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. Add Health relational change statistics How can the global structure remain constant given massive changes at the dyad level? Introduction: Network Structure Puzzles

4. What rules can account for adolescent romantic network structure?

5. I (N=52) II-a (N=4) II-b (N=15) II-c (N=22) II-d (N=81) III (N=384) Han, S-K. Social Networks 2003:251-280. Figure 1 Introduction: Network Structure Puzzles Why are academic PhD exchange markets (hiring/placing) strongly centralized …

6. Burris, ASR 2004 … and positions within systems stable over generations? Introduction: Network Structure Puzzles

7. 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 actor’s 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. 1.Introduction 2.Micro – Macro elements in social networks a)Coleman’s “boat” b)Structural correlates of micro & macro c)Linking rules to structures 3.Simulation Network Structure a)Dynamics of adolescent friendship structure b)Adolescent romantic exogamy c)Inequality in PhD exchange networks 4.Network Diffusion & Disease Spread a)Degree mixing models b)Relational timing 5.Promises & Pitfalls a)Good: Theoretical rigor, clarity, & elegance b)Bad: How to test against observed data c)Ugly: Rule proliferation & specification Introduction: outline

9. Micro-Macro elements in social networks Coleman’s “Boat” Contextual State Individual Response Resulting Action Global Outcome Macro: Micro: 1 1) Macro  Micro: Typically contextual conditions that enable/constrain individual action.

10. Micro-Macro elements in social networks Coleman’s “Boat” Contextual State Individual Response Resulting Action Global Outcome Macro: Micro: 1 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) 2

11. Micro-Macro elements in social networks Coleman’s “Boat” Contextual State Individual Response Resulting Action Global Outcome Macro: Micro: 1 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) 3)Micro  Macro: An aggregation or interaction process that can account for the new global- level outcome. 2 3

12. Micro-Macro elements in social networks Coleman’s “Boat” Contextual State Individual Response Resulting Action Global Outcome Macro: Micro: 1 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) 3)Micro  Macro: An aggregation or interaction process that can account for the new global- level outcome. 4)The observed macro-level correlation is thus accounted for by actors capable of intent and action. 2 3 4

13. “[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 Micro-Macro elements in social networks Coleman’s “Boat” Of these 4 links, the 3 rd 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. Contextual State Individual Response Resulting Action Global Outcome 1 2 3

14. 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. Complete Network Micro-Macro elements in social networks Structural correlates of micro and macro

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 ego’s contacts Number of ties (degree) node attribute mixing 1 2 4 3 e Local + Alter interaction: information on ego and ego’s contacts with each other Number of ties (degree) node attribute mixing Clustering Reciprocity Structure Holes 1 2 4 3 e

18. Micro-Macro elements in social networks Structural correlates of micro and macro Network macro features: Features resting on (a) paths of length > 2. The key element that makes a network a system is the path: it’s 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 > 2. These two graphs have the exact same local properties, but very different global properties. A B

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.

24. 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: 1.Node volume features (number of ties) 2.Dyadic Interaction features (reciprocity, race-mixing rules) 3.Indirect interaction features (Social balance, relational exogamy rules) 4.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: “Explanation”: 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 “Exploration”: Start with a set of local rules you are confident in, then apply to a setting to learn what system-level features emerge.. Examples: Diffusion potential of low-degree networks Diffusion constraints resulting from relational timing

26. 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? Simulating Network Structure Adolescent Friendship Dynamics

27. Data I use the National Longitudinal Survey of Adolescent Health (Add Health). This is a nationally representative survey of adolescents in school (7 th 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. Simulating Network Structure Adolescent Friendship Dynamics

28. 003 (0) 012 (1) 102 021D 021U 021C (2) 111D 111U 030T 030C (3) 201 120D 120U 120C (4) 210 (5) 300 (6) A periodic table of social elements: Simulating Network Structure Adolescent Friendship Dynamics

29. 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 Dynamic Social Balance Adolescent Friendship Networks: Triad distributions A periodic table of social elements:

30. 003 (0) 012 (1) 102 021D 021U 021C (2) 111D 111U 030T 030C (3) 201 120D 120U 120C (4) 210 (5) 300 (6) Triads encapsulate local behavior rules: Simulating Network Structure Adolescent Friendship Dynamics Transitive “A friend of a friend is a friend” Intransitive “A friend of a friend is not a friend” Mixed Mixed: triad contains structures of both types

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. 1.Lots of evidence in the cross section supporting balance models, but almost always unable to account for the over-representation of mixed triad types. 2.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 can’t possibly fit the “finished” state proposed by the model.

32. 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. Simulating Network Structure Adolescent Friendship Dynamics

33. M M N* M M M A* 003 300 012 021D021U030T 120D 120U Triads observed in excess: “Ranked Cluster” Eugene Johnsen (1985, 1986) specifies a number of structures that result from various triad configurations Simulating Network Structure Adolescent Friendship Dynamics

34. 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 People’s position in the popularity distribution is fluid What models allow us to explain a stable macro-structure in the face of dynamic relations? Simulating Network Structure Adolescent Friendship Dynamics

35. 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 ego’s 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. Simulating Network Structure Adolescent Friendship Dynamics

36. 003 102 021D 021U 030C 111D 111U 030T 201 120D 120U 120C 210 300 012 021C vacuous transition Increases # transitive Decreases # intransitive Decreases # transitive Increases # intransitive Vacuous triad Intransitive triad Transitive triad (some transitions will both increase transitivity & decrease intransitivity – the effects are independent – they are colored here for net balance) Simulating Network Structure Adolescent Friendship Dynamics

37. TRIAD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0100200300 Random Walk TRIAD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 100200300 Favor Transitivity only (strong) TRIAD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0100200300 Avoid Intransitivity only (strong) Simulating Network Structure Adolescent Friendship Dynamics: Triad transition state-space simulation

38. -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Same Race SES GPA Both Smoke College Drinking Fight Reciprocity Same Sex Same Clubs Transitivity Intransitivity Same Grade Standardized Coefficients from an Exponential Random Graph Model EndogenousFocal Orgs.Dyadic Similarity/Distance. Simulating Network Structure Adolescent Friendship Dynamics: Testing model on observed data

39. 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 ego’s 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 node’s opportunity to change relations as iterations pass. Simulating Network Structure Adolescent Friendship Dynamics: Actor-oriented simulation model

40. Final Graph Transitivity R 2 = 0.82 Mean over the state space Simulating Network Structure Adolescent Friendship Dynamics: Actor-oriented simulation model

41. Structural Stability Correlation of network structure at t final with t -5% R 2 = 0.52 Mean over the state space Simulating Network Structure Adolescent Friendship Dynamics: Actor-oriented simulation model

42. 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. Simulating Network Structure Adolescent Friendship Dynamics: Actor-oriented simulation model

43. 030T 120D 120U 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. Simulating Network Structure Adolescent Friendship Dynamics: Actor-oriented simulation model

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 don’t 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. It’s theoretical simplicity is the strongest strength of the model. From a simulation methods standpoint, this is a very simple rule set: a)Constrain each actor to make the same number of partners observed in the real world b)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. Explaination problem 2: Academic Caste Systems Simulating Network Structure Academic Castes: inequality in PhD exchange Networks I (N=52) II-a (N=4) II-b (N=15) II-c (N=22) II-d (N=81) III (N=384) Han, S-K. Social Networks 2003:251-280. Figure 1 Why is this network so hierarchical and stable?

54. Merton (1942,1968) Two key features that shape the academic market: Universalistic criteria to evaluate quality “Mathew effect:” the cumulative advantage of prestige Burris (2004:239) 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) Simulating Network Structure Academic Castes: inequality in PhD exchange Networks Particularly in settings, such as science, where unversalism and meritocracy define the system “ethos”?

55. Two types of evidence are used to demonstrate non-universalistic effects: 1.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). Simulating Network Structure Academic Castes: inequality in PhD exchange Networks

56. 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 Simulating Network Structure Academic Castes: inequality in PhD exchange Networks

57. “Social Capital” = Bonacich Centrality on symmetric version of the PhD exchange Network The resulting status-based network has a strong correlation between centrality in the hiring network & quality ranking Simulating Network Structure Academic Castes: inequality in PhD exchange Networks

58. 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). Simulating Network Structure Academic Castes: inequality in PhD exchange Networks

59. 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. Simulating Network Structure Academic Castes: inequality in PhD exchange Networks

60. 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 don’t 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. Simulating Network Structure Academic Castes: inequality in PhD exchange Networks

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. Actors Departments: Collections of faculty who hire applicants & produce new students. (N=100). Initial department size is drawn from a normal distribution with mean = 25, std=12, 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. Simulating Network Structure Persistent inequality in PhD exchange Networks: Simulation Setup

63. 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 1–with 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. Simulating Network Structure Persistent inequality in PhD exchange Networks: Simulation Setup

64. 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 department’s 1 st 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. Simulating Network Structure Persistent inequality in PhD exchange Networks: Simulation Setup

65. Action: Departments The probability a job opening in any given year is a function of size: Simulating Network Structure Persistent inequality in PhD exchange Networks: Simulation Setup

66. Action: Departments Faculty size decreases through retirement Simulating Network Structure Persistent inequality in PhD exchange Networks: Simulation Setup

67. 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 don’t 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. Simulating Network Structure Persistent inequality in PhD exchange Networks: Simulation Setup

68. ParameterDescriptionSpecification 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]. X 1 = 165 ; X 2 = 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 RoundsNumber of offer rounds made. Approximates time by limiting opportunity to make alternative offers. Specify as number. 3 or 4 [2 levels] There are 3*2*3*3*2*2*3 = 648 points in the parameter space; 30 draws from each set  19,440 observations Depth of Search How deeply into the pool of candidates departments are willing to go. Specify as max depth. 10 to 30 [3 levels] Simulating Network Structure Persistent inequality in PhD exchange Networks: parameter summary

69. Simulating Network Structure Persistent inequality in PhD exchange Networks: parameter summary A look under the hood…

70. All results are presented around the competitive field: High Competition Low Competition Disagreement on Candidate Quality Depth of Search 0.30.60.9 10 20 30 Simulating Network Structure Persistent inequality in PhD exchange Networks: Non-network outcomes

71. 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 don’t 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 Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run

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

73. Student-Faculty Quality Correlation Faculty Quality Student Quality Department Quality r=0.65 r=0.49 Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run

74. Distribution of size over time Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run

75. Correlation between final size and target size Quality > Mean + 1std Quality < Mean + 1std Target Size Final Size Target Equality Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run

76. Distribution of quality over time Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run

77. Burris reports the correlation between size and prestige as 0.63 Correlation of Size and Quality over time Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run

78. Correlation of Quality 10 years prior Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run

79. Calculated at final year ( y=100) Size & Quality: Average Department Quality Simulating Network Structure Persistent inequality in PhD exchange Networks: Non-network outcomes

80. Size & Quality: Correlation of Size and Quality Calculated at final year ( y=100) Simulating Network Structure Persistent inequality in PhD exchange Networks: Non-network outcomes

81. Burris reports the correlation between size and prestige as 0.63 Correlation of Size and Quality over time Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run A single example run – taken from the middle competition cell.

82. Calculated at final year ( y=100) Quality Stability: 10 Year Correlation of Quality Simulating Network Structure Persistent inequality in PhD exchange Networks: Non-network outcomes

83. Correlation of Quality 10 years prior Simulating Network Structure Persistent inequality in PhD exchange Networks: A single example run A single example run – taken from the middle competition cell.

84. Calculated at final year ( y=100) Simulating Network Structure Persistent inequality in PhD exchange Networks: Non-network outcomes

85. 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. Simulating Network Structure Persistent inequality in PhD exchange Networks: Network outcomes

86. Disagreement on Candidate Quality Depth of Search For what follows, working within one region of the parameter space A preliminary regression over the entire space shows that hiring rates & quality correlation matter most for centralization Simulating Network Structure Persistent inequality in PhD exchange Networks: Network outcomes

87. Network Centralization by Quality Correlation & Job Openings Simulating Network Structure Persistent inequality in PhD exchange Networks: Network outcomes

88. Correlation of Centrality & Department Size Bonacich Centrality Simulating Network Structure Persistent inequality in PhD exchange Networks: Network outcomes

89. Correlation of Centrality & Department Quality Bonacich Centrality Simulating Network Structure Persistent inequality in PhD exchange Networks: Network outcomes

90. Real data from a all applicants for an open position at a large Midwestern university Simulating Network Structure Persistent inequality in PhD exchange Networks: Network outcomes OLS line Most Productive Line (first sort selects here!)

91. Simulating Network Structure Persistent inequality in PhD exchange Networks: Network outcomes

92. The very simple market model proposed here can account for many of the features we see in real PhD exchange markets: a)Stable quality rankings b)Strong Correlation between Size & Quality c)Highly Centralized Networks d)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. Simulating Network Structure Persistent inequality in PhD exchange Networks: Tentative conclusions

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

94. There are two broad features that shape these networks. 1)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 “seller’s 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 Simulating Network Structure Persistent inequality in PhD exchange Networks: Tentative conclusions

95. There are two primary factors that drive system outcomes in this market simulation: 2)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: Simulating Network Structure Persistent inequality in PhD exchange Networks: Tentative conclusions

96. There are two primary factors that drive system outcomes in this market simulation: 2)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. Simulating Network Structure Persistent inequality in PhD exchange Networks: Tentative conclusions

97. Simulating Network Structure Exploratory Simulation: Epidemic Potential from Low-degree networks In this case, we motivate the work with 4 observations: 1.STD Epidemics have to travel across a connected network 2.The connectivity structure should be robust – since transmission is a low probability result 3.Infectivity is temporally sensitive: for bacterial STDs the window is very short, for virus like HIV, infectivity probability is highest early and late. 1.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). 4.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? Problem 3: Exploration of STD relevant 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. Contextual State Individual Response Resulting Action Global Outcome Macro: Micro: 1 2 3 This modeling strategy moves us from this:

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. Initial Conditions Macro: Micro: …to this: Actor Rules Action Interaction Aggregates of Action (feedback) Stable Equilibrium Unstable (?) Conditions that further motivate individual action

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” doesn’t 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). -We’re 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?