[statnet_help] fragmented bipartite network...

[Martina Morris]

Hi Harald,

You do have a complicated analysis here, and I'm a bit under-equipped to
help you Dx what is going on, as I don't have much experience with either
bipartite or multi-level nets (let alone both together!).

What I can say, though, is that factor and covariate effects on the nodes
are, in the non-multilevel context, one of the most important brakes on the
feedback effects caused by dyad-dependent terms, making them more
well-behaved and more likely to produce the kinds of networks we actually
observe (caveat: sometimes those dependent effects are needed, see Carter's
work on amyloid fibrils).

In this case, it seems like you don't have many attributes to work with --
indeed, only on one of the modes.  For gender, I would fit as a factor btw,
not a quantitative covariate, tho if there are only 2 levels this will not
have much impact.  But when I think about the goals of board composition in
non-profits (the closest I get to your world), it's clear that gender is
not the only attribute that influences board member invitations -- and I
would expect the same would be true here.  You might try adding  family
name as a bxnodefactor (will pick up both family size and family activity
level differentials), or sociality for either (or both) modes (to condition
on the degree of each node).  Your additional terms can then be interpreted
as effects operating beyond these differences in degree.  Degree
distributions definitely influence component size distributions, up to a
point, so if your model is not getting these right, you can start there.

Thinking about the orgs, it seems there must be org attributes that
influence the size and composition of the board.  Org size, sector,
geographic location, age, specialization, etc. -- I can imagine all of
these would influence board memberships.  Properties these nodes show in
the other nets you have might be able to be represented on the cheap here
as nodal attributes in this network. If these effects are at work -- and if
you're not including them in the model, it is a form of mis-specification
that compromises all of the other model estimates.

Then there's homophily, which works differently in bip nets -- for one,
it's a dyad-dependent term.  But it's also more complicated to think
about.  Perhaps families might choose to specialize in an org sector, or
maybe the opposite, they aim to integrate across sectors.  Orgs might want
diversity (on some measure) for members, which would show up as
anti-homophily in bip two-paths.  Again though, this would require more
measured attributes for both orgs and persons.

Adding model terms like components is different.  In my modeling world, we
want our (parsimonious) models to represent the mechanistic effects that
may actually generate the ties in the network.  For us, component size
distributions are an *output* of a network formation process, not the
generating mechanism (people aren't creating ties with the explicit intent
of structuring the network component size distributions, with one key
exception, and that we do model).  We instead use the component size
distribution as a goodness-of-fit indicator -- to test whether the
mechanistic terms we included in our model reproduce these higher order
excluded network stats.

But your context may be different.  When an org board is formed, if there
is an explicit strategy to create specific component structures in the
overall network then those intentions should be included as model terms.  I
can imagine that bridging structural holes might be one of those
strategies.  But again, not my area of expertise.

I'm not sure how much any of this helps your specific issues.  But when
models don't fit the data properly, it's worth thinking about specification
from first principles.  So I hope this helps.

best,
Martina

On Mon, Dec 4, 2023 at 12:28 AM Harald Waxenecker <waxenecker at fss.muni.cz>
wrote:


> Dear Tom, Martina, Carter and Daniel

>

> Thank you for your supportive answers.

>

>

>

> First, I will try to address some of your questions. The dependent network

> is a bipartite business network (6902 persons x 5178 companies), based

> exclusively on interlocking directorates. This dependent bipartite network

> represents the business ties of elite members in their home country. We

> include two covariates for the first node set (persons): *traditional

> surname* and *gender*. Isolates in this network represent elite members

> without any business ties. We belief that isolated nodes are meaningful in

> this network; e.g., women are often constrained to ‘reproduction’ rather

> than participating in ‘production’ (businesses). However, in different

> network layers they contribute to elite cohesion.

>

>

>

> Regarding these different layers: we have six more networks. The first is

> a one-mode kinship network (6902x6902), and the others are bipartite

> networks (based on interlocks), where persons form the first node set and

> entities the second. Hence, all matrices share a consistent number of rows

> (n = 6902), while the number of columns varies according to the number of

> entities in each network layer: offshore companies in Panama (n = 1537),

> business associations (n = 128), non-profit organizations (n = 236),

> political parties (n = 55), and public entities (n = 431).

>

>

>

> We employ ‘bipartite homophily terms’, as proposed by Metz et al. (2018)

> https://doi.org/10.1017/S0143814X18000181

> <https://urldefense.com/v3/__https://doi.org/10.1017/S0143814X18000181__;!!K-Hz7m0Vt54!mZ6U-5ef-FwMtvk7aI512iZKTS20PMt72wzLingnjcBUoo1ETmzgxIYYk_qPcMmHbtcEowX7XXdRKk_R_lJbhAPBGYqXcg$>,

> to test whether a common property (‘homophily’) of the nodes in the first

> node set, such as a shared attribute (gender, traditional surname), a

> direct tie (kinship relation), or a mutual membership in other bipartite

> layers (offshore companies, business associations, etc.) contribute to the

> probability of two individuals forming ties with the same company in the

> dependent network.

>

>

>

> Regarding the modeling process, it´s true that the model we shared relies

> only on dyad-dependent terms. We always ‘come back’ to this model

> specification because all our attempts, which certainly were also based

> primarily on dyad-dependent terms, did not produce better results. We

> explored various options, including nodematch to control for component

> membership to split the network into smaller fragments. Then we

> incorporated component membership of the nodes as constraint to induce

> network fragmentation. While this partially improved network fragmentation,

> problems with goodness-of-fit persisted. Additionally, we encountered some

> computational limitations while running these options.

>

>

>

> Now, we have incorporated several of your recommendations, introducing

> dyad-independent terms and utilizing components() from the ergm.components

> package. Please find the new outcomes (model 0) attached. We've also

> attached summary files and component distribution for a comparative

> analysis between the observed network and the simulated network.

>

>

>

> We also tried to include the terms compsizesum() and dimers() into the

> model; however, we observe degeneracy issues. In addition, we still could

> not get results with bridges(), because it seems to be very time consuming

> and/or needs much computational capacity.

>

>

>

> I think this bridges-term relates somehow to your question @Martina about

> cross-group ties in the simulated data. Or maybe I am wrong. Please, could

> you explain that in more detail? Thanks.

>

>

>

> Thank you again for your support. Looking very forward to read your

> thoughts and advice.

>

>

>

> Kind regards,

>

> Harald

>

>

>

>

>

>

>

>

>

>

>

>

>

>

>

>

>

> El 1/12/23, 21:53, "[NOMBRE]" <daniel.gotthardt at uni-hamburg.de> escribió:

>

> Hello Harald,

>

>

>

> if I understand you correctly you have a within-mode network as well as

>

> a bipartite network. James Hollway et al. (2017) has described an

>

> approach to handle these kinds of combined networks as multilevel social

>

> spaces with stochastic actor-oriented models:

>

>

> https://www.cambridge.org/core/journals/network-science/article/abs/multilevel-social-spaces-the-network-dynamics-of-organizational-fields/602BB810A44497EBDE2A111A6C2771A3

> <https://urldefense.com/v3/__https://www.cambridge.org/core/journals/network-science/article/abs/multilevel-social-spaces-the-network-dynamics-of-organizational-fields/602BB810A44497EBDE2A111A6C2771A3__;!!K-Hz7m0Vt54!mZ6U-5ef-FwMtvk7aI512iZKTS20PMt72wzLingnjcBUoo1ETmzgxIYYk_qPcMmHbtcEowX7XXdRKk_R_lJbhAOR74XZsg$>

>

> - There are also some tricks to transform these types of networks into

>

> an extended multimodal network matrix, exemplified e.g. in Knoke et al.

>

> (2021):

>

>

> https://www.cambridge.org/core/books/abs/multimodal-political-networks/agency-influence-power/57CB185C6E9429B34A9DE181C37EADF3

> <https://urldefense.com/v3/__https://www.cambridge.org/core/books/abs/multimodal-political-networks/agency-influence-power/57CB185C6E9429B34A9DE181C37EADF3__;!!K-Hz7m0Vt54!mZ6U-5ef-FwMtvk7aI512iZKTS20PMt72wzLingnjcBUoo1ETmzgxIYYk_qPcMmHbtcEowX7XXdRKk_R_lJbhAMG16sRdw$>

>

>

>

> I personally don't know of any ergm model that can handle this kind of

>

> co-evolution of one-mode and two-mode networks but some kind of

>

> multilevel ergms (see Wang et al. (2013)

>

> https://www.sciencedirect.com/science/article/abs/pii/S0378873313000051

> <https://urldefense.com/v3/__https://www.sciencedirect.com/science/article/abs/pii/S0378873313000051__;!!K-Hz7m0Vt54!mZ6U-5ef-FwMtvk7aI512iZKTS20PMt72wzLingnjcBUoo1ETmzgxIYYk_qPcMmHbtcEowX7XXdRKk_R_lJbhAMb4-hbuA$>)

>

>

> might be the way to go: - I'm sure others here know more about the

>

> capabilities of ergm.multi though.

>

>

>

> If these kinship structures explain the fragmentation of the bipartite

>

> network, you might need to include them either directly with the

>

> approaches above or construct some corresponding dyadic or monadic

>

> covariates to represent the kinship structure in your single level network.

>

>

>

> Best Regards,

>

>

>

> Daniel

>

>

>

> Am 01.12.2023 um 02:13 schrieb Martina Morris:

>

> >

>

> > Hi Harald,

>

> >

>

> > I'm looking for some clarification here, which I think Tom Kraft might

>

> > also have wondered about.

>

> >

>

> > You say:

>

> >>

>

> >> Our research focuses on tie formation and elite cohesion, specifically

>

> >> examining interlocking directorates and kinship relations. The

>

> >> dependent bipartite business network comprises 6,902 individuals and

>

> >> 5,178 companies, exhibiting sparsity (density = 0.00012) and

>

> >> fragmentation with 4,455 components, including 3,850 isolates in the

>

> >> first mode (persons)

>

> >>

>

> > For a bipartite network ties are allowed only between modes (persons,

>

> > companies), not within.  It's clear how interlocking directorates would

>

> > meet that criteria.  But kinship relations would be among persons, so

>

> > within-mode, not between, and this would not be a bipartite network.

>

> >

>

> > Is the model you've sent us for the interlocking directorships only?

>

> > And by isolates in the person mode, do you mean persons who are not

>

> > affiliated with any of the companies?  If so, then it's a bit odd to

>

> > include them in the bipartite network.

>

> >

>

> > I'm wondering if this problem is better posed as a multilevel network

>

> > (not my area of expertise).

>

> >

>

> > thanks,

>

> > Martina

>

> >

>

> >

>

> > On Thu, Nov 30, 2023 at 4:33 PM Carter T. Butts <buttsc at uci.edu

>

> > <mailto:buttsc at uci.edu>> wrote:

>

> >

>

> >     __

>

> >

>

> >     Hi, Harald -

>

> >

>

> >     Coexistence of large complex components does not generally occur

>

> >     unless something drives the fragmentation, and this is what your

>

> >     models are telling you: the terms you are currently using do not

>

> >     include the forces that are sufficient to reproduce your component

>

> >     size distribution.  That means that you need to think about why your

>

> >     network is split into fragments, and include terms that capture the

>

> >     relevant social forces.  Thinking about likely mechanisms is step

>

> >     zero, so do that before anything else!  Guided by your substantive

>

> >     knowledge of what is likely going on, you will next (as others have

>

> >     said) want to look at covariate effects relating to differential

>

> >     mixing, since those are your most obvious and most important sources

>

> >     of heterogeneity.  If you find that there is still more

>

> >     fragmentation that can be explained by other means, you may need to

>

> >     consider model terms relating directly to component count or size.

>

> >     These are still somewhat experimental, and are currently sequestered

>

> >     in an add-on package called ergm.components

>

> >     (https://github.com/statnet/ergm.components

> <https://urldefense.com/v3/__https://github.com/statnet/ergm.components__;!!K-Hz7m0Vt54!mZ6U-5ef-FwMtvk7aI512iZKTS20PMt72wzLingnjcBUoo1ETmzgxIYYk_qPcMmHbtcEowX7XXdRKk_R_lJbhAMQjqlvCA$>

>

> >     <

> https://urldefense.com/v3/__https://github.com/statnet/ergm.components__;!!K-Hz7m0Vt54!iKts-XLv39sY0gvmpW6MWLIxNMCNKjKQKOhJszIbp3PIy_J5mdLCs0MytfHsBu-cjnQjk997tCRX0MMs6LDW$

> <https://urldefense.com/v3/__https:/github.com/statnet/ergm.components__;!!K-Hz7m0Vt54!iKts-XLv39sY0gvmpW6MWLIxNMCNKjKQKOhJszIbp3PIy_J5mdLCs0MytfHsBu-cjnQjk997tCRX0MMs6LDW$>>).

> However, this package can be installed from github (see the github page),

> and the terms will work automagically with ergm() and friends once the

> package is loaded.  Depending on your situation, you may need or want to

> examine the components() or compsizesum() terms, both of which are

> documented within the package.

>

> >

>

> >     Hope that helps,

>

> >

>

> >     -Carter

>

> >

>

> >     On 11/30/23 9:58 AM, Harald Waxenecker wrote:

>

> >>

>

> >>     Dear ‘statnet community’,____

>

> >>

>

> >>     __ __

>

> >>

>

> >>     Our research focuses on tie formation and elite cohesion,

>

> >>     specifically examining interlocking directorates and kinship

>

> >>     relations. The dependent bipartite business network comprises

>

> >>     6,902 individuals and 5,178 companies, exhibiting sparsity

>

> >>     (density = 0.00012) and fragmentation with 4,455 components,

>

> >>     including 3,850 isolates in the first mode (persons). The attached

>

> >>     documents contain descriptives and the component size distribution

>

> >>     from the observed network.____

>

> >>

>

> >>     ____

>

> >>

>

> >>     The fragmented structure is important, as other network layers,

>

> >>     like kinship relations, are expected to contribute to the cohesion

>

> >>     of this business network. We apply ERGM to model these processes,

>

> >>     but we struggle to capture the fragmented structure of the

>

> >>     observed network. The component size distribution of the simulated

>

> >>     network differs significantly. In addition, the goodness-of-fit

>

> >>     (GOF) for k-stars (in both modes) and geodesic distances (Inf)

>

> >>     shows significant results. All these results are also attached.____

>

> >>

>

> >>     ____

>

> >>

>

> >>     We've explored various options, including constraints, MCMC

>

> >>     propositions, and simulated annealing, but haven't achieved

>

> >>     success. Please, we would like to ask for your help to improve our

>

> >>     model. Thank you!____

>

> >>

>

> >>     __ __

>

> >>

>

> >>     Kind regards,____

>

> >>

>

> >>     Harald____

>

> >>

>

> >>     __ __

>

> >>

>

> >>     __ __

>

> >>

>

> >>     __ __

>

> >>

>

> >>     --- ____

>

> >>

>

> >>     *Harald Waxenecker

>

> >>

>

> >>     *____

>

> >>

>

> >>     *Masaryk University | Faculty of social studies*

>

> >>     Department of Environment Studies

>

> >>     A: Jostova 10 | 602 00 Brno | Czech Republic

>

> >>     E: waxenecker at fss.muni.cz <mailto:waxenecker at fss.muni.cz>____

>

> >>

>

> >>     __ __

>

> >>

>

> >>

>

> >>     _______________________________________________

>

> >>     statnet_help mailing list

>

> >>     statnet_help at u.washington.edu  <mailto:

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>

> >>

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> --

>

>

>

> Daniel Gotthardt, M.A.

>

>

>

> Wissenschaftlicher Mitarbeiter / Research Associate

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