[statnet_help] fragmented bipartite network...

[Martina Morris]

Those are all great suggestions Steffen -- thx for posting :)

On Sat, Dec 9, 2023 at 4:08 AM steffentriebel at icloud.com <
steffentriebel at icloud.com> wrote:


> 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

> ZjQcmQRYFpfptBannerStart

> This Message Is From an Untrusted Sender

> You have not previously corresponded with this sender.

> See https://itconnect.uw.edu/email-tags for additional information.

> Please contact the UW-IT Service Center, help at uw.edu 206.221.5000, for

> assistance.

>

> ZjQcmQRYFpfptBannerEnd

>

> 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

> <https://urldefense.com/v3/__https://www.jstatsoft.org/article/view/v085i01__;!!K-Hz7m0Vt54!gmKcD84bDbZPyEX2zuv5T4o8Kb1GYd6JBBX1ouXCnvi3c1-y5Khz2nCubUmO0JoP3sAavbxSVlMVxupQ8UudI4q3Kz1PYkM$>),

> 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> 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> *On

> Behalf Of *Carter T. Butts

> *Sent:* Friday, December 8, 2023 4:53 AM

> *To:* 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>

> <statnet_help-bounces at mailman13.u.washington.edu> im Auftrag von Carter

> T. Butts <buttsc at uci.edu> <buttsc at uci.edu>

> *Gesendet:* Freitag, 8. Dezember 2023 07:06:46

> *An:* 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> <morrism at uw.edu>

> *Gesendet:* Donnerstag, 7. Dezember 2023 23:45:59

> *An:* Harald Waxenecker

> *Cc:* Gotthardt, Daniel; 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>

> 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:

> statnet_help at u.washington.edu>

>

> >>

> https://urldefense.com/v3/__http://mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!KK5UcPVRvb25ILHn7wJt4TEsP-Ic39L133WdzimKJv-378bLqah-hO8Gm9Yd_qoWgV_tbzbT6swweifmS5mRRQ$

> <https://urldefense.com/v3/__http:/mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!KK5UcPVRvb25ILHn7wJt4TEsP-Ic39L133WdzimKJv-378bLqah-hO8Gm9Yd_qoWgV_tbzbT6swweifmS5mRRQ$>

>   <

> https://urldefense.com/v3/__http://mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!KK5UcPVRvb25ILHn7wJt4TEsP-Ic39L133WdzimKJv-378bLqah-hO8Gm9Yd_qoWgV_tbzbT6swweifmS5mRRQ$

> <https://urldefense.com/v3/__http:/mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!KK5UcPVRvb25ILHn7wJt4TEsP-Ic39L133WdzimKJv-378bLqah-hO8Gm9Yd_qoWgV_tbzbT6swweifmS5mRRQ$>

> >

>

> >     _______________________________________________

>

> >     statnet_help mailing list

>

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

>

> >     http://mailman13.u.washington.edu/mailman/listinfo/statnet_help

> <https://urldefense.com/v3/__http:/mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!Jy0dmFtPSz9FGZILsxIzHWpAcAK5wDvLWuQ2s4hKJdX0uaJX7imnKxe9w1W52yrNrJRKiI-YzcF0M4kcXbfma0JgQ7mPF8AH$>

>

> >     <http://mailman13.u.washington.edu/mailman/listinfo/statnet_help>

> <https://urldefense.com/v3/__http:/mailman13.u.washington.edu/mailman/listinfo/statnet_help*3e__;JQ!!CzAuKJ42GuquVTTmVmPViYEvSg!Jy0dmFtPSz9FGZILsxIzHWpAcAK5wDvLWuQ2s4hKJdX0uaJX7imnKxe9w1W52yrNrJRKiI-YzcF0M4kcXbfma0JgQ4LfDjoH$>

>

> >

>

> >

>

> > _______________________________________________

>

> > statnet_help mailing list

>

> > statnet_help at u.washington.edu

>

> > http://mailman13.u.washington.edu/mailman/listinfo/statnet_help

> <https://urldefense.com/v3/__http:/mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!Jy0dmFtPSz9FGZILsxIzHWpAcAK5wDvLWuQ2s4hKJdX0uaJX7imnKxe9w1W52yrNrJRKiI-YzcF0M4kcXbfma0JgQ7mPF8AH$>

>

>

>

> --

>

>

>

> 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__;!!K-Hz7m0Vt54!mZ6U-5ef-FwMtvk7aI512iZKTS20PMt72wzLingnjcBUoo1ETmzgxIYYk_qPcMmHbtcEowX7XXdRKk_R_lJbhAPAULQvFQ$>

>

>

>

>

>

> _______________________________________________

> statnet_help mailing list

> statnet_help at u.washington.edu

> http://mailman13.u.washington.edu/mailman/listinfo/statnet_help

> <https://urldefense.com/v3/__http:/mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!Jy0dmFtPSz9FGZILsxIzHWpAcAK5wDvLWuQ2s4hKJdX0uaJX7imnKxe9w1W52yrNrJRKiI-YzcF0M4kcXbfma0JgQ7mPF8AH$>

>

>

>

> _______________________________________________

>

> statnet_help mailing list

>

> statnet_help at u.washington.edu

>

> https://urldefense.com/v3/__http://mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!Jy0dmFtPSz9FGZILsxIzHWpAcAK5wDvLWuQ2s4hKJdX0uaJX7imnKxe9w1W52yrNrJRKiI-YzcF0M4kcXbfma0JgQ7mPF8AH$ <https://urldefense.com/v3/__http:/mailman13.u.washington.edu/mailman/listinfo/statnet_help__;!!CzAuKJ42GuquVTTmVmPViYEvSg!Jy0dmFtPSz9FGZILsxIzHWpAcAK5wDvLWuQ2s4hKJdX0uaJX7imnKxe9w1W52yrNrJRKiI-YzcF0M4kcXbfma0JgQ7mPF8AH$>

>

> _______________________________________________

> statnet_help mailing list

> statnet_help at u.washington.edu

> http://mailman13.u.washington.edu/mailman/listinfo/statnet_help

>

> _______________________________________________

> statnet_help mailing list

> statnet_help at u.washington.edu

> http://mailman13.u.washington.edu/mailman/listinfo/statnet_help

>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman13.u.washington.edu/pipermail/statnet_help/attachments/20231209/372aa9c1/attachment.html>