Social Sub-groups II

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Social Sub-groups II

• Outline
• How?
• - Review group-finding strategies
• - Evade PCA (SVD for the
  math-oriented!)
• - Theory Problem What should
  group-structure be?
• Why?
• Wayne Baker
• Social structure in a place where there should be
  none
• Scott Feld
• What causes clustering in a network? Opportunity
  and interests
• Examples from Add Health Prosper
• Practical
• Software Program examples.
• Next week Roles Blockmodels

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Methods How do we identify primary groups in a
network?
Strategies for identifying primary groups
Search 1) Fit Measure Identify a measure of
groupness (usually a function of the number of
ties that fall within group compared to the
number of ties that fall between group). 2)
Algorithm to maximize fit. Once we have the
index, we need a clever method for searching
through the network to maximize the fit. See
Jiggle, Factions etc. Destroy Break
apart the network in strategic ways, removing the
weakest parts first, whats left are your primary
groups. See edge betweeness MCL
Evade Dont look directly, instead find a
simpler problem that correlates Examples
Generalized cluster analysis, Factor Analysis, RM.
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Strategies for identifying primary groups
Search - UCINETs Factions - Rs
FastGreedy - PAJEKs Generalized
block-modeling - Franks KliqueFinder
Destroy Edge-betweenness reduction MCL Flow
model Evade Leading Eigenvector
model Clustering Distance (or other)
matrix Principle Component / Factor / SVD
methods RNM Hybrids Use a
simple evade technique for starting values and
then use a search technique. (CROWDS, JIGGLE)
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Strategies for identifying primary groups

Evade
Factor Analysis Treat the adjacency/similarity
matrix as a set of N variables and look for
latent factors that explain the variance in the
data.
IQ
SES
1.0
1.0
Math Score
Income
0.0
0.0
d
d
We often use simple indicators and assume they
measure our concepts
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Strategies for identifying primary groups

Evade
Factor Analysis Treat the adjacency/similarity
matrix as a set of N variables and look for
latent factors that explain the variance in the
data.
IQ
SES
Income
Reading Score
Occupation
Highest Degree
House Size
Languages Spoken
Math Score
d
d
d
d
d
d
d
But we dont have to! We can imagine that each
latent concept causes our indicators, and build a
measurement model.
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Strategies for identifying primary groups

Evade
Factor Analysis Treat the adjacency/similarity
matrix as a set of N variables and look for
latent factors that explain the variance in the
data.
But we dont have to! We can imagine that each
latent concept causes our indicators, and build a
measurement model.
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Strategies for identifying primary groups

Evade
Factor Analysis Treat the adjacency/similarity
matrix as a set of N variables and look for
latent factors that explain the variance in the
data.
In a network, we assume that the tie pattern is
an imperfect measure of an underlying latent
structure that we can explain with similar
factors. Instead of lots of measurements we
have many columns in the adjacency (sim) matrix,
and we can summarize that with factor scores. --
works best if the similarity matrix has more
information so multiple account data are
perfect. or you can transform the data in some
way to more information (like use a distance
matrix.
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Strategies for identifying primary groups

Evade
Factor Analysis Treat the adjacency/similarity
matrix as a set of N variables and look for
latent factors that explain the variance in the
data.
Here is code I used in the PROSPER data
/ this section builds info on how to weight
dyads for in-group, out-group. / twostp((adjma
tadjmat)gt0)adjmat / make it either direction
w. the first term / ttieadjmattwostp /1 if
tie contributes to a transitive triple
/ ttie((ttiettie)) adjrawadjmat
adjmat(adjmatadjmat) / force it to be
symetric, 1asym 2reciped / adjmatadjmat-diag(
adjmat) / remove any self ties
/ d2reachlim((adjmatgt0),3) / re-weight to
bias toward recip ties / wm_4
(d21)(adjmat2)8 / recip direct ties
/ wm_2a (d21)(adjmat1)4 / unrecip
direct ties / wm_1 2(d22)/ ties 2-steps
out / wm_p5 0(d23) / ties 3-steps out -
note it's zeroed out here/ wmwm_4wm_2awm_1w
m_p5(3(ttie/(max(ttie)))) / transitivity is
at the end/ wmwm-diag(wm)
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Strategies for identifying primary groups

Evade
Factor Analysis Treat the adjacency/similarity
matrix as a set of N variables and look for
latent factors that explain the variance in the
data.
Here is code I used in the PROSPER data
/ run factor analysis. Note nfactors is a high
value, should only take those w. EV gt 2, but
this gives us room... / proc factor
rotatevarimax minminev outfactset
datasymmat nfactors175 outstatfscores
noprint run quit
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Strategies for identifying primary groups

Evade
Result
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Strategies for identifying primary groups

Evade
Result
Each column is a person, these are the factor
loadings for each person on each retained factor.
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Strategies for identifying primary groups

Evade
Result
Sociogram for a single school
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Strategies for identifying primary groups

Evade
Result

• Sociogram for a single school.
• Problem is that there are no necessary
  connectivity checks you can get groups that
  are disconnected.
• Biggest strengths are
• Really fast
• Allows for overlapping groups
• Gives you embeddedness scores based on factor
  loadigs

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Strategies for identifying primary groups

Hybrid
The Crowds Algorithm 1. Identify members of
network bicomponents, remove people not included.
2. Cluster the reduced network. - Identify
optimal number of groups (TREEWALK) -
For each level of the cluster partition tree do
(BFS) -Move up the tree from smaller to
larger groups. -If the fit for both groups
is improved by joining them then do so. -If
not, then identify group at that level.
-End TREEWALK. Do until all groups are
identified (GLOBAL LOOP) 3. Evaluate node
fit. Do until nodes cannot be moved
For each identified cluster do
(GRPCHECK) - Ensure group is a
bi-component. -Calculate effect on
group a of moving node j to group a.
-Calculate effect on j's present group of
removing j. - If there is a
positive net gain to moving j from own group to
a, then do so. End. 4. Identify
Bridging members. -If removing j from group a
would improve the fit of group a, AND assigning j
to any other group would lower the fit for that
group, then j is considered a bridge. Place all
bridges in separate class. 5. Group Check. Check
returns to combining groups. IF merging groups
would improve the fit of all groups to be merged,
then do so. - Evaluate bridges, to be sure that
they are not bridging two groups that have now
merged. End Global loop.  
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Return to first question What is a group?

• The simple notions of a complete clique are
  difficult to square w. real-world data.
• Density is an indicator, but subject to
  over-grouping (no connectivity) and
  star-patterns.
• Groups are likely internally differentiated
  with core vs. periphery members
• Most sociological theories of groups rest on
  transitive closure and short distances
• Theres a sense that members are equal a
  tight-knit group
• The group should be fairly small face-to-face
  scale
• The social processes underlying the group turn on
  reciprocity, trust, communication, homogeneity of
  norms beliefs.
• Almost all require a comparative set in-group to
  out-group. It is relational not essential.
• Cross-cutting social circles would lead us to
  expect overlapping groups, but in practice most
  methods do not do that, as its analytically too
  cumbersome.
• Practically, group detection is hard and most
  methods will give you (slightly) different
  results. You can compare results using a Rand
  statistic (proportion of pairs similarly
  categorized in two partitions), but for small
  settings these differences can matter.

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Social Sub-groups why look?
Wayne Baker The Social Structure of a National
Securities Market 1) Behavioral assumptions of
economic actors 2) Micro-structure of
networks 3) Macro-structure of networks 4)
Price Consequences
Under standard economic assumptions, people
should act rationally and act only on price.
This would result in expansive and homogeneous
(I.e. random) networks. It is, in fact, this
structure that allows microeconomic theory to
predict that prices will settle to an optimal
equilibrium
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Bakers Model
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Bakers Model
He makes two assumptions in contrast to standard
economic assumptions a) that people do not have
access to perfect information and b) that some
people act opportunistically
He then shows how these assumptions change the
underlying mechanisms in the market, focusing on
price volatility as a marker for
uncertainty. The key on the exchange floor is
market makers people who will keep the process
active, keep trading alive, and thus not hoard
(and lower profits system wide)
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Bakers Model
Micronetworks Actors should trade extensively
and widely. Why might they not? A) Physical
factors (noise and distance) B) Avoid risk and
build trust
Macro-Networks Should be undifferentiated. Why
not? A) Large crowds should be more
differentiated than small crowds. Why?
Price consequences Markets should clear. They
often dont. Why? Network differentiation
reduces economic efficiency, leading to less
information and more volatile prices
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Baker Use frequency of exchange to identify the
network, resulting in
Baker finds that the structure of this network
significantly (and differentially) affects the
price volatility of the network Groups found
w. NEGOPY
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The one other program you should know about is
NEGOPY. Negopy is a program that combines
elements of the density based approach and the
graph theoretic approach to find groups and
positions. Like CROWDS, NEGOPY assigns people
both to groups and to outsider or between
group positions. It also tells you how many
groups are in the network. Its a DOS based
program, and a little clunky to use, but
NEGWRITE.MOD will translate your data into NEGOPY
format if you want to use it. There are many
other approaches. If youre interested in some
specifically designed for very large networks
(10,000 nodes), Ive developed something I call
Recursive Neighborhood Means that seems to work
fairly well.
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Baker Because size is the primary determinant of
clustering in this setting, he concludes that the
standard economic assumption of large market
efficient is unwarranted.
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Scott Feld Focal Organization of Social Ties
Feld wants to look at the effects of constraint
opportunity for mixing, to situate relational
activity within a wider context. The contexts
form Foci, A social, psychological, legal or
physical entity around which joint activities are
organized (p.1016) People with similar foci
will be clustered together. He contrasts this
with social balance theory. Claim that much of
the clustering attributed to interpersonal
balance processes are really due to focal
clustering. (note that this is not theoretically
fair critique -- given that balance theory can
easily accommodate non-personal balance factors
(like smoking or group membership) but is a good
empirical critique -- most researchers havent
properly accounted for foci.)
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Observed Clustering within Adolescent Social
Networks
Network Characteristics of Sub Groups

• On average, 65 of a schools adolescents are in
  cohesive sub-groups.
• 87 of all relations are within sub-groups.
• The average sub-group has 22 members.
• The average diameter for a sub-group is 3 steps.
• The mean segregation index is .96 (1Complete,
  0Random)

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Observed Clustering within Adolescent Social
Networks
Distribution of Characteristic within groups,
relative to school distribution
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Group Data in Add Health
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Group data in Add Health
Inter-Group Relations
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Group data in Prosper

• We have 368 network observations based on 2
  cohorts observed over 5 waves in 2 states. Using
  a variant of the CROWDs algorithm, I identified
  groups in every network.
• Results in about 4500 groups averaging in size of
  about 10 kids, though some settings are really
  too cohesive to break into small bits, resulting
  peer groups of 40ish kids.

Network Group Characteristics
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Group data in Prosper

• We have 368 network observations based on 2
  cohorts observed over 5 waves in 2 states. Using
  a variant of the CROWDs algorithm, I identified
  groups in every network.
• Results in about 4500 groups averaging in size of
  about 10 kids, though some settings are really
  too cohesive to break into small bits, resulting
  peer groups of 40ish kids.

30
Group data in Prosper

• We have 368 network observations based on 2
  cohorts observed over 5 waves in 2 states. Using
  a variant of the CROWDs algorithm, I identified
  groups in every network.
• Results in about 4500 groups averaging in size of
  about 10 kids, though some settings are really
  too cohesive to break into small bits, resulting
  peer groups of 40ish kids.

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Group data in Prosper