1. Tutorial: Analyzing real network data
1) Creating data from survey
Getting Started:
Log into the machine (directions on board)
Create a directory on the machine you are using called “c:\Nets\”
Go to the course webpage:
Download the first 3 or 4 files and save them, including the SPAN zip file

2. Tutorial: Analyzing real network data
1) Creating data from survey
You can download all of the needed files from here:
Outline:
From survey to analysis files
Exploring the network: visualization
Moving data among programs
SAS, PAJEK, UCINET, R
Network Position Measures
Centrality, Reachability, Reciprocity, Constraint, Mixing/Homophily.
Network Behavior & Peer Influence Models
Network structure as indep variable
Peer influence models
Dyad similarity models
Network Structure analyses
Clustering for peer groups
Block models
Statistical Models for networks (STANET).

3. Tutorial: Analyzing real network data
1) Creating data from survey
This is what students filled out in the Add Health, in school survey. One set for male friends, another for female friends.
This is the foundation of our data….

4. Tutorial: Analyzing real network data
1) Creating data from survey
This is what students filled out in the Add Health, in school survey. One set for male friends, another for female friends.
This is the foundation of our data….
Resulting in a nomination data file that looks something like this (actual numbers changed).
We want to turn this file into something PAJEK, UCINET, etc. can read.
Open “netcreate.sas” & walk through logic of the file.

5. Tutorial: Analyzing real network data
1) Creating data from survey
Netcreate.sas used files from SPAN to create PAJEK files.
After reading in the data, we use an %include statement to get the needed subroutines from SPAN.
The %include statement reads in subroutines for network analysis

6. Tutorial: Analyzing real network data
1) Creating data from survey (aside to SPAN manual!)

7. Tutorial: Analyzing real network data
1) Creating data from survey (aside to SPAN manual!)

8. Tutorial: Analyzing real network data
1) Creating data from survey (aside to SPAN manual!)

9. Tutorial: Analyzing real network data
1) Creating data from survey
We first use the adj() routine to create an adjacency matrix.
Then we select just ties matching within the nominated set and then write out a set of node-level attribute files.

10. Tutorial: Analyzing real network data
1) Creating data from survey
We can also store the main files for later use in matrix format.

11. Tutorial: Analyzing real network data
1) Creating data from survey
*Vertices
*Arcs
*Edges
The PAJEK format is a simple text file:
This is the minimum specification for a file. In addition, you can add cols in the *Vertices section to specify shape, color, xyz coords. Ditto w. arcs & edges.

12. Tutorial: Analyzing real network data
2) Exploring the network graphically
I think it’s useful to simply “play” with the network in various ways and get a sense of the shape of the network. This is perhaps PAJEK’s most useful purpose.
-- Load a network and work through good/bad plots, basic PAJEK interface.
-- Note the diff btwn the full nomination matrix and the in-school only matrix.

13. Tutorial: Analyzing real network data
2) Exploring the network graphically
Once you have a network, how do you create a print-ready image?
Screen shots (good for .ppt)
Export to .eps or FLASH and edit in Illustrator

14. Tutorial: Analyzing real network data
3) Basic Network Statistics
We often want to calculate some of the network statistics we discussed yesterday. These are structural features of the network.
First run through some points in PAJEK, since our net is already there
Components & Bicomponents
Centrality scores
Operations on network: selection, grouping.
Sets within sets
Run though some SAS code to generate similar statistics
Explore UCINET version of some of these as well

15. Tutorial: Analyzing real network data
3) Network Behavior & Peer Influence
Open nodestats1.sas to see how to code these same stats, plus a few, in SAS…

16. Tutorial: Analyzing real network data
3) Moving Data from program to program
There is no single canned program that does everything, so you can spend lots of time moving data around. A couple of keys and then let’s play:
The PAJEK format is getting pretty standard; lots of routines use it.
Most network programs have some basic text file as input, so it’s usually pretty simple to write a program to transfer the data if you have to.
There are lots of tools out there to make the move from one set to another.
Some examples:
SAS  Pajek (above)
Pajek  UCINET
Pajek  R, SPSS

17. Tutorial: Analyzing real network data
3) Moving Data from program to program
Pajek  UCINET
Use the File command to save a .NET file.
Open PAJEK
Read the files directly
Note you can save out .DL files (UCINET’s text format), but I find it somewhat unreliable.
Once opened, look at directory and see the file format..
UciNet does everything in matricies, and every new operation creates a new matrix.
See: for details

18. Tutorial: Analyzing real network data
3) Moving Data from program to program
Pajek  R
Locate R from PAJEK.
Export the set of files you want

19. Tutorial: Analyzing real network data
3) Moving Data from program to program
Pajek  R
Locate R from PAJEK.
Export the set of files you want

20. Tutorial: Analyzing real network data
3) Moving Data from program to program
Pajek  R
Locate R from PAJEK.
Export the set of files you want
We have a simple set of tools in the example .r file: Pajek2R1.r

21. Tutorial: Analyzing real network data
3) Moving Data from program to program
Pajek  R
Locate R from PAJEK.
Export the set of files you want
We have a simple set of tools in the example .r file: Pajek2R1.r
Note you have to have the race partition saved as a vector!
library(sna);
library(network);
help(package="sna");
help(package="network");
#the gplot function makes the matrix a network
gplot(n1);
#better to make that explicit
net1<-as.network(n1);
btwn1<-betweenness(net1);
summary(btwn1);
#plot based on the race vector
#add constant to adjust the color...
gplot(net1,vertex.col=(v1+2))
#can use these in an ergm
#attache the race variable
help(attribute.methods)
set.vertex.attribute(net1,"race",v1[1:255])
library(statnet)
eg1<-ergm(net1~edges+nodematch("race"))
summary(eg1)

22. Tutorial: Analyzing real network data
3) Moving Data from program to program

23. Tutorial: Analyzing real network data
3) Network Behavior & Peer Influence
We often want to know how some simple features of the network position affect students. These are “network behavior” models, where some indicator measure of network position is used to predict an outcome.
One should think carefully about a theoretical model here. Cause is often very difficult to disentangle. Here we’ll leave those questions aside and simply look for correlates of network position in behavior.
We’ll look at:
a) network volume (degree)
b) centrality (Closeness)
c) local reciprocity (proportion of ties ego send that are received)
We can get most of these from either SAS or PAJEK, though I’m not sure PAJEK can give you node-level reciprocity rates…
Paj_nodestatread.sas is the SAS file…

24. Tutorial: Analyzing real network data
3) Network Behavior & Peer Influence
Paj_nodestatread.sas is the SAS file…
After running some models we get:

25. Tutorial: Analyzing real network data
3) Network Behavior & Peer Influence
QAP is an alternative method that doesn’t make as many strong assumptions about the model.
To use QAP, we can run in SAS (but it’s slow and basic), or export to UCINET (which is fast, sophisticated and all that jazz).
The “qapstats.sas” file moves the data for us….

26. Tutorial: Analyzing real network data
3) Network Behavior & Peer Influence
We can also estimate the network autocorrelation model directly. We can get “QAD” estimates just by adding the W*Y term to the base model, which typically performs fairly well.
Open peerinfl1.sas to see this routine.
Alternatively, UCINET calculates a simple network correlation between any vector (Nx1) and any matrix (NxN) to estimate the bivariate peer effect, and Carter Butts’ LNAM routine in R (as part of SNA), let’s you run a full linear network autocorrelation model.
For stats details:
Leenders, T.Th.A.J. (2002) ``Modeling Social Influence Through Network Autocorrelation: Constructing the Weight Matrix'' Social Networks, 24(1),
Anselin, L. (1988) Spatial Econometrics: Methods and Models. Norwell, MA: Kluwer

27. Tutorial: Analyzing real network data
3) Network Behavior & Peer Influence
To run the R version, we need to export the data. We can get started using the send2r.mac routine and reshape some of the files.
The sas program “sas2r_peerinfl.sas” creates the needed external files
The r script “lname_example.r” is the needed r script.
Run the example models….
Call:
lnam(y = fights, x = cv, W1 = w1, W2 = clbs)
Residuals:
Min Q Median Q Max
Coefficients:
Estimate Std. Error Z value Pr(>|z|)
FEMALE *
WHITE
S e-05 ***
rho ***
rho
---
Result of “fights” as Y, friendship as W1, club overlap as W2

28. Tutorial: Analyzing real network data
3) Network Behavior & Peer Influence
Getting measures from PAJEK.
PAJEK has no direct ID link to files. These are simply text files, so sort order matters.
The basic routine to get any measure in PAJEK is to create the measure using the dropdown menus, then save the files and read them into SAS, SPSS or whatever stats program you use.
Open the PAJEK files and create in-degree, out-degree, closeness centrality, & reciprocity.

29. Tutorial: Analyzing real network data
4) Network Structure: Clustering the network
As part of the description, we often want to identify significant clusters in the network. There are lots of ways to do this, we’ll sample a few.
a) Using UCINET’s routines
b) Clustering a distance matrix (SAS)
c) The “Jiggle” routine (SAS, Moody)
d) The “Crowds” algorithm
e) Using PAJEK’s blockmodel routine to fine-tune a peer group model.

30. Tutorial: Analyzing real network data
4) Network Structure: Clustering the network
Clustering in UCINET
-I find it simplest to read PAJEK files. Then the best “general” routine is FACTIONS, though it is slow for large (100s) nets. Very effective for small nets.
In a pinch, CONCOR will often yield reasonable peer groups, and it’s faster in UCINET
Clustering in SAS
- We can often get a quick starting point by simply using a hierarchical clustering on the distance matrix. This is a fair place to start for nets in the 100s of nodes size.
- Two algorithms that work fairly well are “Jiggle” for large nets and “Crowds” for smaller nets. Both work by extending the RNM approach of Moody (2001), but jiggle is faster for large nets, Crowds includes more checks for particular structures (like biconnected sets) and thus is slower.

31. Tutorial: Analyzing real network data
4) Network Structure: Clustering the network
Clustering in PAJEK
Pajek doesn’t have a dedicated clustering routine for finding peer groups in nets. But you can coerce the blockmodel routine to find block-diagonal structures (slow) or use some of it’s neighboring partitions.
Keep an eye on this, as I bet they implement Newman’s algorithm soon…
Let’s try running some of these….

32. Tutorial: Analyzing real network data
4) Network Structure: Clustering the network
Sample results
This is the resulting graph from a “Jiggle” run on the school net. Note this is a randomized algorithm, so you will get dif. Results from dif. runs

33. Tutorial: Analyzing real network data
4) Network Structure: Clustering the network
Sample results
This is the resulting graph from a “Crowds” run on the school net. We end up with smaller clusters, and a larger “background” set. By construction, the clusters must be bi-connected, so they are “rounder” than in the prior algorithm.

34. Tutorial: Analyzing real network data
4) Network Structure: Clustering the network
Sample results
This is the resulting graph from a “Crowds” run on the school net. We end up with smaller clusters, and a larger “background” set. By construction, the clusters must be bi-connected, so they are “rounder” than in the prior algorithm.

35. Tutorial: Analyzing real network data
4) Network Structure: Clustering the network
Sample results
This is the resulting graph from a “Crowds” run on the school net. We end up with smaller clusters, and a larger “background” set. By construction, the clusters must be bi-connected, so they are “rounder” than in the prior algorithm.

36. Tutorial: Analyzing real network data
4) Network Structure: Block modeling a network
Split 1
Sample results
The most commonly used blockmodel routine is ConCorr, which is simple and fast. The result is a set of nested “splits” – to some pre-specified depth.
Here I apply that result to the school net, working to a depth of 3 splits.

37. Tutorial: Analyzing real network data
4) Network Structure: Block modeling a network
Split 2
Sample results
The most commonly used blockmodel routine is ConCorr, which is simple and fast. The result is a set of nested “splits” – to some pre-specified depth.
Here I apply that result to the school net, working to a depth of 3 splits.
Note that the 2nd split in the bottom half captures a “periphery” position

38. Tutorial: Analyzing real network data
4) Network Structure: Block modeling a network
Split 3
Sample results
The most commonly used blockmodel routine is ConCorr, which is simple and fast. The result is a set of nested “splits” – to some pre-specified depth.
Here I apply that result to the school net, working to a depth of 3 splits.

39. Tutorial: Analyzing real network data
4) Network Structure: Block modeling a network
More in keeping w. the spirit of the original block modeling papers, “regular equivalence” models are less likely to generate block-diagonal models.
A simple positional model is the “core-periphery” model. This searches for a single “core” in the net. Since we know this net is split in two “wings”, we’ll just look within one of them.

40. Tutorial: Analyzing real network data
4) Network Structure: Block modeling a network
003
012_S
012_E
012_I
102_D
102_I
021D_S
021D_E
021U_S
021U_E
021C_S
021C_B
021C_E
111D_S
111D_B
111D_E
111U_S
111U_B
111U_E
030T_S
030T_B
030T_E
030C
201_S
201_B
120D_S
120D_E
120U_S
120U_E
120C_S
120C_B
120C_E
210_S
210_B
300
Triadic Position Census: 36 Positions within 16 Directed Triads
Indicates the position.
Another simple way to get at positions in a network is to compare nodes across a vector of triad-positions. In a directed network, the vector giving the count of which positions an actor is part of nicely summarizes the type of role the actor plays in the net.

41. Tutorial: Analyzing real network data
4) Network Structure: Block modeling a network
Another simple way to get at positions in a network is to compare nodes across a vector of triad-positions. In a directed network, the vector giving the count of which positions an actor is part of nicely summarizes the type of role the actor plays in the net.

42. Tutorial: Analyzing real network data
4) Statistical Models for Networks
The exponential random graph (ERGM) class of models are designed to let you model an observed network as a function of local-network, node, and dyad-level features.
These models take the form:

43. Tutorial: Analyzing real network data
Statistical Models for Networks

44. Tutorial: Analyzing real network data
Statistical Models for Networks

45. Tutorial: Analyzing real network data
Statistical Models for Networks
From Handcock (2006):

46. Tutorial: Analyzing real network data
Statistical Models for Networks
Note this is a very simple “dyad independence” model.
From Handcock (2006):

47. Tutorial: Analyzing real network data
Statistical Models for Networks
The dyad-independence model had been extended to other “node” features
From Handcock (2006):

48. Tutorial: Analyzing real network data
Statistical Models for Networks
Lots of other structural features can be included, though not all imply reasonable models
From Handcock (2006):

49. Tutorial: Analyzing real network data
Statistical Models for Networks
From Handcock (2006):

50. Tutorial: Analyzing real network data
Statistical Models for Networks
The STATNET statistical package in R is the best way to estimate these models.
We will:
walk through exporting our school friendship data from SAS and bringing it into R.
Specify some simple models
Demonstrate getting goodness of fit stats on these models
Demonstrate simulating from a model
The ultimate set of stats one can add to a model are growing quickly….
Open “statnet_datawrite.sas” to see how to create data for export.
From Handcock (2006):

51. Tutorial: Analyzing real network data
Statistical Models for Networks
Results from a model (takes too long to run in real time!):
Summary of model fit
==========================
Formula: s_friends ~ edges + mutual + ttriad + nodematch("S3") + nodematch("WHITE") +
edgecov(s_clubs, "ovlpec")
Newton-Raphson iterations: 87
MCMC sample of size 10000
Monte Carlo MLE Results:
estimate s.e p-value MCMC s.e.
edges < 1e
mutual < 1e
ttriad < 1e
nodematch.S < 1e
nodematch.WHITE
edgecov.s_clubs.ovlpec
Null Deviance: on degrees of freedom
Residual Deviance: on degrees of freedom
Deviance: on degrees of freedom
AIC: BIC:
From Handcock (2006):