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Thanks for all the recommendations.  I had come across many of them
previously but also have a whole new batch which I hadn't seen/read
previously so many thanks.

One thing that I've noticed about much of the research in this area is its
focused on contagion as measured through "adoption" (discrete values of
"Adopter" & "Non-Adopter").  Once adoption has occurred, what are the best
measures for determining ongoing influence/contagion among those connected
when you have behavior data that is continuous?   I have a stack of papers
to read here that were recommended so apologize if any of them address
and/or speak directly to the question of measuring ongoing contagion after
adoption.  Wondering if its best to convert the continuous behavior data
into discrete values (Decile/Quartile/etc/) and then apply some of the
measures for adoption outlined in the provided articles to see if those in
higher deciles/quartiles "influence" those connected to them to follow them
"up".

Thanks,
Steve

2011/2/28 Dugundji, E.R. <[log in to unmask]>

> ***** To join INSNA, visit http://www.insna.org *****
>
> Here's my two cents on the excellent points raised by Tom, Christian and
> Sinan:
>
> Manski highlights three hypotheses in his classic 1995 monograph “to
> explain the common observation that individuals belonging to the same group
> tend to behave similarly... endogenous effects, wherein the propensity of an
> individual to behave in some way varies with the prevalence of that behavior
> in the group; contextual effects, wherein the propensity of an individual to
> behave in some way varies with the distribution of background
> characteristics in the group; and correlated effects, wherein individuals in
> the same group tend to behave similarly because they face similar
> institutional environments or have similar individual characteristics.”
> (Identification problems in the social sciences, Harvard University Press)
>
> The first two hypotheses express inter-agent causality in a model. The
> third hypothesis does not. The important distinction between the two
> inter-agent causal effects is that the first involves feedback that can be
> reinforcing over the course of time. The policy implications of the
> approaches are widely different, especially if there does indeed exist a
> case of an inherent dynamic with feedback depending on the strength of the
> endogenous effect in relation to other effects. Access to temporal panel
> data is highly desirable in order to better empirically distinguish the
> effects.
>
> An important econometric issue also arises in the empirical estimation of
> discrete choice models using a multinomial logit specification in that the
> Gumbel error terms are assumed to be identically and independently
> distributed across choice alternatives and across individuals. It is not
> obvious that this is in fact a valid assumption when we are specifically
> considering interdependence between individuals’ choices. As above, we might
> reason that if there is a systematic dependence of each individual’s choice
> on an explanatory variable that captures the choices of other individuals
> who are in some way related to that individual, then there might be an
> analogous dependence in the error structure. Otherwise said, the same
> unobserved effects might be likely to influence the choice made by a given
> individual as well as the choices made by those in the individual’s
> reference group. The results and coefficients of such a model are likely to
> be biased.
>
> Furthermore, when considering longitudinal panel data, there may be also be
> an additional correlation across the responses of a single individual over
> time.
>
> In work with Michiel van Meeteren (who replied to the list recently in the
> query about snowball sampling) and Ate Poorthuis, we demonstrate an example
> of the empirical estimation of discrete choice model with network
> interaction effects, specifically testing for correlation in the error
> structure in the particular empirical case study, through the use of a mixed
> multinomial panel logit model. We presented this work at Sunbelt last year
> in Riva del Garda, at the RC33 Social Network Analysis session organized by
> Anuška Ferligoj, Vladimir Batagelj and Peter Carrington at the 17th ISA
> world congress of sociology, at the WIN workshop hosted by Sinan and
> colleagues at NYU, and most recently at a workshop on Transportation and
> Social Networks in Manchester hosted by Martin Everrett together with the
> Futurenet team at Nottingham and Loughborough. We have been a little slow to
> write up the paper, but we have an extended 5-page abstract including the
> estimation results in the WIN proceedings. If anyone is interested, please
> send us a mail! We'd love to hear from you. Capturing correlation shows a
> substantial increase in model fit even in a previously seemingly saturated
> model.
>
> In this same research, we also compare the contribution of several
> different classical centrality measures in explaining choice behavior.
> Drawing on insights from transportation research we introduce a measure to
> answer your question, Steve, about "adoption contagion" that incorporates
> not only network characteristics, but also relevant individual
> characteristics.
>
> In a different application in earlier work with Laszlo Gulyas, we embed
> estimation results from a simpler discrete choice model in an agent-based
> model to observe the theoretical simulated evolution of choice behavior over
> time. We compare cases where unobserved heterogeneity is captured to some
> extent in the original estimation, and when it is not. We find that even
> when the estimation results show little statistical difference between the
> choice models for many of the estimated utility parameters, the long run
> impact over time of accounting for the unobserved heterogeneity or not has a
> dramatic effect due to the difference in the feedback from the endogenous
> effect. Conclusion: capturing heterogeneity matters, even when it is
> unobserverd!
>
> Dugundji ER, Gulyás L (2008) Socio-dynamic discrete choice on networks:
> Impacts of agent heterogeneity on emergent equilibrium outcomes. Environment
> & Planning B: Planning and Design 35(6): 1028-1054
> http://www.envplan.com/abstract.cgi?id=b33021t
>
> Best regards,
> Elenna
>
>
>
> ________________________________
>
> Van: Social Networks Discussion Forum [mailto:[log in to unmask]<[log in to unmask]>]
> Namens Sinan Aral
> Verzonden: zondag 27 februari 2011 21:52
> Aan: [log in to unmask]
> Onderwerp: Re: Measuring contagion in longitudinal behavior data
>
>
> ***** To join INSNA, visit http://www.insna.org *****
>
>
> Excellent point Christian and I agree that Tom is right. In the Marketing
> Science commentary I pointed to I make this exact point - experiments are
> difficult and observational data is abundant. That's why we need statistical
> methods that try to tease out contagion from selection/homophily and other
> confounds. In that review I list your work with Tom Snijders as one of those
> methods (as well as our own dynamic propensity score methods published in
> the PNAS -- I pointed to this article in a previous post as well). Both of
> these are excellent dynamic methods for teasing out influence/contagion from
> other confounds. But, again, the problem is *very* difficult in my opinion.
> The reason I think we have to focus on this problem as a community and make
> it such a high priority in networks research (and thus the reason I focus on
> it so much in my own research) is because a) it is critical to knowing when
> we are observing "network effects" and when we are not, which is then in
> turn critical to policy choices...(for example peer-to-peer contagion
> management policies won't work if our estimates tell us contagion is at play
> when it really isn't) and b) because it is such a hard nut to crack.
>
> For those of you that will be at the SONIC/ANN/NICO conference at
> Northwestern this weekend, Michael Macy and I will have a session on
> "Causality in Networks" on Saturday.
>
> Here is the schedule of the Workshop portion of the event:
> http://sonic.northwestern.edu/events/webnetsciworkshop/conference-schedule/
>
> And, here is the abstract of my talk for those that are interested:
>
> Title: "Causality in Networks"
>
> Abstract: Many of us are interested in whether "networks matter." Whether
> in the spread of disease, the diffusion of information, the propagation of
> behavioral contagions, the effectiveness of viral marketing, or the
> magnitude of peer effects in a variety of settings, a key question that must
> be answered before we can understand whether networks matter, is whether the
> statistical relationships we see can be interpreted causally. Several
> sources of bias in analysis of interactions and outcomes among peers can
> confound assessments of peer influence and social contagion in networks. If
> uncorrected, these biases can lead researchers to attribute observed
> correlations to causal peer influence, resulting in misinterpretations of
> social network effects as well as biased estimates of the potential
> effectiveness of different intervention strategies. Several approaches for
> identifying peer effects have been proposed. However, randomized trials are
> considered to be one of the most effective ways to obtain unbiased estimates
> of causal peer effects. I will review a) the importance of establishing
> causality in networks, b) the various methods that have been proposed to
> address causal inference in networks, and in particular focus on c) the use
> of randomized trials to establish causality. I will provide an example from
> a randomized field experiment we conducted on a popular social networking
> website to test the effectiveness of "viral product design" strategies in
> creating peer influence and social contagion among the 1.4 million friends
> of 9,687 experimental users. In addition to estimating the effects of viral
> product design on social contagion and product diffusion, our work also
> provides a model for how randomized trials can be used to identify peer
> influence effects in networks.
>
>
> Best
>
> Sinan
>
>
> Sinan Aral
> Assistant Professor, NYU Stern School of Business.
> Research Affiliate, MIT Sloan School of Management.
> Personal Webpage: http://pages.stern.nyu.edu/~saral
> SSRN Page: http://ssrn.com/author=110270
> WIN Workshop: http://www.winworkshop.net
> Twitter: http://twitter.com/sinanaral
>
> On 2/27/2011 12:38 PM, Christian Steglich wrote:
>
>         ***** To join INSNA, visit http://www.insna.org ***** Hi Steve,
>
>         as I understand, your network is static and not changing in itself?
> If it does change as well, this can potentially undermine all sorts of
> conclusions you may want to draw from an analysis, as any behaviour
> association between connected actors could be due to selection effects as
> well.
>
>         See here and article I participated in for some methodological
> arguments, a brief critical review of methods, and a proposal to use
> actor-based modelling in Snijders' tradition:
> http://dx.doi.org/10.1111/j.1467-9531.2010.01225.x
>
>         For a static network, the most serious confounders of contagion are
> context effects - so you should capture all context information you can.
> Cohen-Cole & Fletcher wrote a funny piece illustrating how some analysis
> methods, when failing to include context, can provide patently misleading
> results (they showed how some methods would diagnose e.g. body height as
> socially contagious): http://dx.doi.org/10.1136/bmj.a2533
>
>         In general, I agree with Sinan that experiments are the best way to
> obtain "unequivocal" contagion effects, but Tom is right when pointing out
> that this is very often is not possible in applied research settings...
>
>         Greetings,
>         Christian
>
>
>         Am 25/02/2011 20:28, schrieb Steve Eichert:
>
>                 ***** To join INSNA, visit http://www.insna.org *****
> Hello SOCNET,
>
>                 I'm looking for books, papers, algorithms, and/or ideas on
> how best to measure contagion in a network.  We have longitudinal behavior
> data for all actors in a directed network and want to calculate the degree
> of contagion occurring between all connected nodes.  We would like to use
> the calculated "contagion score" to identify nodes that we can do further
> analysis on, as well as to measure the overall level of contagion in the
> network.  The longitudinal behavior data we have indicates how much of
> something the nodes within the network are using over time.  We're
> interested in better understanding the algorithms folks are using for
> "adoption contagion" (someone who has already adopted influences a non
> adopter to adopt) as well as "behavior contagion" (a high user influences
> those connected to them to use more).
>
>                 Thoughts?
>
>                 Thanks,
>                 Steve
>
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