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Longitudinal Network Analysis
Applying SIENA
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Content

• Basic model assumptions in SIENA
• Exercise
• Interpretation of results
• Improvement of model
• Further relevant topics

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Basic model assumptions in SIENA What are the
assumptions SIENA makes and can you apply SIENA
to test your hypotheses?
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Lets start with a small movie

• Communication in a class room with two teachers
• All communication was observed.

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Model assumptions 1 / 2

• 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?
• Networks change in micro steps. Micro steps of
  actors in the network account for large changes
  in the observed networks (t1, t2, t3, .. tn).
• 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

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Model assumptions 2 / 2

• 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)
• No more than one tie can change at a time
• Sequential change. Denies the possibility of
  coordinated action.

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The stochastic estimation processes

• 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?
• Estimation of user-specified effects on the
  probabilities of tie change
• E.g., Does and actors 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 -gt conditional method
  of moments estimation.
• t1 is not modeled but only used as input.
• 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

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Defining a model

• 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!
• 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.

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Example

• Objective function 0.8 reciprocity 0.5
  homophily
• Imagine the given function and that it is the
  middle actors turn to make a choice. What will
  the choice be?

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Time for an example

• Objective function 0.8 reciprocity (- 0.5
  )homophily
• Imagine the given function and that it is the
  middle actors turn to make a choice. What will
  the choice be?

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Basic effects Effects you should consider to
control for

• 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.
• Reciprocity effect Seems to be a basic feature
  of social structure (Gouldner, 1960 Wasserman
  Faust, 1994)
• 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

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A typology of effects

• Degree related effects

Triadic effects
Covariate effects
e.g. indegree popuarity
e.g. transitivity
e.g. alter/ receiver effect
endogenous effects
can be both, endogenous and exogenous effects
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• Getting SIENA started
• A guideline for applying SIENA

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Data requirements

• Panel waves gt 2 preferably gt 3.
• When number gets high (lets say gt 5) check if
  effects are homogeneous or if they change with
  time. See SIENA manual section 6.6.1
• Advisable to have at least 20 actors.
  Technically, the amount of actors is only
  restricted by your computers working memory and
  its 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?
• 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 dont 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.
• No less that 80 response. But actors may enter
  and leave the network -gt See composition change
  in SIENA manual section 5.7 for an elegant
  solution

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Running SIENA

• This is done in 5 steps
• Data
• Transformation
• Selection
• Model
• Results
• Example here van den Bunt friendship Data.
  Available at SIENA homepage

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0. Getting started

• For starting a new project choose Start with new
  project
• (who would have not guessed that?)

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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.
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1. Data

• 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).
• 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.

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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).

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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, ..)

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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

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2. Transformation

• SIENA can only handle dichotomized networks (0
  1)
• Work in progress valued graphs might be possible
  in near future
• Indicate missing values

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2. Transformation

1. Choose all the networks and define the missing
   values (see data description)

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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 -gt 1 345 -gt 0)

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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 -gt 1 345 -gt 0)

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3. Selection

• Here you can remove actors from the analysis.
• Does not reflect social reality. Removing an
  actor in reality probably would affects whole
  network.
• If you want to test differences in effect for a
  range of actors use covariates (e.g. dummies)

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4. Model Data specification

• The networks
• Dyadic variables
• Constant covariates E.g., gender
• Changing covariates
• If endogenous then should be modeled as dependent
  variable (e.g., individuals performance)
• If exogenous then then treated as independent
  changing covariate
• Composition change. See manual section 5.7

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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

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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

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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

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5. Results

• Dont jump to the parameter estimates first!
• 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.
• 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
• 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 lt .05 two-tailed
• Parameters above 2 and certainly above 5 are
  doubtful.
• 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.

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Improving your model

• 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!

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Improving your model
Model -gt Model specification -gt Tab Options
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More advanced issues

• Evolution of covariates Influence of ties or
  influence within networks
• Multilevel
• Endowment effects
• Interactions (between parameters, with time, rate
  parameter)
• Score type test -gt SIENA manual section 9.1

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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
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Useful information sources

• SIENA homepage http//stat.gamma.rug.nl/siena.html
  
• Yahoo StocNet user Group http//tech.groups.yahoo.
  com/group/stocnet/

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Notes

• 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.