Part III Models Part 1 Introduction amp Theory History amp Big Picture Network Relevance to Health Research Network Theory Connections amp Positions Part 2 Points amp Lines Network data ID: 932244
Download Presentation The PPT/PDF document "Social Networks & Health" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Social Networks & Health
Part III: Models
Slide2Part 1: Introduction & Theory
History & Big PictureNetwork Relevance to Health ResearchNetwork TheoryConnections & PositionsPart 2: Points & LinesNetwork dataVisualizationNetwork metricsPart 3: Network ModelsDiffusionDiseaseNetwork autocorrelationRandom Graph ModelsExperimental interventions (brief)SOAMOpen Questions
Outline
Social
Networks & Health
Slide3Network Models: Diffusion
The primary route from networks to health is via diffusion, either of a pathogen or a health-related behavior.We start by discussing biological diffusion as it’s a clear and mechanistic model that we can build from for social diffusion. The treatment here is *very brief,* aimed at giving a sense of the issues at play.
Slide4Network Diffusion & Peer Influence
BasicsClassic (disease) diffusion makes use of compartmental models. Large N and homogenous mixing allows one to express spread as generalized probability models.
Works very well for highly infectious bits in large populations…SI(S) model – actors are in only two states, susceptible or infectious. See: https://wiki.eclipse.org/Introduction_to_Compartment_Models for general introduction.SIIR(S) model – adds an “exposed” but not infectious state and recovered.
Slide5In addition to*
the dyadic probability that one actor passes something to another (pij), two factors affect flow through a network:Topologythe shape, or form, of the network- Example: one actor cannot pass information to another unless they are either directly or indirectly connectedTime - the timing of contact matters- Example: an actor cannot pass information he has not receive yet
*This is a big conditional! – lots of work on how the dyadic transmission rate may differ across populations.
Key Question: What features of a network contribute most to diffusion potential?
Network Diffusion & Peer Influence
Network diffusion features
Use simulation tools to explore the relative effects of structural connectivity features
Slide6Network Diffusion & Peer Influence
BasicsNetwork ModelsSame basic SI(R,,etc) setup, but connectivity is not assumed random, rather it is structured by the network contact pattern.If probability of transmission - pij - is small or the network is very clustered, these two can yield very different diffusion patterns.*
RealRandom*these conditions do matter. Compartmental models work surprisingly well if the network is large, dense or the bit highly infectiousness…because most networks have a bit of randomness in them. We are focusing on the elements that are unique/different for network as opposed to general diffusion.
Slide7Network Diffusion & Peer Influence
Basics
If 0 < pij < 1
Slide8Network Diffusion & Peer Influence
BasicsIf 0 < pij < 10.01
0.060.110.260.46
Slide9A network has to be connected for a bit to pass over it
If transmission is uncertain, the longer the distance the lower the likelihood of spread.
0
0.2
0.4
2
3
4
5
6
Path distance
probability
Distance
and
diffusion (p(transfer)=
p
ij
dist
Here
p
ij
of 0.6
Network Diffusion & Peer Influence
Network diffusion features
We need:
(1) reachability
(2)
distance
(3) local clustering
(4)
multiple routes
(5) star spreaders
Slide10Local clustering turns flow “in” on a potential transmission tree
Arcs: 11
Largest component: 12,Clustering: 0
Arcs: 11
Largest component: 8,
Clustering: 0.205
We need:
(1) reachability
(2)
distance
(3) local clustering
(4)
multiple routes
(5) star spreaders
Network Diffusion & Peer Influence
Network diffusion features
Slide11The more
alternate routes one has for transmission, the more likely flow should be.Operationalize alternate routes with structural cohesion
We need: (1) reachability (2) distance (3) local clustering (4) multiple routes (5) star spreaders
Network Diffusion & Peer Influence
Network diffusion features
Slide12Probability of transfer
by distance and number of non-overlapping paths, assume a constant p
ij of 0.6
0
0.2
0.4
0.6
0.8
1
1.2
2
3
4
5
6
Path distance
probability
1 path
10 paths
5 paths
2 paths
Cohesion
Redundancy
Diffusion
Network Diffusion & Peer Influence
Network diffusion features
Slide130
1
2
3
Node Connectivity
As number of node-independent paths
Structural Cohesion:
A network’s
structural cohesion
is equal to the
minimum number of actors
who, if removed from the network, would disconnect it.
Network Diffusion & Peer Influence
Network diffusion features
Slide14STD Transmission danger: sex or drugs?
Structural core more realistic than nominal core
Data from “Project 90,” of a high-risk population in Colorado Springs
Network Diffusion & Peer Influence
Network diffusion features
Slide15Much of the work on “core groups” or “at risk” populations focus on high-degree nodes. The assumption is that high-degree nodes are likely to contact lots of people.
We need:
(1) reachability (2) distance (3) local clustering (4) multiple routes (5) star spreaders
Network Diffusion & Peer Influence
Network diffusion features
Slide16Much of the work on “core groups” or “at risk” populations focus on high-degree nodes. The assumption is that high-degree nodes are likely to contact lots of people.
We need:
(1) reachability (2) distance (3) local clustering (4) multiple routes (5) star spreaders
Network Diffusion & Peer Influence
Network diffusion features
Slide17Network Diffusion & Peer Influence
Network diffusion featuresAssortative mixing:A more traditional way to think about “star” effects.
Slide18Partner
Distribution
Component
Size/Shape
Emergent Connectivity in low-degree networks
Network Diffusion & Peer Influence
A closer look at emerging connectivity
Slide19In both distributions, a giant component & reconnected core emerges as density increases,
but at very different speeds and ultimate extent.
Network Diffusion & Peer Influence
A closer look at emerging connectivity
Slide20In addition to*
the dyadic probability that one actor passes something to another (pij), two factors affect flow through a network:Topologythe shape, or form, of the network- Example: one actor cannot pass information to another unless they are either directly or indirectly connectedTime - the timing of contact matters- Example: an actor cannot pass information he has not receive yet
*This is a big conditional! – lots of work on how the dyadic transmission rate may differ across populations.
Key Question: What features of a network contribute most to diffusion potential?
Network Diffusion & Peer Influence
Relational Dynamics
Use simulation tools to explore the relative effects of structural connectivity features
Slide21Contact network: Everyone, it is a connected component
Who can “A” reach?
Network Diffusion & Peer Influence
Relational Dynamics
Discussions of network effects on STD spread often speak loosely of “the network.”
There are three relevant networks that are often conflated
:
Three relevant networks
Slide22Exposure network: here, node “A” could reach up to 8 others
Who can “A” reach?
Network Diffusion & Peer Influence
Relational Dynamics
Discussions of network effects on STD spread often speak loosely of “the network.”
There are three relevant networks that are often conflated
:
Three relevant networks
Slide23Transmission network: upper limit is 8 through the exposure links (dark blue). Transmission is path dependent: if no transmission to B, then also none to {K,L,O,J,M}
Who can “A” reach?
Exposable Link (from A’s p.o.v.)
Contact
Network Diffusion & Peer Influence
Relational Dynamics
Discussions of network effects on STD spread often speak loosely of “the network.”
There are three relevant networks that are often conflated
:
Three relevant networks
Slide24The mapping between the contact network and the exposure network is based on relational timing. In a
dynamic network, edge timing determines if something can flow down a path because things can only be passed forward in time. Definitions:Two edges are adjacent if they share a node.A path is a sequence of adjacent edges (E1, E2, …E
d). A time-ordered path is a sequence of adjacent edges where, for each pair of edges in the sequence, the start time Si is less than or equal to Ej S(E1) < E(E2)Adjacent edges are concurrent if they share a node and have start and end dates that overlap. This occurs if: S(E2) < E(E1
)
Concurrency
Network Diffusion & Peer Influence
Relational Dynamics
Slide25A
B
C
D
time
1 2 3 4 5 6 7 8 9 10
AB
BC
CE
E
CD
2 - 7
1 - 3
5 - 6
8 - 9
S(ab)
E(ab)
S(bc)
E(bc)
S(ce)
E(ce)
The mapping between the contact network and the exposure network is based on relational timing. In a
dynamic
network, edge timing determines if something can flow down a path because
things can only be passed forward in time
.
Concurrency
Network Diffusion & Peer Influence
Relational Dynamics
Slide26The constraints of time-ordered paths change our understanding of the system structure of the network. Paths make a network a
system: linking actors together through indirect connections. Relational timing changes how paths cumulate in networks.Indirect connectivity is no longer transitive:
A
B
C
D
1 - 2
3 - 4
1 - 2
Here A
can reach C, and C and reach D. But A cannot reach D (nor D A). Why? Because any infection A passes to C would have happened
after
the relation between C and D ended.
A
B
C
D
1 - 2
3 - 4
1 - 2
Network Diffusion & Peer Influence
Relational Dynamics
Slide27Edge time structures are characterized by sequence, duration and overlap.
Paths between i and j, have length and duration, but these need not be symmetric even if the constituent edges are symmetric.
Network Diffusion & Peer InfluenceRelational Dynamics
Slide28Implied Contact Network of 8 people in a ring
All relations Concurrent
Reachability = 1.0
Network Diffusion & Peer Influence
Relational Dynamics
Slide29Implied Contact Network of 8 people in a ring
Serial Monogamy (1)
1
2
3
7
6
5
8
4
Reachability = 0.71
Network Diffusion & Peer Influence
Relational Dynamics
Slide30Implied Contact Network of 8 people in a ring
Mixed Concurrent
2
2
1
1
2
2
3
3
Reachability = 0.57
Network Diffusion & Peer Influence
Relational Dynamics
Slide31Implied Contact Network of 8 people in a ring
Serial Monogamy (3)
1
2
1
1
2
1
2
2
Reachability = 0.43
Network Diffusion & Peer Influence
Relational Dynamics
Slide321
2
1
1
2
1
2
2
Timing alone can change mean reachability from 1.0 when all ties are concurrent to 0.42.
In general, ignoring time order is equivalent to assuming all relations occur simultaneously – assumes perfect concurrency across all relations.
Network Diffusion & Peer Influence
Relational Dynamics
Slide33Resulting infection trace from a simulation (Morris et al, AJPH 2010).
Observed infection paths from 10 seeds in an STD simulation, edges coded for concurrency status.
Network Diffusion & Peer Influence
Relational Dynamics
Slide34Resulting infection trace from a simulation (Morris et al, AJPH 2010).
Network Diffusion & Peer Influence
Relational Dynamics
Observed infection paths from 10 seeds in an STD simulation, edges coded for concurrency status.
Slide35Timing constrains potential diffusion paths in networks, since bits can flow through edges that have ended.
This means that:Structural paths are not equivalent to the diffusion-relevant path set.Network distances don’t build on each other. Weakly connected components overlap without diffusion reaching across sets.Small changes in edge timing can have dramatic effects on overall diffusionDiffusion potential is maximized when edges are concurrent and minimized when they are “inter-woven” to limit reachability.Combined, this means that many of our standard path-based network measures will be incorrect on dynamic graphs.
Network Diffusion & Peer Influence
Relational Dynamics
Slide36Network Diffusion & Peer Influence
Structural Transmission Dynamics: beyond disease diffusionComplex ContagionThus far we have focused on a “simple” dyadic diffusion parameter, pij, where the probability of passing/receiving the bit is purely dependent on discordant status of the dyad, sometimes called the “independent cascade model” (), which suggests a monotonic relation between the number of times you are exposed through peers. High exposure could be due to repeated interaction with one person or weak interaction with many, effectively equating:
Alternative models exist. Under “complex contagion” for example, the likelihood that I accept the bit that flows through the network depends on the proportion of my peers that have the bit.
Slide37Network Diffusion & Peer Influence
Structural Transmission Dynamics: beyond disease diffusion11
23
Complex Contagion
Assume adoption requires
k
neighbors having adopted, then transmission can only occur within dense clusters:
Slide38Network Diffusion & Peer Influence
Structural Transmission Dynamics: beyond disease diffusionComplex ContagionAssume adoption requires k neighbors having adopted, then transmission can only occur within dense clusters:For this network under weak complex diffusion (k=2), the maximum risk size is reaches 98%.
One of the Prosper schools:Start
Slide39Network Diffusion & Peer Influence
Structural Transmission Dynamics: beyond disease diffusionComplex ContagionCan lead to widely varying sizes of potential diffusion cascades. Here’s the distribution across all PROPSPER schools:Distribution is largely bimodal (even with a connected pair start)
Slide40Network Diffusion & Peer Influence
Structural Transmission Dynamics: beyond disease diffusionComplex ContagionCan lead to widely varying sizes of potential diffusion cascades. Here’s the distribution across all PROPSPER schools:The governing factors are (a) curved effect of local redundancy and (b) structural cohesion
Network Average Proportion Reached k=2 complex contagionMean Cascade SizeCoh=0.3
Coh
=1.2
Coh
=2.2
Coh
=3.2
Coh
=4.1
Slide41Background
: Long standing research interest in how our relations shape our attitudes and behaviors. Most often assumed mechanism is that people (through conversation or similar) change each others beliefs/opinions, which changes behavior.This implies that position in a communication network should be related to attitudes.Alternatives:Modeling behavior: ego copies behavior of alter to gain respect, esteem, etc.Distinction: Ego tries to be different from (some) alter to gain respect, esteem, etc.Access: Ego wants to do Y, but can only do so because alter provides access (say, being old enough to buy cigarettes).
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide42Background
:Early work was ego-centric – people informed on their peersSeems to have inflated PI effects by ~50% or so…either through projection of ego behavior onto peers or selective interaction (what alters do with ego may be different than what alter does all the time).Then to cross sectional associations based on alter self-reportsBetter, but still likely conflates selection with influenceNext to dynamic models:Ego Behavior(t) ~ f(ego behavior(t-1) + alter behavior (t-1) + controlsMuch better; still debate on (a) correct estimation functions, (b) unobserved selection features that confound causal inference.Development of Actor-oriented models (SIENA)
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide43Background
:Finally: Experimental manipulation of peer exposure“Gold standard” for isolation of peer effectsLikely strongly underestimates effects (as measure intent to treat, not take-up of treatment, since people may not care about relations that can be manipulated).b(Peer(y)): Ego Inform < Alter Inform < Cross Sectional < Dynamic < Experimental. Still often find peer effects, but my sense is that we’ve (strongly) over-corrected at this point.
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide44Freidkin’s
Structural Theory of Social Influence :
Two-part model:Beliefs are a function of two sources: a) Individual characteristicsGender, Age, Race, Education, Etc. Standard sociology b) Interpersonal influencesActors negotiate with others
Network Diffusion & Peer Influence
Peer Influence Dynamics
Slide45(1)
(2)
Y(1) = an N x M matrix of initial opinions on M issues for N actorsX = an N x K matrix of K exogenous variable that affect YB
= a K
x
M matrix of coefficients relating X to Y
a
= a weight of the strength of endogenous interpersonal influences
W
= an N x N matrix of interpersonal influences
Network Diffusion & Peer Influence
Peer Influence Dynamics
Slide46The key to the peer influence part of the model is
W, a matrix of interpersonal weights. W is a function of the communication structure of the network, and is usually a transformation of the adjacency matrix. In general: Various specifications of the model change the value of wii, the extent to which one weighs their own current opinion and the relative weight of alters.
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide47Formal Properties of the model
The model is directly related to spatial econometric models:If we allow the model to run over t and W remains constant:
Where the two coefficients (a and b) are estimated directly (See Doreian, 1982, SMR).This is the linear network auto correlation model, best bet with cross-sectional data (and randomization trick to estimate se)
Network Diffusion & Peer Influence
Peer Influence Dynamics
Slide48Extended example: building intuition
Consider a network with three cohesive groups, and an initially random distribution of opinions:
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide49Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations
Slide50Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations
Slide51Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations
Slide52Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations
Slide53Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations
Slide54Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations
Slide55Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations
Slide56Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations
Slide57Extended example: building intuition
Consider a network with three cohesive groups, and an initially random distribution of opinions:Now weight in-group ties higher than between group ties
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide58Simulated Peer Influence:
75 actors, 2 initially random opinions, Alpha = .8, 7 iterations, in-group tie: 2
Slide59Slide60Slide61Slide62Slide63Slide64Further extensions of the model might:
Time dependent a: people likely value other’s opinions more early than later in a decision contextInteract a with XB: people’s self weights are a function of their behaviors & attributesMake W dependent on structure of the network (weight transitive ties greater than intransitive ties, for example)Time dependent W: The network of contacts does not remain constant, but is dynamic, meaning that influence likely moves unevenly through the networkAnd others likely abound….
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide65There are two common ways to test for peer associations through networks.
The first estimates the parameters (a and b) of the network autocorrelation model directly, the second transforms the network into a dyadic model, predicting similarity among actors.Peer influence model:
Network Diffusion & Peer InfluencePeer Influence Dynamics
This is the linear network autocorrelation model, and as specified, the model makes strong assumptions about equilibrium opinion and static relations.
Some variants on this also expand e to include alternative autocorrelation in the error structure.
Slide66There are two common ways to test for peer associations through networks.
The first estimates the parameters (a and b) of the network autocorrelation model directly, the second transforms the network into a dyadic model, predicting similarity among actors.Peer influence model:
Network Diffusion & Peer InfluencePeer Influence Dynamics
Note that since WY
is
a simple
vector
-- weighted mean of friends Y -- which
can be
constructed and added
to your
GLM model
. That is, multiple Y by a W matrix, and run the regression with WY as a new variable, and the regression coefficient is an estimate of
a
.
This
is what
Doriean
calls the QAD estimate of peer influence. It’s wrong, a will be biased, but it’s often not terribly wrong if most obvious selection factors are built int0 X
Slide67An obvious problem
with this specification is that cases are, by definition, not independent, hence “network autocorrelation” terminology. In practice, the QAD approach (perhaps combined with a GLS estimator) results in empirical estimates that are “virtually indistinguishable” from MLE (Doreian et al, 1984)The proper way to estimate the peer equation is to use maximum likelihood estimates, and Doreian gives the formulas for this in his paper, and Carter Butts has implemented in in R with the LNAM procedure. An alternative is to use non-parametric approaches, such as the Quadratic Assignment Procedure, to estimate the effects.
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide68Peer influence through Dyad Models
Another way to get at peer influence is not through the level of Y, but by assessing the similarity of connected peers. Recall the simulated example: peer influence is reflected in how close points are to each other.
Network Diffusion & Peer InfluencePeer Influence Dynamics
Slide69Peer influence through Dyad Models
The model is now expressed at the dyad level as:Where Y is a matrix of similarities, A is an adjacency matrix, and Xk is a matrix of similarities on
attributesAdvantages include ease of specifying relation-specific similarity functions. You can add different features of a relation by adjusting/adding “Aij” variables.Disadvantage is that now in addition to network autocorrelation, you have repeated cases (on both sides).But these can be dealt with using non-parametric modeling & testing techniques (QAP, for example). (which we will go over this afternoon)
Network Diffusion & Peer Influence
Peer Influence Dynamics
Slide70Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & Controversies
Slide71Used the friend/relative tracking data from a larger heart-health study to identify network contacts, including friends.
Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & Controversies
Slide72The network shows significant evidence of weight-homophily
Used the friend/relative tracking data from a larger heart-health study to identify network contacts, including friends.
Network Diffusion & Peer InfluencePeer Influence & Health: Current Lit & Controversies
Slide73Effects of peer obesity on ego, by peer type
Edge-wise regressions of the form:
Ego is repeated for all alters; models include random effects on ego idUsed the friend/relative tracking data from a larger heart-health study to identify network contacts, including friends.
Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & Controversies
Slide74This modeling strategy pools observations on edges and estimates a global effect net of change in ego/alter as a control. Here color is a single ego, number is wave (only 2 egos and 3 waves represented).
Effects of peer obesity on ego, by peer type
1Ego-CurrentAlter Current1
1
2
2
2
3
3
3
1
1
1
2
2
2
3
3
3
Peer Effect
Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & Controversies
Slide75Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & ControversiesCritiques of C&FThe C&F studies – of obesity, but also other work on the FHS data – turn on the validity of the causal association. All turn on some issue of model miss-specification, typically:Can’t truly distinguish a network effect from other sources of common influence“Selection” (“homophily”) or “Common influence” (“Shared environment”)
The most strident work in this area (Salizi & Thomas)Statistical errorsMisinterpretation of confidence intervalsPoorly specified/estimated modelsC&H do a nice job of laying out their responses here: http://jhfowler.ucsd.edu/examining_dynamic_social_networks.pdf and here:http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2597062/
Slide76Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & ControversiesShalizi & Thomas: PI is *generally* confounded
So long as there is an unobserved X that causes both ties and behavior, the effect of peers is unidentified.
Slide77Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & ControversiesShalizi & Thomas: PI is *generally* confoundedOnly route out is to make X fully informed (or informing) by an observable Z….but realistically there are few things that (a) cause behavior exclusively without any selection pressure (a) or cause ties exclusively without any influence pressure (b) (though note b is what experimental assignments do)
(X causes Z, not Y directly)(X causes A, not Y directly)
Slide78Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & ControversiesShalizi & Thomas: PI is *generally* confoundedShould be noted that this is true for *any* effect – there’s always the potential that an unobserved latent variable is creating a spurious effect; This sort of work argues that the only solution is to use experimental (or, sometimes, propensity score style models)…but that’s simply not always feasible practically.We need to beware of making the best the enemy of the good enough…lest we make no progress at all…
Slide79How to correct this problem?
Essentially, this is an omitted variable problem, and my “solution” has been to identify as many potentially relevant alternative variables as I can find.The strongest possible correction is to use fixed-effects* models that control for all non-varying individual covariates. These have their own problems…Dual model for influence & selection. Two-stage model “Heckman” and IV sorts of modelsDynamic SAOM modelsExperiments
Network Diffusion & Peer InfluencePeer Influence & Health: Current Lit & Controversies*“Adding fixed effects to dynamic panel models with many subjects and few repeat observations creates severe bias towards zero coefficients. This has been demonstrated both analytically (Nickell 1981) and through simulations (Nerlove 1971) for OLS and other regression models and has been well-known by social scientists, including economists, for a very long time. In fact, CCF even note that they do not add fixed effects to their logit regression model for this reason, but they strangely assert that fixed effects are necessary in the OLS model.” Estimating Peer Effects on Health in Social Networks : A Response to Cohen-Cole and Fletcher; Trogdon, Nonnemaker,
Pais
J.H
. Fowler
, PhD and
N.A. Christakis
, MD,
PhD
Slide80Causal status of such similarity is hard to know,
Identification strategies are stringentMy sense is we’re over-correcting on this front; let’s figure out what’s there first.Selection
Network Diffusion & Peer InfluencePeer Influence & Health: Current Lit & Controversies
Y
X
1
X2
Weak instruments bias us toward null effects
Y
X
1
X2
I
Slide81Possible solutions:
Theory: Given what we know about how friendships form, is it reasonable to assume a bi-directional cause? That is, work through the meeting, socializing, etc. process and ask whether it makes sense that Y is a cause of W. This will not convince a skeptical reader, but you should do it anyway.Models: Time Order. Necessary but not sufficient. We are on somewhat firmer ground if W precedes
Y in time, but the Shalizi & Thomas problem of an as-yet-earlier joint confounder is still there.Simultaneous Models. Model both the friendship pattern and the outcome of interest simultaneously. Best bet for direct estimationSensitivity Analysis: I think the most reasonable solution…take error potential seriously, attempt to evaluate how big a problem it really is.
Network Diffusion & Peer Influence
Peer Influence & Health: Current Lit & Controversies
Slide82Possible solutions:
Sensitivity Analysis: I think the most reasonable solution…take error potential seriously, attempt to evaluate how big a problem it really is.
Network Diffusion & Peer InfluencePeer Influence & Health: Current Lit & Controversies
Slide83Possible solutions:
Sensitivity Analysis: I think the most reasonable solution…take error potential seriously, attempt to evaluate how big a problem it really is.
Network Diffusion & Peer InfluencePeer Influence & Health: Current Lit & Controversies
Sociological Methods & Research 2000
Slide84Statistical
Models for NetworksSimple Random GraphsLong history of model development for networks. Here we are just hinting at what is here and why useful.We often want a way to build models that explain the topology in a network. The foundation of these models are Random Graphs.
Slide85Network inference differs from many of the inference problems we are used to.
We have the population (by assumption)Want to know what the process underlying network formation might beRandom graphs thus create one (reasonable?) comparison group.Question are “Would we see the observed graph if the process was random?”“Is the observed structure random conditional on some feature?”Common association tests (correlations, regressions, etc.) assume case independence; randomization provides a non-parametric way to evaluate statistical significance, since the standard formulas will not work.Difficult to sample: There are few well-established ways to partially sample a network; though random graph tools are making that possible.Simulate social processes. We often want to test measures, models or methods on a large collection of networks with known properties, but have no access to real data. Statistical Models for NetworksInference problems
Slide86That is we can think of this as either a graph of
n nodes and assume all edges have equal probability of being present (G(N,p)) or we can imagine a (set of) graph(s) chosen at random from the set of all graphs with n nodes and m edges (G(N,M)).Number of unique undirected graph patterns by number of nodesBut, enumeration is usually impossible…so we use construction rules that ensure even probability of all graphs in the space.* Note a subtle difference here: the G(N,P) model will have random variability in number of edges due to random chance…ignorable in limit of large networks.Statistical Models for NetworksSimple random graphsNote a core difficulty: We want to compare our observed network to the class of all graphs (with similar properties), but we have no sampling frame of graphs.
Slide87In a
Erdos random graph - each dyad has the same probability of being tied –so algorithm is a simple coin-flip on each dyad.
degree will be Poisson distributed, and the nodes with high degree are likely to be at the intuitive center.
Statistical
Models for Networks
Simple Random Graphs
Slide88Simple random graph with 1000 nodes and average degree=2.4
p=0.0024.
Statistical Models for NetworksSimple Random Graphs
Slide89Network connectivity changes rapidly as a function of network volume.
In a Erdos-reyni random network, when the average degree is <1, the network is always disconnected. When it is >2, there is a “giant component” that takes up most of the network.Note that this is dependent on mean
degree, not density, so applies to networks of any size.Average Degree
Statistical
Models for Networks
Simple Random Graphs
Slide90Simple random is a very poor model for real life, so not really a fair null. Imagine you know the mixing by category in a network, you can use that to generate a network that has correct probability by mixing category:
We can condition on more features – degree distribution, dyad distribution, mixing…These can take us a long ways towards getting a reasonable null.Some are easy: Have analytic solution to some features on some conditionals (like the “configuration model” used for building a null in community detection)Good algorithms exist for fixing both in & out degreegenerate a set of half-edges for each node’s degree, randomly sort, put back togetherOften a tradeoff between *exact* uniform random & speed/tractabiltiy
Statistical Models for NetworksLess Random Graphs
Slide91Simple random is a very poor model for real life, so not really a fair null. Imagine you know the mixing by category in a network, you can use that to generate a network that has correct probability by mixing category:
mixprob wht blk oth wht .0096 .0016 .0065 blk .0013 .0085 .0045 oth .0054 .0045 .0067
…so generate a random graph with similar mixing probabilityObserved
Statistical
Models for Networks
Less Random Graphs
Slide92Simple random is a very poor model for real life, so not really a fair null. Imagine you know the mixing by category in a network, you can use that to generate a network that has correct probability by mixing category:
mixprob wht blk oth wht .0096 .0016 .0065 blk .0013 .0085 .0045 oth .0054 .0045 .0067…so generate a random graph with similar mixing probability
Random
Statistical
Models for Networks
Less Random Graphs
Slide93Simple random is a very poor model for real life, so not really a fair null. Imagine you know the mixing by category in a network, you can use that to generate a network that has correct probability by mixing category:
mixprob wht blk oth wht .0096 .0016 .0065 blk .0013 .0085 .0045 oth .0054 .0045 .0067…so generate a random graph with similar mixing probability
Degree distributions don’t match
Statistical
Models for Networks
Less Random Graphs
Slide940
20%
40%
60%
80%
100%
Percent Contacted
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Remove
Degree = 4
Degree = 3
Degree = 2
Random Reachability:
By number of close friends
Statistical
Models for Networks
Less Random Graphs
Slide95Random graph
Observed
Statistical
Models for Networks
Less Random Graphs
Slide96Comparing multiple networks: QAP
The substantive question is how one set of relations (or dyadic attributes) relates to another. For example: Do marriage ties correlate with business ties in the Medici family network? Are friendship relations correlated with joint membership in a club?
Statistical Models for NetworksRandomization – Net as independent variable
Slide97Assessing the correlation is straight forward, as we simply correlate each corresponding cell of the two matrices:
Marriage 1 ACCIAIUOL 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 ALBIZZI 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 3 BARBADORI 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 4 BISCHERI 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 5 CASTELLAN 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 6 GINORI 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 GUADAGNI 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 8 LAMBERTES 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 9 MEDICI 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 10 PAZZI 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 11 PERUZZI 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 12 PUCCI 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 RIDOLFI 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 14 SALVIATI 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
15 STROZZI 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 16 TORNABUON 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0Business 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 4 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 5 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 6 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 7 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 8 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0
9 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 1
10 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
11 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
Dyads:
1 2 0 0
1 3 0 0
1 4 0 0
1 5 0 0
1 6 0 0
1 7 0 0
1 8 0 0
1 9 1 01 10 0 01 11 0 01 12 0 01 13 0 01 14 0 01 15 0 01 16 0 02 1 0 0
2 3 0 0
2 4 0 0
2 5 0 0
2 6 1 0
2 7 1 0
2 8 0 0
2 9 1 0
2 10 0 0
2 11 0 0
2 12 0 0
2 13 0 0
2 14 0 0
2 15 0 0
2 16 0 0
Correlation:
1 0.3718679
0.3718679 1
Statistical
Models for Networks
Randomization – Net as independent variable
Slide98But is the observed value statistically significant?
Can’t use standard inference, since the assumptions are violated. Instead, we use a permutation approach. Essentially, we are asking whether the observed correlation is large (small) compared to that which we would get if the assignment of variables to nodes were random, but the interdependencies within variables were maintained.Do this by randomly sorting the rows and columns of the matrix, then re-estimating the correlation.
Statistical Models for NetworksRandomization – Net as independent variable
Slide99Procedure:
Calculate the observed correlationfor K iterations do: a) randomly sort one of the matrices b) recalculate the correlation c) store the outcome3. compare the observed correlation to the distribution of correlations created by the random permutations.
Statistical Models for NetworksRandomization – Net as independent variable
Slide100Statistical
Models for NetworksRandomization – Net as independent variable
Slide101Statistical
Models for NetworksModeling the networkOftentimes our goal is to predict the network itself, or a process on the network. We can use QAP/randomization tricks like we describe above; but those are often difficult to generalize across many dimensions. Instead, we can build a statistical model of the network.
Goal is to build a probability model for edges in the
network (
Y
ij
) as
a function of features of
i
(
X
), features of
j
(
Z
) and dyad-specific features (
Q
).
For now, think of this as a simple logit model:Observed Network
Slide102Intercept only model:
Goal is to build a probability model for edges in the network (Yij) as a function of features of i (X), features of j(Z) and dyad-specific features (Q).
ParameterEstimateIntercept
-1.13
All cells equal to density of the network
Statistical
Models for Networks
Modeling the network
Observed density is 0.24
Slide103Add Sender effects
ParameterEstimateIntercept-2.51Sender Degree0.57
Sum of the rows will equal sender degree,
p
ij
constant across columns
Goal is to build a probability model for edges in the
network (
Y
ij
) as
a function of features of
i
(
X
), features of
j
(
Z) and dyad-specific features (Q).
Statistical
Models for Networks
Modeling the network
1
1
2
3
5
1
1
2
2
4
Obs
Slide104Parameter
EstimateIntercept-2.57Target Degree0.59
Sum of the columns will equal target in-degree,
p
ij
constant across rows
or Target effects
Goal is to build a probability model for edges in the
network (
Y
ij
) as
a function of features of
i
(
X
), features of
j
(Z) and dyad-specific features (Q).
Statistical
Models for Networks
Modeling the network
1
1
2
4
4
1
1
2
2
4
Obs
:
Slide105Or both sender & target effects
ParameterEstimateIntercept-4.15Sender Degree0.66
Target Degree
0.69
Cells with same marginal sums will be the same
or both marginal effects
Goal is to build a probability model for edges in the
network (
Y
ij
) as
a function of features of
i
(
X
), features of
j
(
Z) and dyad-specific features (Q).
Statistical
Models for Networks
Modeling the network
1
1
2
4
4
1
1
2
2
4
Obs
:
1
1
2
3
5
1
1
2
2
4
Obs
Slide106Full model has dyad-specific covariates
ParameterEstimateIntercept-9.12Sender Degree0.49
Target Degree
0.87
Dyad
Similarity
1.86
Dyadic similarity sharpens fit within volume-specific dyads and allows us to capture
either mixing features (same race, same sex, etc.) or structural features (reciprocity, shared friends, etc.).
Add dyad-specific features
Goal is to build a probability model for edges in the
network (
Y
ij
) as
a function of features of
i
(
X), features of j(Z) and dyad-specific features (Q).
Statistical
Models for Networks
Modeling the network
Slide107Add dyad-specific features
Goal is to build a probability model for edges in the network (Yij) as a function of features of i (X), features of j(Z) and dyad-specific features (Q). Statistical
Models for NetworksModeling the networkThis simple model does OK… - Bold cells tend to be high-probability
Slide108Add dyad-specific features
Goal is to build a probability model for edges in the network (Yij) as a function of features of i (X), features of j(Z) and dyad-specific features (Q). Statistical
Models for NetworksModeling the networkThis simple model does OK… - Bold cells tend to be high-probability - But some clear misses
Slide109Add dyad-specific features
Goal is to build a probability model for edges in the network (Yij) as a function of features of i (X), features of j(Z) and dyad-specific features (Q). Statistical
Models for NetworksModeling the networkThis simple model does OK… - Bold cells tend to be high-probability - But some clear misses - and false positives
Slide110Add dyad-specific features
Goal is to build a probability model for edges in the network (Yij) as a function of features of i (X), features of j(Z) and dyad-specific features (Q). Statistical
Models for NetworksModeling the networkThis simple model does OK… - Bold cells tend to be high-probability - But some clear misses - and false positivesWe miss because (a) poor model specification or (b) poor model estimation.Most of the work in the last few years has been on fixing these problems.
Slide111A key twist on this simple model above is that while we work with dyads (i.e. our observations in the dataset will be
ij dyads), the model is of the entire network – including all the dependencies.
Substantively, the approach is to ask whether the graph in question is an element of the class of all random graphs with the given known elements. For example, all graphs with 5 nodes and 3 edges, or, put probabilistically, the probability of observing the current graph given the conditions.
Statistical
Models for Networks
Modeling the network: ERGM
Slide112A key twist on this simple model above is that while we work with dyads (i.e. our observations in the dataset will be
ij dyads), the model is of the entire network – including all the dependencies.
Substantively, the approach is to ask whether the graph in question is an element of the class of all random graphs with the given known elements. For example, all graphs with 5 nodes and 3 edges, or, put probabilistically, the probability of observing the current graph given the conditions.
Statistical
Models for Networks
Modeling the network: ERGM
Slide113The “p1” model of Holland and
Leinhardt is the classic foundation – the basic idea is that you can generate a statistical model of the network by predicting the counts of types of ties (asym, null, sym). They formulate a log-linear model for these counts; but the model is equivalent to a logit model on the dyads:
Note the subscripts! This implies a
distinct parameter
for every node
i
and
j
in the model, plus one for reciprocity.
Statistical
Models for Networks
Modeling the network: ERGM
)
Slide114Statistical
Models for Networks
Modeling the network: ERGM
Slide115Results
on
PROSPER datasets
Statistical
Models for Networks
Modeling the network: ERGM
Slide116Once you know the basic model format, you can imagine other specifications:
Key is to ensure that the specification doesn’t imply a linear dependency of terms.
Model fit is hard to
judge, and for all but the simplest specifications, the
se’s
are “approximate”
)
Logit
) – differential reciprocity
Logit
)
+ (node attributes)
Statistical
Models for Networks
Modeling the network: ERGM
Slide117Where:
q
is a vector of parameters (like regression coefficients)
z
is a vector of network statistics, conditioning the graph
k
is a normalizing constant, to ensure the probabilities sum to 1.
Statistical
Models for Networks
Modeling the network: ERGM
Analytic & estimation solutions came with some careful thinking on the underlying structure on this model. Start with a re-expression of a general graph model:
So here, we’re just asking the probability of observing our network, given some network statistics.
Slide118We
need a way to express the probability of the graph that doesn’t depend on that constant. It turns out we can do this by conditioning on a ‘complement’ graph. First some terms:
= Sociomatrix with ij element forced to be 1
=
Sociomatrix
with
ij
element forced to be
0
=
Sociomatrix
array without
ij
element
After some algebra:
Which ends up being a logit model on z, where z are “change statistics” or counts of features on the full graph when that statistic for the
ij
dyad is differenced.
Statistical
Models for Networks
Modeling the network: ERGM
Slide119Statistical
Models for NetworksModeling the network: ERGMSteps in estimating an ERGMSpecify the modelFit the modelExamine MCMC chains for convergence & suchExamine Goodness of fitIf poor, return to 1Else, publish your paper.
Slide120Question is the likelihood of a network given an observed set of network mixing statistics.
The set of such statistics (“terms”) is large…and growing.
Intuitively, these capture a social process you think is driving network formation.
Statistical
Models for Networks
ERGM: Model Specification
Slide121Theory
Small-WorldsPreferential AttachmentHomophilySocial BalanceBirds of a feather…ColloquialismStructural Signature
Model TermA friend of a friend...A friend of an enemy…Don’t I know your… orKevin Bacon game…Rich get richer..First mover advantage
NodeMatch
()
Balance, Transitivity,
GWESP
Clustering & k-paths
In-degree, k-stars
Statistical
Models for Networks
ERGM: Model Specification
Slide122Model Sensitivity
ERGM models are sensitive to model specification, and work best if you have a good intuition about how the interdependencies in a network operate – problem is few of us have that that intuition!Model Degeneracy: Intuitively, it happens when the network sample space implied by the model does not contain any instances of your model.Example: Simple model of edges & triangles. Intuitively, we’d expect from balance a positive coefficient on triangles. Statistical
Models for NetworksERGM: Model Specification
Slide123Statistical
Models for NetworksERGM: Model SpecificationTriangles
Intuition from regression: b(triangle) is positiveP(x=x)
Slide124Statistical
Models for NetworksERGM: Model SpecificationBut the generative model really says “more closed triads is good”
So if this is good…..this is better!
Slide125Statistical
Models for NetworksERGM: Model SpecificationTriangles
..so what you really want is:P(x=x)Or that there are marginal decreasing returns to each *additional* closed triadGWESP
Slide126Introduction to Random & Stochastic
Latent Space Models
Slide127Introduction to Random & Stochastic
Latent Space ModelsSimple latent distance model:Given a distribution of points in the space defined by z, probability of a tie decreases with their distance in the latent space.Z can be as many dimensions as you want; typically we try to fit the minimum number of dimensions that provide reasonable fit to the data.
Slide128Introduction to Random & Stochastic
Latent Space Models2d solution for Sampson monistary data
Slide129Z = a dimension in some unknown space that, once accounted for makes ties independent.
In addition, we can now embed z within a group structure, which adds probability of ingroup ties.
Introduction to Random & Stochastic
Latent Space Models: with groups
Slide130Introduction to Random & Stochastic
Latent Space Models
Slide131Example with the Prosper
data, with three groups
Introduction to Random & StochasticLatent Space Models
Slide132Introduction to Random & Stochastic
GeneralizationsAMEN: Additive & multiplicative effects models (Hoff & Volfovsky)Basic social relations modelDyad effects
Row effectsColumn effectsRowerrorColerrordyaderror
More general frame:
Latent
multiplicative
covariance
Model is very general; can deal with y on any scale (binary to real values), fits latent space & observed covariates.
Computationally intensive…
Slide133Introduction to Random & Stochastic
Generalizations
Slide134Network Experiments & Interventions
Exogenous Behavior (Y)4 types of interventions:IndividualsFinding opinion leaders or flow blocking nodes that play a key role in the network process. usually some centrality score, or an adaptive algorithm. Here highlighted “keyplayer” nodes.SegmentationInductionAlteration
Slide135Network Experiments & Interventions
Exogenous Behavior (Y)4 types of interventions:IndividualsSegmentationUse communities to break the groups into parts, treat some use others as controls.InductionAlteration
Slide136Network Experiments & Interventions
Exogenous Behavior (Y)4 types of interventions:IndividualsSegmentationInductionEnhance relations & communicationAlteration
Slide137Network Experiments & Interventions
Exogenous Behavior (Y)4 types of interventions:IndividualsSegmentationInductionAlterationPrograms that seek to change the shape of the network, add/remove ties or nodes
Slide138Introduction to Random & Stochastic
Stochastic Actor Oriented Models.From a modeling standpoint; the most comprehensive approach to solving the behavior-network endogeneity problem are Stochastic Actor-Oriented Models (SOAM) or “Siena” models.Key is to simultaneously model changes in the network structure and actor behavior(s) over time. Do this by positing two utility functions: one for ties, one for behavior.
Slide139Introduction to Random & Stochastic
Stochastic Actor Oriented Models.
f
i
is the
utility
for actor
i
, given the state of the current parameter estimates
β
, the current state of the network (
x
)
Ski(X) are network structure effect
Z are behaviors
Network Change Utility
Slide140Introduction to Random & Stochastic
Stochastic Actor Oriented Models.
f
i
is the
utility
for actor
i
of behavior z,
given the state of the current parameter estimates
β
, the current state of the network (x
) and behavior (z).
Behavior Change Utility
Slide141Introduction to Random & Stochastic
Stochastic Actor Oriented Models.SIENA EstimationIntuitively these two equations are estimated via direct parameter search embedded within an agent-based model, where we are trying to find parameters to fit the (averaged) observed changes in behavior and network structure simultaneously. This allows one to estimate simultaneously the selection and the influence parameters.
Slide142Markov Chain Algorithm
Initialize at first observationActors draw:Waiting time for networkWaiting time for behaviorDetermined by rate functionsShortest waiting time/type identifiedTime up?
Actor changes tie|behaviorDetermined by objective functionsUpdate time(next micro step)“STOP”
Yes
No
For each step in a
Markov chain:
Max
i
terations?
No
Yes
If Phase 2,
update
parameters
Store ending network
& behavior
Slide credit:
Dr. David R.
Schaefer
, Social Networks & Health 2018
Slide143Introduction to Random & Stochastic
Stochastic Actor Oriented Models.Models work well if there is some change between waves, but not too muchThe network is moderately sized (O)1000sBehavior is ordinal or binaryThe estimation problem is difficult; and the estimation is finicky.
Slide144Open Problems
Methods: Large-scale dynamic DiffusionMissing dataBounding causal questionsTheory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms
Data:Return to community studiesElectronic TracesEMR
Slide145Open Problems
Methods: Large-scale dynamic DiffusionMissing dataBounding Causal questionsTheory:Roles & Multiplex Network dynamics
Network “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMRModels that allow for real-time feedback & data updates, population dynamics, etc. It's doable now in a compartmental framework but largely ad hoc
Slide146Open Problems
Methods: Large-scale dynamic DiffusionMissing dataBounding Causal questionsTheory:Roles & Multiplex Network dynamics
Network “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMR
Slide147Open Problems
Methods: Large-scale dynamic Diffusion
Missing dataBounding Causal questionsTheory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMRPeer
Behavior
Substantively, peers and behavior co-constitute each other in a naturally endogenous and over-determined way. Notions of
partialing
out the causal effect of peers on behavior net of behavior on peers miss-asks the question. We need some radical new thinking on this.
Is not equal to
Peer
Behavior
+
Peer
Behavior
Slide148Open Problems
Parent
Parent
Child
Child
Child
Positional models are fundamentally under-developed; yet hold the greatest promise of realizing the potential of relational models to provide deep insights into social organization and behavior.
Methods:
Large-scale dynamic Diffusion
Missing data
Bounding Causal questions
Theory:
Roles & Multiplex Network dynamics
Network “life history”: relational evolution
Health Mechanisms:
Data:
Return to community studies
Electronic Traces
EMR
Slide149Open Problems
Example: Social Exchange in developing contextsMethods: Large-scale dynamic DiffusionMissing data
Bounding Causal questionsTheory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMR
Slide150Open Problems
Example: Social Exchange in developing contextsRequired: probably need to include content of relation in the theory (at least valence, likely more)Methods: Large-scale dynamic DiffusionMissing data
Bounding Causal questionsTheory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMR
Slide151Open Problems
Do we know how relations should change over time? A 4 year old should not relate the same way to parents as a 14 year old. But what about old friends? Neighbors? Etc.? What is the life-history of a relation?Methods: Large-scale dynamic DiffusionMissing data
Bounding Causal questionsTheory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMR
Slide152Open Problems
The real controversy over the Framingham studies turned on social mechanism: how do relations get “inside”?Current models are largely passive transmission or stress-response; both seem much too simple.
Methods: Large-scale dynamic DiffusionMissing dataBounding Causal questionsTheory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMR
Slide153Open Problems
Networks exist within an institutional context; only way to know that is to return to communitiesMethods:
Large-scale dynamic DiffusionMissing dataBounding Causal questionsTheory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMR
Slide154Open Problems
Radio collar studies of people might be a bit much (though talk to Kitts!), but we leave clear digital traces…can we use that smartly?Methods: Large-scale dynamic Diffusion
Missing dataBounding Causal questionsTheory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMR
Slide155Open Problems
Methods: Large-scale dynamic DiffusionMissing dataBounding Causal questions
Theory:Roles & Multiplex Network dynamicsNetwork “life history”: relational evolutionHealth Mechanisms:Data:Return to community studiesElectronic TracesEMR