Inquiry about Multilevel/Within-layer ties support in ALAAMEE

[ybxgood]

Hi Alex and team,

First of all, thank you for developing ALAAMEE – it's a great open-source tool!

I have a question regarding the support for multilevel (or multilayer) network structures in ALAAMEE.

1. Support for within-layer ties as covariates
I noticed that in BipartiteGraph.py, the insertEdge function explicitly raises a ValueError if an edge is inserted between nodes in the same mode. This makes sense for maintaining a strict bipartite structure for the dependent network.

However, for many empirical applications (e.g., organizational or social networks), we often have within-layer ties (e.g., ties among Mode A nodes, and ties among Mode B nodes) that are theoretically important to include as fixed covariates. These intra-layer networks might influence the formation of bipartite (cross-layer) ties or the contagion of an outcome attribute.

Does ALAAMEE currently support including such within-layer networks (as fixed, exogenous matrices) in the model? If not, is there a recommended workaround or best practice to incorporate these internal structures into an ALAAM analysis?

2. Future plans for multilevel ALAAMs
Since your other software, MPNet, supports more complex multilevel structures (e.g., configurations involving A, B, and X layers simultaneously, such as the ones listed in its manual), I was wondering if you are considering adding similar multilevel ALAAM capabilities to ALAAMEE in the future. This would be extremely valuable for researchers working with data where intra-layer and inter-layer dynamics co-exist.

3. A quick question about MPNet
Finally, since you are one of the core developers of MPNet, may I ask a quick question? When fitting certain models (especially with complex multilevel terms), MPNet sometimes fails to converge or shows an error. What are the most common causes for this, and what diagnostic steps would you recommend to identify the issue (e.g., model degeneracy, collinearity, insufficient MCMC iterations)?

Thank you again for your work and for your time!

Best regards

[stivalaa]

Thank you for your interest in ALAAMEE and your kind words.

There is no direct support for the kind of fixed within-layer networks you want as change statistics in ALAAMEE, although it should be easy enough to create such change statistics for your needs, based on those for dyadic covariates for auxiliary or "setting" networks (see changeStatisticsALAAM.changeSettingHomophily()) or distance matrices (see changeGeographicHomophily() and changeContagionDist()).

The "auxiliary" or "setting" network is briefly mentioned in:

Stivala, A., Wang, P., & Lomi, A. (2024). ALAAMEE: open-source software for fitting autologistic actor attribute models. PLOS Complex Systems, 1(4), e0000021. https://doi.org/10.1371/journal.pcsy.0000021

There is an example of using distance matrices in examples/simple/badgers/runALAAMSAbadgersDistance.py.

I no longer work in academia so do no further work on ALAAMEE (or MPNet). I did plan to implement multilevel structures (such as MPNet supports) in ALAAMEE, but that is not going to happen now (unless someone else does it).

The main (really, only) developer of MPNet is Dr Peng Wang (https://www.melnet.org.au/pnet) so you will have to contact him for technical questions about MPNet, but probably model near-degeneracy is the most common problem with complex models. You might have noticed that for ERGM there are special terms (like AltKTriangles for example) with decay values to help overcome these problems, but for ALAAM this is far more recent and experimental work with such terms only available in ALAAMEE but not MPNet. See:

Stivala, A. (2023). Overcoming near-degeneracy in the autologistic actor attribute model. arXiv preprint arXiv:2309.07338. https://arxiv.org/abs/2309.07338

Regards,
Alex.