should already have stored in your dedicated network folder)
3.
Click into the box to change the name of the network (e.g., 1, 2, 3 ,4 ,5, ..)
1. Data
1.
Click “Add” to add covariate files in any order
2.
Choose the file (which you should already have stored in your dedicated folder)
3.
Click into the boxes to change the names of the file and the covariates it contains. Click apply
2. Transformation
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SIENA can only handle dichotomized networks (0 & 1)
– Work in progress: valued graphs might be possible in near
future
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Indicate missing values
2. Transformation
1.
Choose all the networks and define the missing values (see data description)
2. Transformation: Networks
1.
Choose all the networks and click on “Recode”
2.
Recode the network into 1 and 0 (see data description of example: 1 & 2 -> 1 & 3;4;5 -> 0)
2. Transformation: Attributes
1.
Choose the covariate you want to recode and click on “Recode”
2.
Recode the covariate into 1 and 0 (see data description: 1 & 2 -> 1 & 3;4;5 -> 0)
3. Selection
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Here you can remove actors from the analysis.
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Does not reflect social reality. Removing an actor in reality
probably would affects whole network.
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If you want to test differences in effect for a range of actors use
covariates (e.g. dummies)
4. Model: Data specification
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The networks
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Dyadic variables
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Constant covariates: E.g., gender
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Changing covariates:
– If endogenous then should be modeled as dependent variable
(e.g., individuals’ performance)
– If exogenous then then treated as independent changing
covariate
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Composition change. See manual section 5.7
4.Model: Data selection
1.
Click on “data selection”
2.
Put networks (and dyadic covariates) in successive order into the box.
3.
Put the file containing gender, program, and smoking into the constant covariate box
4.Model: Model specification
1.
Click on “Model specification”
2.
Choose the effects you want to test according to your theory. Check under “v”
3.
Click “ok” and then “run” to start the estimation process
5. Results
1.
Scroll to the bottom of the results section or click on “full report” and go to the end of the report
2.
Results of the last estimation process can be found here. New ones are placed beneath.
3.
Results will be deleted if you enter new data in the “data specification” section
5. Results
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Don’t jump to the parameter estimates first!
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First, check if convergence is good. That is, if your model describes
your observed data well. If not, then you cannot trust the
parameter estimates!
– Good convergence is indicated by t-rations close to zero
– t-rations below |0.1| indicate convergence.
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Check rate parameters: This are the unobserved changes an actor
makes between two observations. You have to decide what is
reasonable
– Remember: An actor can also decide to do nothing
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Significance of parameters / T-test: Divide the parameter by the
standard error and look in a t-test table if the value is significant
for an unlimited amount of degrees of freedom.
– Above 1.96 is significant for p < .05 two-tailed
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Parameters above 2 and certainly above 5 are doubtful.
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Check covariance/ correlation matrix.
– If you find high correlations they wont be problematic but
might explain high standard errors in your parameters. In this
case, you might exclude one of the two variables and re-run
the estimation.
Improving your model:
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Bad convergence is probably due to a mis-specified model.
–You can add/remove effects. But again: This should be guided
by theory.
–Increase the multiplication factor, e.g. to 10, then 15, then 20,
etc.
–Decrease the initial value of gain parameter, e.g. to 0.01, then
0.001, etc.
–Increase the number of iterations (enough time to get a coffee…)
•Should be 2000 for results to be reported..
–One change at a time!
Improving your model:
Model -> Model specification -> Tab: Options
More advanced issues
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Evolution of covariates: Influence of ties or influence within
networks
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Multilevel
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Endowment effects
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Interactions (between parameters, with time, rate parameter)
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Score type test -> SIENA manual section 9.1
Multilevel Analysis (SIENA manual section 14)
Meta Analysis
Multi-Group Option
Structural Zeros
Parameters are not
constrained within Networks
Only rate parameters are not
constrained within networks
All parameters are the same
for all networks
Networks need to be of
sufficient size
Networks are combined and,
therefore, yield higher power
Networks are combined and,
therefore, yield higher power
Can differ in number of
observation moments
Can differ in number of
observation moments
Need to have same amount
of observation moments
* If one interacts sub-group
dummies with rate
parameters, same results as
in multi-group option
Preferred method because
makes less strict assumption
Preferred above “structural
zero” approach with
dummies because takes less
time in SIENA
Least preferred
Useful information sources
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SIENA homepage http://stat.gamma.rug.nl/siena.html
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Yahoo StocNet user Group http://tech.groups.yahoo.com/group/stocnet/
Notes
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The literature on SIENA spends some effort in explaining relative
effect size. However, in social sciences we are generally interested
in the significance of an effect and not its relative effect size
because adding or removing an effect would change the relative
effect size….and how do we know we added all the effects that
“truly” predict the network.