[statnet_help] ergm inquiry

[Carter T. Butts]

Hi, Julia -

To add to Michal's excellent observations:

   - You seem to have a lot of out-isolates and in-isolates that you are 
not catching.  (They may be isolates per se - both out and in - but we 
can't tell from these plots.)   Not accounting for that can lead to 
edges being too uniformly dispersed through the network.  You may thus 
want to consider idegree(0), odegree(0), and/or isolates() terms, if 
there is not a covariate that accounts for the structure.

   - As Michal observes, you clearly have some very locally dense 
clusters, and it is unlikely that you will capture them using a 
homogeneous clustering term - while exceptions exist, these are usually 
associated with inhomogeneity, generally clustering around a specific 
attribute, affiliation, etc.  His suggestions for dealing with that are 
very apposite.  But an even more basic suggestion is to do more 
exploratory investigation of your network.  Have you tried plotting the 
sociogram, and coloring the nodes by their attributes?  If the graph is 
too dense to easily see what is going on, the following can help:

      - Increase the translucency of your edges.  This One Weird Trick 
is very simple, but very useful - if the graph is dense, don't be afraid 
to make the edges so transparent that they are barely visible!  When 
combined with varying the shape/color of nodes by attribute, this can be 
very revealing of internal structure, and particularly of where your 
clustering is coming from.  The edge.col option in plot.network or sna's 
gplot function can be used for this quite easily.

      - Take the graph apart, using degree kcores.  The kcores() command 
in sna will give you the core number for every vertex in the network, 
using your favorite centrality measure; the default is Freeman degree, 
which is probably a good starting point for your network.  Try 
sequentially plotting the induced subgraphs for each core (i.e., 
everything in the 1 core, the 2 core, the 3 core, etc.), again coloring 
the nodes by their attributes.  (Page 24, figure 4 of this paper has an 
example of this approach: 
https://sciendo.com/article/10.21307/joss-2019-027)  What this will do 
is strip away the less cohesive parts of the network, revealing highly 
cohesive subgraphs that may otherwise be obscured by the surrounding 
structure.  If you look at figure 8 in that same paper, you'll see an 
example where that is used to reveal the presence of several highly 
cohesive, homophilous clusters that are not evident if you look at the 
whole graph (which is both very large and adorned with pendant trees).  
Knowing the composition of the "deep" portions of the network will often 
give you strong indications of what is shaping it, and of what terms you 
will need in your model.

      - Plot distributions of degree and other structural indices by 
attribute.  Simply looking at these distributions can be revealing - in 
addition to in/outdegree heterogeneity, examining e.g. cycle or clique 
membership can be another way to detect heterogeneity in local 
structure, all of which can inform your choice of graph statistics.  
(Beyond nodal covariate effects and terms like nodematch/nodemix, note 
that inhomogeneous versions of e.g. degree and gwdegree exist, and can 
be useful when you have groups that interact in very different ways.  
Even localtriangle can sometimes be helpful, if you have very small 
groups whose patterns of cohesion cannot be captured with mixing terms.)

Those are just a few examples, but the general suggestion is to do more 
exploratory analysis to try to understand the network and its structure 
(and build your model around that), rather than trying to rely entirely 
on gof plots to infer what is going on. The latter does sometimes work, 
especially if the network is very simple, but complex cases usually 
require a combination of substantive insight (i.e., thinking about what 
the network is, where it came from, how it was measured, etc., and about 
how those things would be expected to shape the observed structure) and 
exploratory analysis (to reveal major quirks and inhomogeneities, 
provide clues about good term candidates, etc.).  Another benefit of 
putting more time into these pre-modeling efforts is that they usually 
give you a much better sense of what is interesting/important about the 
structure, which can greatly improve your model assessment strategy (by 
giving you more refined targets) and help you use and interpret the 
resulting model more effectively.  I know that, in my own work, I've 
often (almost always?) discovered that the things that turned out to be 
interesting/important about a network were not the ones that I expected, 
and that building effective models has really depended on developing 
those insights.  Fortunately, we have a very rich array of tools and 
concepts from classical social network analysis that can help us here!  
When one's modeling efforts are stuck, I find it can often be useful to 
go back to basics in order to determine what to try next.

Hope that helps,

-Carter

On 8/11/23 7:50 AM, Julia Vassey wrote:

> Thank you Michal! Good to hear from you.

>

> Please, see the plots, attached. I have tried changing the decay

> parameter multiple times, and the model fit gets better when

> increasing the parameter: from 0 to 0.3 (gwesp(0.3, fixed = TRUE)),

> but beyond 0.3 the model starts having issues with convergence.

> p values for all esps are always very low.

>

> Thank you for helping!

>

> Julia

>

>

> On Fri, Aug 11, 2023 at 8:53 AM Michał Bojanowski <michal2992 at gmail.com> wrote:

>> Hi Julia,

>>

>> Can you send the GOF plots attached? In what way does the ESP not fit

>> well? Perhaps it is a matter of changing the decay parameter?

>>

>> Michal

>>

>> On Wed, Aug 9, 2023 at 1:00 PM Julia Vassey <vassey at usc.edu> wrote:

>>>

>>> Dear All,

>>>

>>> This is my first time posting a question in statnet help. If the question needs to be posted/sent to a different email please let me know.

>>>

>>> I have a question related to ergm. I am running an ergm model on a directed unipartite network of ~100 nodes (certain social media users) and ~700 edges. The model includes geolocation attributes of the nodes (geographic regions) and themes the nodes post about on social media.  The model also includes terms (mutual, gwesp) provided in the code below.

>>>

>>> I am struggling with achieving a decent goodness of fit for edgewise shared partners using gof function. i/o degree, geodesic distance and model statistics look much better. I tried different things to try to improve edgewise shared partners, but nothing seems to work. The configuration below provides the best fit, however, I want to keep trying to improve the fit for edgewise shared partners. I appreciate any thoughts and comments on how to achieve this.

>>>

>>> model = ergm::ergm(netg_infl ~ edges + nodefactor('region_code', levels = -4) + nodematch('region_code', diff = T, levels = -3) + nodefactor('topic_sum_binary', levels = -LARGEST) + nodefactor('marijuana_recode', levels = -c(1,3)) + nodefactor('nature_recode', levels = -c(1,3)) + nodefactor('health_life_recode', levels = -c(1,3)) + nodefactor('gaming_recode', levels = -c(1,3)) + nodefactor('food_recode', levels = -c(1,3)) + nodefactor('clothing_recode', levels = -c(1,3)) + mutual  + gwesp(0.28, fixed = TRUE) + offset(isolates), offset.coef = -Inf, control=control.ergm(parallel=2, parallel.type="PSOCK"))

>>>

>>> Thank you,

>>>

>>>

>>> --

>>> Julia Vassey

>>> Health Behavior Research

>>> Department of Population and Public Health Sciences

>>> Keck School of Medicine

>>> University of Southern California

>>>

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