[statnet_help] fragmented bipartite network...

[steffentriebel at icloud.com]

Dear Harald,

I’ll also chime in, albeit with a less statistically profound lens than the others.

First, I’ll encourage you to take a look at the manuscript David will share on arXiv; it may prove helpful and will hopefully allow you to capture theoretical considerations better.

Second, maybe it makes sense to “dumb down” your model a bit and take an iterative approach to refiner your theory. You write that there are many different types of ties to the second mode, ranging from off-shore companies to businesses or non-profits. It is probably safe to assume that all of these will follow different theoretical logics – e.g., for businesses, we know that geographical proximity plays a major role in business networks as well as sectors (in less regulated economies, at least), but this will likely not be true for off-shore affiliations, which will perhaps be facilitated through the same broker organizing these off-shore affiliations? That would imply a different mechanism leading to the fragmented components you’re observing. These different institutional logics will be difficult to capture.

Remember, the components you observe are a function of these (social) mechanisms – at least typically – and not a driving force. So, I think obtaining clarity on which mechanisms theory (and prior research) suggests to be especially pertinent will help obtain a clearer picture of what’s happening. I’m sure you did your due diligence here, but with networks as complex as this, it might make sense first to understand the different micro-processes underpinning them better, refine your theory, and then tackle the “full network”. Perhaps you could model the bipartite affiliation per organizational type in the second mode and include dyadic covariates for “on the same non-profit”, “on the same company board”, .. depending on which network you are modelling? I assume this could help with honing in on the solution.

Best wishes & best of luck
Steffen

Von: statnet_help <statnet_help-bounces at mailman13.u.washington.edu> im Auftrag von Hunter, David <dhunter at stat.psu.edu>
Datum: Samstag, 9. Dezember 2023 um 03:45
An: Martina Morris <morrism at uw.edu>, James Moody <jmoody77 at duke.edu>
Cc: statnet_help at u.washington.edu <statnet_help at u.washington.edu>, Schweinberger, Michael <michael.schweinberger at psu.edu>
Betreff: Re: [statnet_help] fragmented bipartite network...
Following up on Martina’s observations among others…

In case it helps, the b1nodematch and b2nodematch terms in the ergm package do not merely provide a census of 2-paths with matching end-nodes. They do provide this census, but merely as one end of a spectrum (two spectra, actually) of statistics created in the same spirit as the geometrically weighted statistics (GWESP, GWD, etc.) pioneered by Snijders et al back in 2006 (“New Specifications for Exponential Random Graph Models”).  The full spectra entail a more flexible way to capture homophily in a bipartite network.

We’ve just submitted a manuscript on this, and coincidentally we use a bipartite network of interlocking directorates to illustrate the method in this article.  I’ll try to get it up on arXiv soon, but if anyone wants a copy please send me an email individually.

Best,
Dave

From: statnet_help <statnet_help-bounces at mailman13.u.washington.edu> on behalf of Martina Morris <morrism at uw.edu>
Date: Friday, December 8, 2023 at 3:47 PM
To: James Moody <jmoody77 at duke.edu>
Cc: statnet_help at u.washington.edu <statnet_help at u.washington.edu>, Schweinberger, Michael <michael.schweinberger at psu.edu>
Subject: Re: [statnet_help] fragmented bipartite network...
This is a great conversation; many thanks to the contributors.

As I read through the proposed stats, though, I keep stumbling on the bipartite bit:  how would some of these translate into bip net terms?  I appreciate Jim's effort to bring this back to practical advice.

So, some really basic thoughts here.  There are two general types of blocks:  those based on exogenous attributes, and those based on endogenous processes.  I think the reason we're circling around the idea of blocks is that these depictions tend to capture the clustering observed in real world networks, and that blocking can help explain why dyad-dependent effects operate locally, rather than globally across a network.

The exogenous type of block is captured by nodemix and nodematch type terms in ergm (which have a number of different specifications).  In the bip net context these terms become more complicated as they no longer represent the crosstabulation of pairwise nodal attributes, but instead a crosstab of the terminal node attributes of a 2-mode triad.  What's interesting about the bip net version of these terms is that this 2-path configuration is also a building block of equivalence.  More on this below.

The endogenous type of block is captured as latent block structures in hergms (for the ergm framework, other frameworks are out there).  HERGMs are an interesting approach to identifying observed or latent neighborhoods of dependence (https://www.jstatsoft.org/article/view/v085i01), but I don't know if the package (or the models) can handle bipartite nets.

I've added Michael Schweinberger to this email in case he would like to comment.

Back to the exogenous blocking then.  Family name could be a powerful blocking effect (e.g. Jim's example of Tata), showing up in this bip net as org board memberships shared by people with the same family name.  Ignoring the modes, these 2paths would be Nullwise (or non-edgewise) Shared Partner (NSP) statistics.  If two people shared all of their org memberships, they are structurally equivalent (whether they share an exogenous attribute or not) -- and more generally, the more NSPs, the higher the equivalence.  And if the nodal name attribute is not driving these 2 paths, these high value NSPs are indicators of latent structure.

The 2-paths can also be used to examine the org equivalence pattern in the same way.

And my intuition would be that, conditioned on density, NSP distributions with higher means or longer tails would lead to fragmentation in the network.

So, that makes me think perhaps the place to start is with EDA --  look at the NSP distributions, for both persons and orgs.  Compare these to the expected distributions under a simple null random graph.  If the distributions differ significantly, then start to look for exogenous effects that help to explain the deviation from the null (using the bip homophily terms with some more attributes on the nodes of both modes).  And look into whether endogenously defined blocks (a la HERGM) can be used for bip nets.  For me, the ideal would be to identify the latent blocks, and then explain almost all of that blocking in terms of exogenous/observed attributes.  The blocks capture the structure.  The explicit exogenous effects "explain" it.

best,
mm


On Fri, Dec 8, 2023 at 6:28 AM James Moody <jmoody77 at duke.edu<mailto:jmoody77 at duke.edu>> wrote:
Fun discussion, thanks for sharing, always learn something in these sorts of posts.

As to this this application per se; a couple of pragmatic (i.e. may not be elegant!) ideas:

- theory should be able to inform some unlikely mixing that one could specify using a mixingmatrix term or two, no?  So family, private/public, industry, etc.
 - For many business group applications, the actual family name is embedded in many of the subsidiaries (Tata group, tata inc, tata industries, etc.) so a name-similarity score could help (if you have nodenames)
- The interlock limit will be size of the boards.  While its possible to change the size of each board in a company, its not trivial, and I think you can justifiably take that as exogenous in the time-frame you have. I’m betting most of your small components are single family companies without external board memberships.  Those create small stars in the bipartiate network (cliques in the projection).  So that would imply:
a) a hard-constraint on target degree.  You could just fix that as a constraint.  Again, not elegant (Carter’s cutting at joints and all), but likely true.
b) a size mixing logic.  Family-only/small-board cliques are isolated, leaving big-with-big, so there’s effectively a two-mode degree assortativity here.  If you can’t induce this by an attribute (family name/ownership), then use assortativity on degree.
- Cheating a little, but you could make component membership at attribute and hard-code mixing within/between. That means you can’t model what drives membership in the largest components vs. the small fractions, but, again, this is such a weird case (from a graph expectation sense), as anything that had even a little random noise in it would link across those small components, so the restriction here is almost certainly a legal/possibility restriction that should be treated as exogenous.
- that’s, of course,  just the crudest version of Daniel’s idea – find a structural pattern that implies high/low probability of mixing across modes and hard-code it.  I.e. do some old-fashioned inductive modeling of your network before the ERGM to generate classes of cases based on your best effort to induce the (to you) invisible restrictions patterning the ties, then add those back into the model as appropriate node/edge attributes.

PTs
Jim



From: statnet_help <statnet_help-bounces at mailman13.u.washington.edu<mailto:statnet_help-bounces at mailman13.u.washington.edu>> On Behalf Of Carter T. Butts
Sent: Friday, December 8, 2023 4:53 AM
To: statnet_help at u.washington.edu<mailto:statnet_help at u.washington.edu>
Subject: Re: [statnet_help] fragmented bipartite network...


Hi, Daniel -

Most of the cases to which I believe you are referring deal with differential mixing; the "blocks" here are what are sometimes called "density" blocks, which are quantitative relaxations of the complete/null blocks.   I don't think anyone doubts that differential mixing exists, but that is very far from e.g. nontrivial global automorphism orbits or the like.  Indeed, John Boyd had a running bet for some years, in which he offered to pay a sum of money (I forget how much) to anyone who could show a statistically significant regular equivalence pattern (above and beyond SE - he also had some other boundary conditions that ruled out "easy" cases).  My vague recollection was that Steve Borgatti claimed to have one, and they then haggled over John's way of calculating "significance," but my memory on the subject is hazy and doubtless untrustworthy; I never did buy John's extreme conjecture, but it is true that he was not exactly overwhelmed with claimants.   At any rate, models for differential mixing with discrete group structure are well-trod.  As far as other kinds of generalized blocks (moving away from complete/null blocks), you can fit models with strict versions of e.g. regular, row/column dominant, and row/column functional blocks with clever use of constraints (in ergm, the bd() constraint term).  The most obvious path to soft versions of those block types is to create statistics that count violations of the block pattern.  Some can be implemented using the degrange() term, together with appropriate use of the optional attribute arguments.  (Obviously, these are all "confirmatory" models, in the sense that one has to specify the block structure one wants to impose/parameterize.  But that is not without its virtues.)

Vis a vis dependence, I'm not sure that it is very helpful to think in terms of "violating assumptions."  It is probably more useful to think of H-C and friends as giving you a "recipe" for the statistics you need to implement particular kinds of dependence conditions (should you want to do so).  So, e.g., if you want edges to depend on each other when they share endpoints, then you will want (in the unvalued case) indicators for each edge variable, and indicators for each mutual dyad.  If you also want the corresponding effects to be homogeneous, then this reduces to the edge count and the count of mutuals.  Adding e.g. a 2-outstar term to a model with edges and mutuals is not violating any particular assumption imposed by the latter - it's just that this new model will now belong to a different (and broader) dependence class than the original one.  (It will, in particular, have a form of Markov graph dependence.)  Nothing says that your model has to belong to any particular dependence class - unless you want to impose such a condition.  Of course, if you do want to restrict your dependence to a particular class, then you will indeed need to ensure that your statistics are a subset of those admitted by that class (which, for H-C, can be determined from the cliques of the conditional dependence graph).  In my experience, this is rarely a useful way to proceed; however, it sometimes can be handy to know the type of dependence class to which your terms belong.  Likewise, it can sometimes be handy to start by positing a form of dependence that makes sense in a specific situation, and then deriving the statistics that result.   Pip, in particular, has done a great deal to elucidate these sorts of connections.

As far as long-range dependence, there's again nothing ruling it out.  (Pip and Tom, IIRC, have a very nice typology working out statistics for dependence classes at different distances.)   For instance, k-cycles can be long-range, for large k.  The various component and bridging statistics can be arbitrarily long-range.  The statistics that arise from density and dyad census mixtures do them one better by being completely global (i.e., they create conditional dependence between edge variables irrespective of whether there is even a path of any length between their endpoints).  All of these lead to well-defined models - those models just happen not to belong e.g. to the Markov graphs (or the social circuit graphs, the Bernoulli graphs, the u|man family, etc.).  If there is a reason that you need your model to belong to such a family, then you would not want to use terms that are not within the class specifying that family.  But otherwise, such restrictions are arbitrary, and may get in the way of specifying important mechanisms.

Hope that helps,

-Carter


On 12/7/23 11:02 PM, Gotthardt, Daniel wrote:
Hello Carter,

i agree that stricter types oft equivalence are very rare and I would personally also look at either generalized blockmodeling or actually just measures of structural or positional similarity - but indeed not only local ones (which are already included in ergm of course). I did mention them here because most results of the relevance of more global equivalence structures I know have been found in especially kinship research and organisational science (Krackhardt & Porter 1986 and e.g. in insitutuional fields DiMaggio 1996 and Alsaas & Taamneh 2019). There has also been some recent research in foreign trade and political conflicts that indicate that block structures might matter (Guler et al. 2002, Zhou & Park 2012, Olivella et al. 2022). I am curious though which tools you are thinking about for implementing aspects oft generalized block structures?

Regarding hammersley-clifford I mostly wanted to be careful here, but I did think that H-C and extensions like social circuit dependency (which allows partial depensence) did matter to ensure some (conditional) independence assumption with a few parameters (one for each clique of the dependence graph) in ergms (see e.g. Koskinen & Daraganova 2012 and Block er al. 2019). I thought dependencies (far) beyond the local neigborhood might violate these properties. This is probably beyond Harald's concerns but I would be happy if you could indicate any literature to alleviate my misunderstanding.

Best Regards
Daniel

--
Daniel Gotthardt, M.A.

Wissenschaftlicher Mitarbeiter / Research Associate

Universität Hamburg
Fakultät für Wirtschafts- und Sozialwissenschaften / Faculty of Business, Economics and Social Sciences
Fachbereich Sozialwissenschaften / Department of Social Sciences
Soziologie, insb. Digitale Sozialwissenschaft / Sociology, esp. Digital Social Science

Max-Brauer-Allee 60
22765 Hamburg
www.uni-hamburg.de<https://urldefense.com/v3/__http:/www.uni-hamburg.de__;!!CzAuKJ42GuquVTTmVmPViYEvSg!JdYBcV_E6DZQNgeXEHvFyB1XtKMZAxcMdc_AkjSbQU_HEoYKHjJfk8sROxBVNRM1pQa_K-uy5aEJXHEf_1N44xpY6bYmHv1j$>
________________________________
Von: statnet_help <statnet_help-bounces at mailman13.u.washington.edu><mailto:statnet_help-bounces at mailman13.u.washington.edu> im Auftrag von Carter T. Butts <buttsc at uci.edu><mailto:buttsc at uci.edu>
Gesendet: Freitag, 8. Dezember 2023 07:06:46
An: statnet_help at u.washington.edu<mailto:statnet_help at u.washington.edu>
Betreff: Re: [statnet_help] fragmented bipartite network...


Local automorphism orbits and their associations with covariates can be modeled using graphlet statistics; see e.g. ergm.graphlets.  Nontrivial global automorphisms are extremely rare in typical social networks, so such terms would be unlikely to be useful - what one might call the "strong algebraic paradigm" of network analysis (the idea that we could explain most social network structure in terms of small numbers of roles, as defined through algebraic equivalences) was a very compelling idea that didn't really work out, and I don't think many folks are pushing in that direction right now.  (See also compositional factorization, as famously illustrated by the semigroup on the cover of Wasserman and Faust (1994).  Beautiful idea with some lovely technical results, but one with few if any real-world success stories.  Sometimes, things just don't work out.)  I think there could be some potential uses for terms for adherence to (confirmatory) generalized blockmodel structure (in the Doreian/Ferligoj/Batagelj tradition), though some of this can already be emulated using existing tools; there has also been a relative dearth of empirical cases in which complex block types have been shown to be important for capturing network structure.  If such cases were to become more often encountered, this would naturally motivate more work to model them.

With respect to your second comment, I am not sure what you mean by "violating" Hammersley-Clifford.  H-C provides one way of establishing an equivalence between sets of network statistics and associated dependence conditions; Pip Pattison, Gary Robbins, and others have obtained various refinements to the original result (allowing for more subtle conditions to be treated).  H-C and friends simply say (effectively) that certain classes of statistics implement certain kinds of dependence.  These are important results for constructing and interpreting statistics, but they are not rules that can be violated.

Hope that clarifies things,

-Carter
On 12/7/23 8:52 PM, Gotthardt, Daniel wrote:
Dear Harald,

after Martinas very insightful message and considering that you have kinship and business ties but not so many node covariates, I am wondering if you need or should think of structural equivalance as a driving factor. With White and others there is a strong tradition of focussing on this for kinship networks and DiMaggio and Burt have studied the importance oft business roles and structural position. In your case that probably means non-local forms of equivalence (automorphic, role, etc) that might matter directly in the network behavior or could represent unmeasured node attributes. Feature and embedding based measures are more scalable and now allow to measure those concepts better in larger networks.

To the best of my knowledge this is not considered offen in generative network models and i don't think that we can include those less-localized mechanisms directly (yet). Plesae let me know if this is a direction that makes sense for you from a theoretical point of view and also something that could be identified in your data. I am currently working on this in the context oft actor-oriented models but am interested in the potential of ergms in this regard as well.  At least as exogenous covariates this might be possible but otherwise we might violate conditional independence (Hammersley-Clifford theorem). I am curious to hear about the thoughts of experienced ergm modelers on this, though.

Best Regards,
Daniel

--
Daniel Gotthardt, M.A.

Wissenschaftlicher Mitarbeiter / Research Associate

Universität Hamburg
Fakultät für Wirtschafts- und Sozialwissenschaften / Faculty of Business, Economics and Social Sciences
Fachbereich Sozialwissenschaften / Department of Social Sciences
Soziologie, insb. Digitale Sozialwissenschaft / Sociology, esp. Digital Social Science

Max-Brauer-Allee 60
22765 Hamburg
www.uni-hamburg.de<https://urldefense.com/v3/__http:/www.uni-hamburg.de__;!!CzAuKJ42GuquVTTmVmPViYEvSg!Jy0dmFtPSz9FGZILsxIzHWpAcAK5wDvLWuQ2s4hKJdX0uaJX7imnKxe9w1W52yrNrJRKiI-YzcF0M4kcXbfma0JgQ-N6zkZ-$>
________________________________
Von: Martina Morris <morrism at uw.edu><mailto:morrism at uw.edu>
Gesendet: Donnerstag, 7. Dezember 2023 23:45:59
An: Harald Waxenecker
Cc: Gotthardt, Daniel; statnet_help at u.washington.edu<mailto:statnet_help at u.washington.edu>
Betreff: Re: [statnet_help] fragmented bipartite network...

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<mailto: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<mailto: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>

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

>>

>>     __ __

>>

>>

>>     _______________________________________________

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--

Daniel Gotthardt, M.A.

Wissenschaftlicher Mitarbeiter / Research Associate

Universität Hamburg
Fakultät für Wirtschafts- und Sozialwissenschaften / Faculty of
Business, Economics and Social Sciences
Fachbereich Sozialwissenschaften / Department of Social Sciences
Soziologie, insb. Digitale Sozialwissenschaft / Sociology, esp. Digital
Social Science

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