Simulating%20Social%20Networks

1
Simulating Social Networks
James Moody Duke University
The Population Sciences and Agent Based
Methodology An Answer to the Macro-Micro
Link? September 27, 2006, NIH
Work reported in this presentation has been
supported by NIH grants DA12831, HD41877, and
AG024050. Thanks to the Center for Advanced
Study in the Behavioral Sciences (CASBS) for
office and tech support for this work.
2
Introduction Network Structure Puzzles
Distribution of Popularity
By size and city type
Why are high school popularity distributions
constant across vastly different communities ?
3
Introduction Network Structure Puzzles
Add Health relational change statistics
How can the global structure remain constant
given massive changes at the dyad level?
4
Introduction Network Structure Puzzles
What rules can account for adolescent romantic
network structure?
5
Introduction Network Structure Puzzles
Why are academic PhD exchange markets
(hiring/placing) strongly centralized
Han, S-K. Social Networks 2003251-280. Figure 1
6
Introduction Network Structure Puzzles
Burris, ASR 2004
and positions within systems stable over
generations?
7
Introduction Network Structure Puzzles

• In each case, the interdependent activity of
  each actor affects the conditions shaping action
  for everyone else in the setting.
• History matters in a deterministic (rather than
  stochastic) sense
• The process shaping actors choices are locally
  bounded
• The resulting network structure is often very far
  from a random null.
• Statistical Models fail for either data or deep
  endogeneity reasons.
• Actor-oriented simulation methods
• Provide a way of thinking about interdependent
  action
• Create multiple replications with known variation
  on independent variables.

8
Introduction outline

• Introduction
• Micro Macro elements in social networks
• Colemans boat
• Structural correlates of micro macro
• Linking rules to structures
• Simulation Network Structure
• Dynamics of adolescent friendship structure
• Adolescent romantic exogamy
• Inequality in PhD exchange networks
• Network Diffusion Disease Spread
• Degree mixing models
• Relational timing
• Promises Pitfalls
• Good Theoretical rigor, clarity, elegance
• Bad How to test against observed data
• Ugly Rule proliferation specification

9
Micro-Macro elements in social networks
Colemans Boat
Contextual State
Global Outcome
Macro
1
Resulting Action
Micro
Individual Response
1) Macro ? Micro Typically contextual
conditions that enable/constrain individual
action.
10
Micro-Macro elements in social networks
Colemans Boat
Contextual State
Global Outcome
Macro
1
Resulting Action
2
Micro
Individual Response

1. Macro ? Micro Typically contextual conditions
   that enable/constrain individual action.
2. Micro ? Micro A direct-action correlate of the
   contextually constrained behavior in (1)

11
Micro-Macro elements in social networks
Colemans Boat
Contextual State
Global Outcome
Macro
3
1
Resulting Action
2
Micro
Individual Response

• Macro ? Micro Typically contextual conditions
  that enable/constrain individual action.
• Micro ? Micro A direct-action correlate of the
  contextually constrained behavior in (1)
• Micro ? Macro An aggregation or interaction
  process that can account for the new global-level
  outcome.

12
Micro-Macro elements in social networks
Colemans Boat
4
Contextual State
Global Outcome
Macro
3
1
Resulting Action
2
Micro
Individual Response

• Macro ? Micro Typically contextual conditions
  that enable/constrain individual action.
• Micro ? Micro A direct-action correlate of the
  contextually constrained behavior in (1)
• Micro ? Macro An aggregation or interaction
  process that can account for the new global-level
  outcome.
• The observed macro-level correlation is thus
  accounted for by actors capable of intent and
  action.

13
Micro-Macro elements in social networks
Colemans Boat
Of these 4 links, the 3rd is often the trickiest.
Here we face questions about emergent
properties features of the macro system that
cannot be seen as simple (mean, sum, proportion)
aggregations of individual action, but instead
are seen as some interactive effect of the
combined action.
Social facts assume a shape, a tangible form
peculiar to them and constitute a reality sui
generis vastly distinct from the individual facts
which manifest that reality Durkheim
Rules Of Sociological Method
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Micro-Macro elements in social networks
Structural correlates of micro and macro
Network micro features Anything you can measure
on a local ego-network.
Ego-Net
15
Micro-Macro elements in social networks
Structural correlates of micro and macro
Local-romantic Networks
16
Micro-Macro elements in social networks
Structural correlates of micro and macro
Complete Network
17
Micro-Macro elements in social networks
Structural correlates of micro and macro
Network micro features Anything you can measure
on a local ego-network.
Purely local information on ego about egos
contacts Number of ties (degree) node
attribute mixing
1
2
e
3
4
18
Micro-Macro elements in social networks
Structural correlates of micro and macro
Network macro features Features resting on (a)
paths of length gt 2.
The key element that makes a network a system is
the path its how sets of actors are linked
together indirectly. A walk is a sequence of
nodes and lines, starting and ending with nodes,
in which each node is incident with the lines
following and preceding it in a sequence. A path
is a walk where all of the nodes and lines are
distinct. Paths are the routes through networks
that make diffusion possible, they govern
connectivity, clustering and reflect clump
structure as well.
19
Micro-Macro elements in social networks
Structural correlates of micro and macro
Network macro features Features resting on (a)
paths of length gt 2.
B
A
These two graphs have the exact same local
properties, but very different global properties.
20
Micro-Macro elements in social networks
Structural correlates of micro and macro
Micro-Macro elements in social networks
Structural correlates of micro and macro
Network macro features Features resting on (b)
the distribution of local features.
Distribution of Popularity
By size and city type
21
Micro-Macro elements in social networks
Structural correlates of micro and macro
Micro-Macro elements in social networks
Structural correlates of micro and macro
Network macro features Features resting on (b)
the distribution of local features.
22
Micro-Macro elements in social networks
Structural correlates of micro and macro
Micro-Macro elements in social networks
Structural correlates of micro and macro
Network macro features Features resting on (b)
the distribution of local features.
23
Micro-Macro elements in social networks
Structural correlates of micro and macro
Network macro features Features resting on (c)
outcomes distributed across nodes.
Define as a general measure of the diffusion
susceptibility of a graph as the ratio of the
area under the observed curve to the area under a
random baseline curve. As the ratio ? 1.0, you
get effectively faster diffusion.
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Micro-Macro elements in social networks Linking
actor rules to network structure

• For most simulation settings, we are often
  interested in identifying behavioral rules that
  (a) fit the micro network features of interest
  and (b) give rise (in combination) to the global
  features of interest.
• Types of network rules
• Node volume features (number of ties)
• Dyadic Interaction features (reciprocity,
  race-mixing rules)
• Indirect interaction features (Social balance,
  relational exogamy rules)
• Timing rule (relation duration, concurrency, and
  order)

25
Micro-Macro elements in social networks Linking
actor rules to network structure
For most simulation settings, we are often
interested in identifying behavioral rules that
(a) fit the micro network features of interest
and (b) give rise (in combination) to the global
features of interest. Two ways to think of
rule-action links for network modesl Explanatio
n Identifying a (small) set of rules that, when
applied, account for feature difficult to explain
otherwise. Examples Adolescent friendship
dynamics Romantic network structure PhD
Exchange network structure Stability Explorati
on Start with a set of local rules you are
confident in, then apply to a setting to learn
what system-level features emerge.. Examples D
iffusion potential of low-degree
networks Diffusion constraints resulting from
relational timing
26
Simulating Network Structure Adolescent
Friendship Dynamics

• Sociologist revel in the diversity of social
  settings, but a primary motivation for theories
  of social structure is to explain common features
  across settings and account for social
  differentiation endogenously. Consider
• Cartwright, Harary, Davis, Leinhardt Clustering
  in social networks
• Axelrod Social Cooperation in competitive
  settings
• Chase The development of hierarchy
• Johnsen Process agreement models for social
  hierarchy
• Gould Peer influence embellishments on quality
  stratification
• Mark Social Differentiation from first
  principles
• McFarland Development of ritualized structure in
  dynamic networks
• Adolescent school networks vary on myriad
  exogenous factors, such as the distribution of
  race, SES, grades, health behaviors and so forth.
  But what features are common across these
  diverse settings and how can we explain them?

27
Simulating Network Structure Adolescent
Friendship Dynamics

• Data
• I use the National Longitudinal Survey of
  Adolescent Health (Add Health). This is a
  nationally representative survey of adolescents
  in school (7th through 12 grade), with
  (approximately) complete network data in 129
  schools, including data over time for a smaller
  subset of schools.
• These data are available through the Carolina
  Population Center
• Methods
• Features of the global network structure are
  identified through triad distribution methods and
  block models
• Specific hypotheses about social balance are
  tested with exponential random graph models
• Dynamic implications for these models are derived
  from simulation studies grounded in the observed
  data.

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Simulating Network Structure Adolescent
Friendship Dynamics
A periodic table of social elements
(0)
(1)
(2)
(3)
(4)
(5)
(6)
003
012
102
111D
201
210
300
021D
111U
120D
021U
030T
120U
021C
030C
120C
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Dynamic Social Balance Adolescent Friendship
Networks Triad distributions
A periodic table of social elements
Type Number of
triads ---------------------------------------
1 - 003 21 ----------------------
----------------- 2 - 012 26
3 - 102 11 4 - 021D
1 5 - 021U 5 6 -
021C 3 7 - 111D
2 8 - 111U 5 9 - 030T
3 10 - 030C 1
11 - 201 1 12 - 120D
1 13 - 120U 1 14 -
120C 1 15 - 210
1 16 - 300
1 --------------------------------------- Sum (2
- 16) 63
30
Simulating Network Structure Adolescent
Friendship Dynamics
Triads encapsulate local behavior rules
(0)
(1)
(2)
(3)
(4)
(5)
(6)
003
012
102
111D
201
210
300
021D
111U
120D
021U
030T
120U
021C
030C
120C
31
Simulating Network Structure Adolescent
Friendship Dynamics

• Traditional social balance models tested the
  theory against observed triad distributions. If
  there were more of the all balanced triads and
  fewer of the contradictory triads, then the
  data were (more or less) consistent with the
  theory.
• Lots of evidence in the cross section supporting
  balance models, but almost always unable to
  account for the over-representation of mixed
  triad types.
• Cross-sectional models assume a dynamic system
  that has finished where there are no
  actor-level incentives to make further change.
• But while observed networks often fit a balance
  model, they also have massive amounts of change
  at the local level and thus cant possibly fit
  the finished state proposed by the model.

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Simulating Network Structure Adolescent
Friendship Dynamics
For the 129 Add Health school networks, the
observed distribution of the tau test statistic
for various triad distribution models is
Suggesting that the ranked-cluster models beat
random chance in all schools.
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Simulating Network Structure Adolescent
Friendship Dynamics
Triads observed in excess
Eugene Johnsen (1985, 1986) specifies a number of
structures that result from various triad
configurations
Ranked Cluster
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Simulating Network Structure Adolescent
Friendship Dynamics

• These results (w. more detail) suggest that
• Most of the school networks have a rank-strata
  structure
• The structure remains even though nearly half of
  all relationships are new
• Peoples position in the popularity distribution
  is fluid
• What models allow us to explain a stable
  macro-structure in the face of dynamic relations?

35
Simulating Network Structure Adolescent
Friendship Dynamics

• Two crucial insights help inform a (slightly)
  modified approach to social balance
• Triples instead of triads. Operationalizing
  balance theory as transitivity allows us to
  simplify the behavioral assumptions (cf. Hummel
  and Soduer (1987, 1990)), but at the cost of
  divorcing the behavior from the macro-structure
  implications of previous triad based models.
• Structural implications differ depending on your
  point of view. Because transitivity is directed
  from a particular egos point of view, the same
  structure will be experienced differently by each
  person in the network.
• Carley and Krackhardt (1996) show this clearly at
  the relationship level, and we would expect
  similar effects at the triple level. This implies
  that changes made by one person to alleviate
  strain, can create strain for others.
• We can also distinguish transitivity seeking from
  the intransitivity avoidance.

36
Simulating Network Structure Adolescent
Friendship Dynamics
030C
120C
102
111U
021C
201
012
111D
300
003
210
021D
120U
vacuous transition
Increases transitive
Decreases intransitive
030T
Decreases transitive
Increases intransitive
021U
Vacuous triad
120D
Intransitive triad
Transitive triad
(some transitions will both increase transitivity
decrease intransitivity the effects are
independent they are colored here for net
balance)
37
Simulating Network Structure Adolescent
Friendship Dynamics Triad transition state-space
simulation
TRIAD
16
TRIAD
16
15
15
14
14
13
13
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
100
200
300
0
100
200
300
Avoid Intransitivity only (strong)
Favor Transitivity only (strong)
38
Simulating Network Structure Adolescent
Friendship Dynamics Testing model on observed
data
Standardized Coefficients from an Exponential
Random Graph Model
0.8
Endogenous
Focal Orgs.
Dyadic Similarity/Distance.
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
GPA
SES
Fight
College
Drinking
Same Sex
Transitivity
Same Race
Both Smoke
Same Clubs
Intransitivity
Same Grade
Reciprocity
39
Simulating Network Structure Adolescent
Friendship Dynamics Actor-oriented simulation
model

• Based on these results, I simulate network
  dynamics controlling the extent to which actors
  seek transitivity and avoid intransitivity.
• This simulation builds on the empirical models in
  specifying separate effects for transitivity and
  intransitivity based on egos returns to a change
  in relations.
• Adds a parameter to limit the marginal returns to
  forming new relations, that effectively dampens
  (but does not hard-code) out-degree. Plus a
  parameter that punishes continued asymmetry
  (Gould parameter).
• Reciprocity dyad attribute parameters are held
  constant across all simulations.
• Time is encoded as each nodes opportunity to
  change relations as iterations pass.

40
Simulating Network Structure Adolescent
Friendship Dynamics Actor-oriented simulation
model
Final Graph Transitivity
R2 0.82
Mean over the state space
41
Simulating Network Structure Adolescent
Friendship Dynamics Actor-oriented simulation
model
Structural Stability Correlation of network
structure at tfinal with t-5
R2 0.52
Mean over the state space
42
Simulating Network Structure Adolescent
Friendship Dynamics Actor-oriented simulation
model
Total Graph Transitivity At moderate
transitivity/intransitivity
A single simulation run, showing the wide swings
in graph transitivity. Similar trends evident in
reciprocity, though the number of arcs and
general shape (variance/skew) of the popularity
distribution does not fluctuate much.
43
Simulating Network Structure Adolescent
Friendship Dynamics Actor-oriented simulation
model

• I think part of this process is affected by not
  paying close enough attention to the dyadic
  implications of repeated asymmetry. Consider
  these triads

As currently specified, the model rewards
reciprocation, but does not penalize asymmetry.
So if i?j, then j is more likely to nominate i,
but if j does not reciprocate, i has no
(independent) reason to change tie
patterns. Gould (AJS 2002), builds a model of
emergent hierarchy based (partially) on the
notion that people will not maintain a relation
that is not reciprocated. Building this
feature into the model will make these triads
temporarily attractive, but unstable in the long
run, which should lessen the tendency for
structures to lock-in on largely asymmetric
hierarchical structures.
44
Simulating Network Structure Adolescent
Friendship Dynamics Actor-oriented simulation
model
Dynamic simulation movie, representative
parameter weights.
Green ties are reciprocated, blue asymmetric.
45
Simulating Network Structure Adolescent Romantic
Networks
Explanation problem 1 Romantic relations at
Jefferson high school
Source Bearman, Moody and Stovel (2004) AJS
46
Simulating Network Structure Adolescent Romantic
Networks
Is the network typical? How does it compare to
random networks with the same micro-features?
Circle observed, boxplots simulated networks
w. same volume.
47
Simulating Network Structure Adolescent Romantic
Networks
Is the network typical? How does it compare to
random networks with the same micro-features?
The network is decidedly not random. Moreover,
typical network mixing features dont take us
very far (homophily on number of prior partners
helps constrain component size, and smoking
homophily is evident by inspection). We propose
a network exogamy rule a prohibition on cycles
of length 4
48
Simulating Network Structure Adolescent Romantic
Networks
We propose a network exogamy rule a prohibition
on cycles of length 4
Introduce a prohibition on forming 4-cycles in
the randomly simulated networks.
49
Simulating Network Structure Adolescent Romantic
Networks
We propose a network exogamy rule a prohibition
on cycles of length 4
Here we get a much closer match between the
simulated networks and the observed in each of
our test statistics
50
Simulating Network Structure Adolescent Romantic
Networks
We propose a network exogamy rule a prohibition
on cycles of length 4
and the simulated components have similar
qualitative structures as well.
51
Simulating Network Structure Adolescent Romantic
Networks

• Evaluation
• This single rule addition more than any other
  dyadic feature such as homophily on behavior or
  age mixing generates networks with the
  structure we observe in reality. Its
  theoretical simplicity is the strongest strength
  of the model. From a simulation methods
  standpoint, this is a very simple rule set
• Constrain each actor to make the same number of
  partners observed in the real world
• If a partner choice would close a 4-cycle, choose
  somebody else.

52
Simulating Network Structure Adolescent Romantic
Networks
Evaluation From an implementation standpoint,
the simulation is complicated by an empirical
identification problem there are many possible
configurations where these two constraints cannot
be met simultaneously. In the process of
making choices, we effectively run out of degrees
of freedom where any new choice would lead to a
violation in the degree distribution or create a
4-cycle. - Theoretically, this implies that the
real-world graph is coming from a fairly small
region of the overall graph space. -
Methodologically it means that using only a
simple rule-based simulation was computationally
inefficient. We solved this by adding graph
identification procedures that forced choices
once prior choices implied them. - This
difficutly followed from our desire to fit the
distributions exactly.
53
Simulating Network Structure Academic Castes
inequality in PhD exchange Networks
Explaination problem 2 Academic Caste Systems
I (N52)
II-a (N4)
II-b (N15)
II-c (N22)
II-d (N81)
III (N384)
Why is this network so hierarchical and stable?
Han, S-K. Social Networks 2003251-280. Figure 1
54
Simulating Network Structure Academic Castes
inequality in PhD exchange Networks
Particularly in settings, such as science, where
unversalism and meritocracy define the system
ethos?

• Merton (1942,1968)
• Two key features that shape the academic market
• Universalistic criteria to evaluate quality
• Mathew effect the cumulative advantage of
  prestige
• Burris (2004239) states as fact that prestige is
  ascribed rather than achieved, arguing that
• Moreover, through a process of cumulative
  advantage, academic scientists and scholars who
  secure employment in the more prestigious
  departments gain differential access to resources
  and rewards that enhance their prospects. This
  cycle results in a stratified system of
  departments and universities, ranked in terms of
  prestige, that is highly resistant to change.
  (p.239)

55
Simulating Network Structure Academic Castes
inequality in PhD exchange Networks

• Two types of evidence are used to demonstrate
  non-universalistic effects
• A less-than-perfect association between measures
  of faculty productivity and department rank /
  hiring (Long, Hargens, Jacobs, Baldi, Burris,
  Conrad-Black)
• Burris shows that between 30 and 50 of the
  variance in NRC rankings can be accounted for
  with standard productivity measures
• A strong correlation between simple number of
  faculty and prestige (r 0.63 in sociology).
• Probability / prestige of first job due to origin
  of PhD over publication record (but see
  Cognard-Black, 2004 and below).

56
Simulating Network Structure Academic Castes
inequality in PhD exchange Networks
Two types of evidence are used to demonstrate
non-universalistic effects 2. An extreme
stability of department rankings over time
Burris, ASR 2004
The correlation in NRC faculty quality scores in
Sociology from 1982 to 1993 is 0.92
57
Simulating Network Structure Academic Castes
inequality in PhD exchange Networks
The resulting status-based network has a strong
correlation between centrality in the hiring
network quality ranking
Social Capital Bonacich Centrality on
symmetric version of the PhD exchange Network
58
Simulating Network Structure Academic Castes
inequality in PhD exchange Networks
How can we square universalistic scientific norms
with these facts?
First, research on markets and cultural
consumption suggests that quality is accurately
perceived particularly when external measures
show small differences (White 2002, J. Blau,
Bourdieu). Quality exists, whether
it's defined or not. - Robert Pirsig
(1972) That is, we know quality even if our
systematic measures of quality are poor, which is
reflected (in part) through market convergence on
particular candidates (see below).
59
Simulating Network Structure Academic Castes
inequality in PhD exchange Networks
How can we square universalistic scientific norms
with these facts?
Second, most data on the market structure
systematically selects on the dependent variable,
as only those who are eventually hired are
observed. This has the effect of a) limiting
variation on observed quality measures b) makes
it impossible to disentangle PhD volume from
placement Recent dissertation work by
Cognard-Black, for example, shows that the
independent effect of PhD institution on
placement is often lower than publication quality
measures, once you expand the sample of PhDs
beyond those hired to major research
universities.
60
Simulating Network Structure Academic Castes
inequality in PhD exchange Networks
Given the difficulty getting data on the general
process (rather than historically accidental
draws from that general process), a simulation is
an ideal way to explore the exchange market. In
systems with open markets, merit-based hiring
rational actors 1) How stable will quality
rankings be? 2) Will size and quality be
correlated? 3) Will network exchange centrality
predict quality? Each has been used as evidence
for non-meritocratic prestige systems, but we
dont know how the observed cases match the
expected cases, because we have no reasonable
null distribution. A key advantage of using a
simulation is to identify a range of reasonable
null distributions.
61
Simulating Network Structure Persistent
inequality in PhD exchange Networks Simulation
Setup

• The purpose of this simulation is to examine the
  effect of market-relevant behavior under
  ideal-typical conditions. This involves
  simplifying the real world as much as possible,
  to isolate how particular factors affect outcomes
  of interest.
• Key real-world properties of interest
• Stable quality rankings
• Strong correlation between size and quality
• Centralized hiring networks
• Strong correlation between centrality and
  prestige
• Currently, all actors follow the same strategy,
  and I vary the strategy set across simulation
  runs.
• Future work will vary department strategies
  within runs to see how these affect competitive
  advantage.

62
Simulating Network Structure Persistent
inequality in PhD exchange Networks Simulation
Setup

• Actors
• Departments Collections of faculty who hire
  applicants produce new students. (N100).
  Initial department size is drawn from a normal
  distribution with mean 25, std12, but I
  re-draw if size is less than 10, so the actual
  distribution is slightly skewed.
• Applicants Students from (other) departments who
  apply for jobs.
• Departments seek to hire the best students,
  students want to work at the best departments.
• These actors are rational, honest, and
  risk-averse. But all actors have individual
  preferences errors in vision.
• The simulation does not include tenure or senior
  moves. So you can treat this as the realized
  or final position outcomes.

63
Simulating Network Structure Persistent
inequality in PhD exchange Networks Simulation
Setup

• Attributes
• Quality. Each faculty member and student has an
  overall quality score.
• Initial faculty quality is distributed as random
  normal(0,1).
• Implies that departments are effectively equal at
  time 1with only minor differences due to random
  chance.
• Student quality is a (specifiable) random
  function of faculty quality.
• Department quality is the mean of faculty
  quality.
• While each person has a given quality score,
  actor choices are made based on an evaluation of
  quality, which differs across actors.
• This variation reflects both differences in
  preferences and ability to discern quality.

64
Simulating Network Structure Persistent
inequality in PhD exchange Networks Simulation
Setup

• Action Departments
• Departments hire produce students.
• For each of 100 years
• Every department produces students (conditional
  on size).
• A (random) subset of departments have job
  openings based on (a) prior retirements current
  size relative to a target size.
• Departments rank applicants by their evaluation
  of applicant quality, and make offers to their
  top choices.
• If a departments 1st choice goes elsewhere, they
  go to next for a specifiable number of rounds to
  a specifiable depth into the pool.
• Jobs can go unfilled, which means that
  departments can both grow and shrink.

65
Simulating Network Structure Persistent
inequality in PhD exchange Networks Simulation
Setup
Action Departments The probability a job opening
in any given year is a function of size
66
Simulating Network Structure Persistent
inequality in PhD exchange Networks Simulation
Setup
Action Departments Faculty size decreases
through retirement
67
Simulating Network Structure Persistent
inequality in PhD exchange Networks Simulation
Setup

• Action Students
• Students rank departments that make them an offer
  by their evaluation of department quality, and
  take the best job they are offered.
• If a student does not receive a job offer in a
  given year, they move out of the system
• Lots of students dont get jobs (at PhD granting
  universities)
• Students are not strategic they do not forego a
  good offer while waiting for a better one --
  this is the risk averse quality, though this
  could be changed.

68
Simulating Network Structure Persistent
inequality in PhD exchange Networks parameter
summary
Parameter Description Specification
Hiring probability Likelihood of a job opening beyond retirement replacement. Cubic function of department size. 3 levels
Student production Probability of each faculty member putting a student on the market in a given year. Binomial (0,1), p (0.06 to 0.08). 2 levels. X1 165 X2 220
Faulty - Student Quality Correlation The correlation between student and faculty quality. Specify as a correlation from 0.37 to 0.91 3 levels
Applicant Quality Evaluation Used by departments to rank applicants. Each department assigns applicants an observed quality score based on this function. Observed (Student quality) b(N(0,1)). b 0.3 to 0.9. 3 levels
Department Quality Evaluation Used by applicants to rank job offers. Each student assigns departments an observed quality score based on this function. Observed (Department quality) b(N(0,1)). B 0.1 to 0.25. 2 levels
Hiring Rounds Number of offer rounds made. Approximates time by limiting opportunity to make alternative offers. Specify as number. 3 or 4 2 levels
Depth of Search
How deeply into the pool of candidates
departments are willing to go.
Specify as max depth. 10 to 30 3 levels
There are 3233223 648 points in the
parameter space 30 draws from each set ? 19,440
observations
69
Simulating Network Structure Persistent
inequality in PhD exchange Networks parameter
summary
A look under the hood
70
Simulating Network Structure Persistent
inequality in PhD exchange Networks Non-network
outcomes
Disagreement on Candidate Quality
0.3
0.6
0.9
10
20
Depth of Search
30
All results are presented around the competitive
field
71
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run

• Initial Conditions
• 100 departments
• Size distributed normally with mean of 25 std of
  12 and an initial floor of 10. This is the
  resource-based target size for departments.
• Faculty quality is distributed normally (N(0,1))
• Age is initially distributed uniformly from 0 to
  40 (starting with a distribution means that
  retirements dont go in waves)
• Parameter Settings
• Hiring curve Medium
• Student Production 0.06 (150 applicants per
  year)
• Student-Faculty Quality Correlation 0.67
• Disagreement on applicant quality 0.60
• Disagreement on department quality 0.1
• Hiring Rounds 4
• Depth of Search 20

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Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Market Size

• Over the first 10 years
• 66 to 104 positions advertised
• 147 to 169 students on the market
• 59 to 72 people were hired each year

73
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Student-Faculty Quality Correlation
Student Quality
r0.65
r0.49
Faculty Quality
Department Quality
74
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Distribution of size over time
75
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Correlation between final size and target size
Quality gt Mean 1std
Quality lt Mean 1std
Target Equality
Final Size
Target Size
76
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Distribution of quality over time
77
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Correlation of Size and Quality over time
Burris reports the correlation between size and
prestige as 0.63
78
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Correlation of Quality 10 years prior
79
Simulating Network Structure Persistent
inequality in PhD exchange Networks Non-network
outcomes
Size Quality Average Department Quality
Calculated at final year ( y100)
80
Simulating Network Structure Persistent
inequality in PhD exchange Networks Non-network
outcomes
Size Quality Correlation of Size and Quality
Calculated at final year ( y100)
81
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Correlation of Size and Quality over time
A single example run taken from the middle
competition cell.
Burris reports the correlation between size and
prestige as 0.63
82
Simulating Network Structure Persistent
inequality in PhD exchange Networks Non-network
outcomes
Quality Stability 10 Year Correlation of Quality
Calculated at final year ( y100)
83
Simulating Network Structure Persistent
inequality in PhD exchange Networks A single
example run
Correlation of Quality 10 years prior
A single example run taken from the middle
competition cell.
84
Simulating Network Structure Persistent
inequality in PhD exchange Networks Non-network
outcomes
Calculated at final year ( y100)
85
Simulating Network Structure Persistent
inequality in PhD exchange Networks Network
outcomes
The production and hiring of PhDs generates an
exchange network, connecting the sending
department to the hiring department. Note that,
unlike many simulations, here the edges in the
network are actors (rather than simply the result
of node action). I record this network for all
hires in the last 10 years of the simulation
history, and construct two measures a) The
network centralization score b) The correlation
between network centrality quality size.
86
Simulating Network Structure Persistent
inequality in PhD exchange Networks Network
outcomes
For what follows, working within one region of
the parameter space
Disagreement on Candidate Quality
Depth of Search
A preliminary regression over the entire space
shows that hiring rates quality correlation
matter most for centralization
87
Simulating Network Structure Persistent
inequality in PhD exchange Networks Network
outcomes
Network Centralization by Quality Correlation
Job Openings
88
Simulating Network Structure Persistent
inequality in PhD exchange Networks Network
outcomes
Correlation of Centrality Department Size
Bonacich Centrality
89
Simulating Network Structure Persistent
inequality in PhD exchange Networks Network
outcomes
Correlation of Centrality Department Quality
Bonacich Centrality
90
Simulating Network Structure Persistent
inequality in PhD exchange Networks Network
outcomes
Most Productive Line (first sort selects here!)
OLS line
Real data from a all applicants for an open
position at a large Midwestern university
91
Simulating Network Structure Persistent
inequality in PhD exchange Networks Network
outcomes
92
Simulating Network Structure Persistent
inequality in PhD exchange Networks Tentative
conclusions

• The very simple market model proposed here can
  account for many of the features we see in real
  PhD exchange markets
• Stable quality rankings
• Strong Correlation between Size Quality
• Highly Centralized Networks
• Correlation between Quality ranking and
  Centralization
• Qualitatively, it is appears that you can order
  most of these networks with a pretty clear
  distinction between top or core departments
  and a periphery, characterized by asymmetric flow
  of students.

93
Simulating Network Structure Persistent
inequality in PhD exchange Networks Tentative
conclusions

• There is still some room for non-market effects
  here, however, since the resulting hierarchies
  are not perfect
• Self-selection effects
• Students avoiding applying out of their league
• Adjusting depth of search to be linked to current
  quality
• Social Network Effects
• Give a positive weight to students who come from
  departments where current faculty received their
  PhDs
• Market Segmentation Effects
• Add a dimension of substantive fit to the
  market model.
• Should act as (a) an interaction boost for market
  competition effects
• Will give sending advantages to large diverse
  departments.

94
Simulating Network Structure Persistent
inequality in PhD exchange Networks Tentative
conclusions

• There are two broad features that shape these
  networks.
• Market competition
• Market competition factors (mainly agreement on
  quality depth of search, but also simple
  student production hiring rates) have a huge
  effect on the mean levels of department
  characteristics seen across the simulation
  settings.
• When the competition for students is high, offers
  converge on small numbers of market stars. This
  generates a sellers market, where a small
  number of market stars dominate hiring patters,
  take jobs at the most prestigious institutions,
  leaving many departments with failed searches,
  and ultimately lowering the quality for the
  discipline as a whole.
• This mechanism can account for much of the
  observed stability, growth and quality outcomes
  observed over the simulation runs

95
Simulating Network Structure Persistent
inequality in PhD exchange Networks Tentative
conclusions

• There are two primary factors that drive system
  outcomes in this market simulation
• The development of a hierarchical network
  exchange structure depends on a correlation
  between faculty and students, and though the
  effect appears not to be linear.
• For the most part, a quality correlation
  re-inforces quality rankings due to the main
  reinforcement mechanism sketched below

96
Simulating Network Structure Persistent
inequality in PhD exchange Networks Tentative
conclusions

• There are two primary factors that drive system
  outcomes in this market simulation
• The development of a hierarchical network
  exchange structure depends on a correlation
  between faculty and students, though the effect
  is most evident in tight markets.
• But when the correlation is too high, the
  inequality in student production starts to
  dominate. This has the result of
• (a) flooding the market with relatively
  low-quality students, that
• (b) has the effect of mirroring tight-market
  competition factors.
• Since the hiring practices in this simulation
  were tied to quality ranks instead of cardinal
  values (or values relative to self), this means
  departments are forced by retirements to dig too
  deep in the pool, resulting in a lowering of
  overall quality, which then gets magnified.

97
Simulating Network Structure Exploratory
Simulation Epidemic Potential from Low-degree
networks
Problem 3 Exploration of STD relevant networks

• In this case, we motivate the work with 4
  observations
• STD Epidemics have to travel across a connected
  network
• The connectivity structure should be robust
  since transmission is a low probability result
• Infectivity is temporally sensitive for
  bacterial STDs the window is very short, for
  virus like HIV, infectivity probability is
  highest early and late.
• This implies that the connected set needs to
  occupy a short infectivity window, which severely
  limits the number of partners most people will
  have (i.e. lifetime partner distributions are
  largely irrelevant).
• A great deal of recent attention has been placed
  on extremely heterogeneous (power law) activity
  levels, with implications suggesting that we can
  only hope to contain epidemics like HIV by
  targeting the high-activity hubs.
• But what kind of networks emerge in settings
  where there are no high activity hubs? How do
  these compare to the high-activity distribution
  networks?

98
Simulating Network Structure Exploratory
Simulation Epidemic Potential from Low-degree
networks
Here we simulate networks with a single behavior
rule limiting the number of partners to a known
distribution. -- the weakest form of an ABM
model for networks. We vary the population level
constraint on the distribution of relation
volume, keeping a maximum of 3 partners and
changing the distribution from a mode of 1 to a
mode of 3. Population size of 10,000 nodes.
99
Simulating Network Structure Exploratory
Simulation Epidemic Potential from Low-degree
networks
100
Simulating Network Structure Exploratory
Simulation Epidemic Potential from Low-degree
networks
101
Simulating Network Structure Exploratory
Simulation Epidemic Potential from Low-degree
networks
102
Simulating Network Structure Exploratory
Simulation Epidemic Potential from Low-degree
networks
103
Simulating Network Structure Exploratory
Simulation Epidemic Potential from Low-degree
networks
Very small changes in degree generate a quick
cascade to large connected components. While not
quite as rapid, STD cores follow a similar
pattern, emerging rapidly and rising steadily
with small changes in the degree
distribution. This suggests that, even in the
very short run (days or weeks, in some
populations) large connected cores can emerge
covering the majority of the interacting
population, which can sustain disease, even when
nobody is particularly active. These results
occur faster for low-degree populations than for
the scale free populations, whose hub structure
makes it difficult to form large-reaching robust
sets.
104
Simulating Network Structure Promises and
Pitfalls the good
In both modes of simulation study (explanatory
and exploratory), it is possible to change the
macro conditions directly by affecting
micro-level rules. This is clearly the
strongest factor in bridging the micro-macro
problem.
This modeling strategy moves us from this
Contextual State
Global Outcome
Macro
3
1
2
Resulting Action
Micro
Individual Response
105
Simulating Network Structure Promises and
Pitfalls the good
In both modes of simulation study (explanatory
and exploratory), it is possible to change the
macro conditions directly by affecting
micro-level rules. This is clearly the
strongest factor in bridging the micro-macro
problem.
to this
Unstable (?) Conditions that further motivate
individual action
(feedback)
Initial Conditions
Macro
Aggregates of Action
Stable Equilibrium
Actor Rules
Micro
Action
Interaction
106
Simulating Network Structure Promises and
Pitfalls the bad

• Still many questions about the empirical etiology
  of observed phenomena
• Identifying a particular mechanism that works
  doesnt mean it is the mechanism active in the
  settings of interest.
• Social life may be overdetermined in that
  sense.
• The tradeoff between realism and simplicity
  carries a cost
• Simplicity is best for identifying the
  implications of a theoretical mechanism, but
  tells us little about how the simplified
  assumption will work in other interactive
  contexts. Setting a parameter to 0 is still an
  assumption, even if left unexamined.
• Realism is best for extending external validity,
  but often at the cost of knowing exactly why
  changes in one parameter affect an outcome in a
  given way.

107
Simulating Network Structure Promises and
Pitfalls the bad
Methodologically, simulation work still largely
works on a boutique production
manner Different modelers use different
programs, initial assumptions, etc. Making
replication difficult and increasing startup
costs for everyone. This is getting better with
NetLogo or Repast, widely distributed packages
that share modules (such as work in R), but still
little institutional support of generalized
simulation practice.
108
Simulating Network Structure Promises and
Pitfalls the ugly

• Evaluating presenting results
• Often more results than can reasonably be
  summarized in a single paper (or readable book).
  
• Were often interested in the distribution of
  outcomes, rather than the central tendency, which
  makes sumation that much more challenging.
• Results are not well suited for paper-journal
  distribution
• Color, dynamics, interaction are best treated
  with web-based outlets, but these often lack
  status.
• How do we extend these results to fit or predict
  in empirical settings where our simulated
  assumptions are not (cannot be) met?

109
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