[statnet_help] A couple of questions on modeling two-mode networks

[Michał Bojanowski]

Hi Steffen,



> - The b1degree term works very well, this is great. Do I understand correctly that, given the cross-sectional nature of the data, I should try to think less in terms of tendencies ("Actors who already have a lot of ties will likely form more ties in the future.") but rather try to model observed network features ("Most actors will only have one tie.") and then leave out other features (for reference, only 14 actors out of the 9.5k have 4 ties to groups)?


I think in the cross-sectional ERGM context an
interpretation/narrative referring to tendencies is still valid:

1. ERGM is a probabilistic model so it specifies that certain ties are
more likely than others in the sense of conditional probabilities.
Thus, a statement "girls tend to befriend girls" refers to the fact
that, ceteris paribus, tie probability in girl-girl dyads is higher
than in, say, girl-boy and so on. But, as you wrote, the statement
does not refer to any observed future. In particular, it does not
imply that: should we keep observing the network all the girls will
befriend all the other girls.
2. Cross-sectional ERGM, like a dynamic SAOM, does have a
micro-process behind it, but: (1) the dynamics is tie-based rather
than node-based, and (2) the focus is on the equilibrium of that
process rather than change. In that sense over time the ties will form
and dissolve but with probabilities such that on average, say, the
proportion of connected girl-girl dyads will be stable at a
model-specified level. See also Chapter 11 of Lusher-Koskinen-Robins
book and the dynamic ERGMs such as TERGM and the `tergm` package.
3. Things are similar with node-related network characteristics, e.g.
number of nodes with specific degree, say 1. Given a model, according
to the ERGM micro-process the number of nodes with degree 1 will
fluctuate stochastically but it should be stable in the long run
around the number specified by the model parameter(s).
4. All of the above assuming the model is not degenerate...




> - My actors do not share any attributes with the groups. So if I want to model "likelihood of being part of two firms (groups) from the same industry" I should rather use b1starmix and probably neglect b1star altogether?


Yes, exactly.



> - The help page has a gwb2degree, which I assume is the bipartite version of gwdegree. Say I use this with an interval-scale attribute (values 1-10) which reflects regulation of groups (I am basically modelling institutional oversight), then a positive parameter would mean that: "The more subject a group is to regulation, the higher the likelihood of having actors as members who are also present in other groups."?


Of course! I missed that term, sorry! However, for the above mechanism
I think you rather want the b2cov term, the parameter of which will
essentially have a regression-like interpretation: a positive value
will mean the higher the oversight the more attractive the group is
for the actors (greater group degree). The gw2degree() would rather
represent a kind of "cumulative attractiveness of groups" mechanism,
namely: the more members the group has the more members it tends to
attract (where "tendency" has the meaning as above).



Best, Michał