Categories in RHEM effects

[Jingyi Sun]

Dear Prof. Lerner, 

Hope you are doing well! 

I want to ask if it is possible to specify RHEM effects where actors belong to two distinct categories. For subset repetition (e.g., UHE_SUB_REPETITION_STAT), is there a way to specify separate repetition effects involving only Category 1 actors, only Category 2 actors, and mixed-category subsets? Similarly, for triadic closure, is it possible to distinguish closure processes based on the category of the intermediary actor that induces closure, i.e., a Category 1 actor is the broker? 

Thank you very much for your time!

Best,

Jingyi Sun

[juergen lerner]

Dear Jingyi Sun,

Depending on your setting and data, there might be two different ways to specify this. (1) All the actors are basically of the same type (eg "persons") but they have a binary attribute indicating whether they belong to Category 1 or Category 2. (2) You have two different types of nodes (like "scientists" and "papers", just here called "Cat1" and "Cat2") as in a two-mode network, in which case you could still have interaction events among nodes within each of the categories or between the two categories.

I think that you describe a setting that belongs to the first option, but I also wanted to mention the second possibility.

If it's indeed the first option, then you would define in your data dummy events that set the category of nodes (1 or 2) and you store that in a node attribute "node_category". Then, in addition to subset repetition, you define a statistic of type UHE_NODE_STAT which averages the category-membership values for the nodes in the hyperedge (call that "avg_node_cat"). Then in the output table you can recognize whether all nodes in the hyperedge belong to Category 1 (avg_node_cat=1), or all belong to Category 2 (avg_node_cat=2), or whether it is a mixed hyperedge. So you have an indicator for three different types of events which you can interact with a subset repetition statistic.

For distinguishing triadic closure dependent on the category of the intermediat node, you define the argument "node-level attribute" in the UHE_CLOSURE_STAT. See the explanation here:
https://github.com/juergenlerner/eventnet/wiki/RHEM-effects-(reference-guide)#triadic-closure

If your setting is rather the second option you would set up a model for directed hyperevents with "source nodes" are those from category one and "target nodes" are those in category two. Then you would also have all the possibilities specify different versions of subset repetition and closure. Then it would be similar to the setting described here:

https://github.com/juergenlerner/eventnet/wiki/Coevolution-of-collaboration-and-references-to-prior-work-(tutorial)

Best wishes,

  Juergen

[Jingyi Sun]

Dear Prof. Lerner, 

Thank you very much for the quick response! My setting is essentially the first option. If I understand correctly, UHE_NODE_STAT with the average of category membership values is a hyperedge-level variable for the current hyperedge, rather than a summary of the history. Hence, the interaction effect between subset repetition and UHE_NODE_STAT can be interpreted that the subset repetition effect is stronger/weaker for a certain hyperedge type (e,g,, all Category1, all Category 2, or mixed). I am wondering if it is possible to differentiate subset repetition (e.g., repetition of 2) into three categories: 1) repetition of two nodes both from Category 1, 2) repetition of two nodes both from Category 2, 3) repetition of two nodes from both Categories, and similar differentiation for repetition of 3 or more. 

Thank you very much for your time!

Best,

Jingyi

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[juergen lerner]

Dear Jingyi,


I had to think a while about whether this is possible. Indeed in the solution that I've mentioned before, this differentiation is not achieved. For example, if the new hyperedge has three nodes, two from Cat1, one from Cat2, and the two from Cat1 had co-participated in a prior event. Then subset repetition would tell you that two out of three dyads had a prior event and the node stat statistic would tell you that two out of three nodes are in Cat1. But you would get the same values in both statistics if the prior event involved one node from Cat1 (but not the other) and one from Cat2. So it does not make the distinction you indicated.

I think that this can (almost - see below) be achieved by coding the events as directed hyperedges, where the Cat1 nodes are considered as sources and the Cat2 nodes as targets. (It assumes that nodes keep their category membership forever.) Then the three versions of subset repetition would be achieved by three specifications of DHE_SUB_REPETITION_STAT, where once you have source size = 2 and target size = 0, once the sizes are (0,2) and in the third variant it is (1,1). See:
https://github.com/juergenlerner/eventnet/wiki/RHEM-effects-(reference-guide)#directed-subset-repetition-and-subset-reciprocation

You have to set up the entire configuration, also the observations, and also the input data, for directed hyperedges.

The problem (the "almost") is that these "directed hyperevents" need at least one source and at least one target. (It's simply due to each row in the input data must include one source node and one target node.) This translates to each event must have at least one node from each category - which I think might not always be the case in the data (perhaps we are lucky and it is the case).
I'm currently working on a new version of eventnet supporting "generalized hyperevents" that can have not only sources and targets (as directed hyperevents) but they can decompose in any number of subsets (or categories) and - important for your case - these subsets can also be empty in some events. A pre-release version might be released soon (some weeks).

Hope it helps.

  Juergen

[juergen lerner]

Well it is "one out of three dyads had a prior event" instead of "two
out of three dyads had a prior event" ...
Juergen

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[Jingyi Sun]

Dear Prof. Lerner, 

Thank you very much for the explanation! Indeed, we don't always have one node from each category for each hyperevent. I am very much looking forward to the new version of "generalized hyperevents"! Thank you again for your time!

Best,

Jingyi

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[Jingyi Sun]

Dear Prof. Lerner, 

I am fitting a directed relational hyperevent model with two statistics on the source set. The first is DHE_SUB_REPETITION_STAT of order (2,0) on a DIR_HYPER_LEVEL attribute, capturing whether two nodes have previously appeared in a hyperedge together. The second is DHE_CLOSURE_STAT on a DYAD_LEVEL attribute, capturing whether two nodes share a third-party neighbour. I would like to cross-classify the dyads inside a hyperedge on these two prior relationships, giving four types — neither, shared partner only (indirect only), direct only, and closure (both). The difficulty is that DHE_CLOSURE_STAT aggregates over all dyads in the hyperedge, so it mixes the indirectly only cases and closure cases. Is there a configuration that can separate the four types? I can do the split post hoc, but prefer it to be native from eventnet.

Thank you very much for your time!

Jingyi

[juergen lerner]

Dear  Jingyi,

Currently, there is no such statistic. If you interact the subset-repetition statistic and the closure statistic as given in the eventnet output table, then (as you correctly pointed out) the interaction is done after values are aggregated over all dyads within the hyperedge. For example, the hyperedge may contain some dyads with and without prior interaction and some dyads with and without indirect connections but you don't know how the two times two cases are matched. In contrast you want to interact the two criteria, direct connection or not and indirect connection or not, per dyad (and maybe then aggregate these values over dyads afterwards). Such a statistic would indeed be different to the interaction after aggregation, but it is currently not implemented. 

I'll keep it in mind for future extensions. To better understand the scope of such an extension, could you sketch an application (if possible)? I would like to see some setting and research question in which the interaction of the aggregated values is insufficient but where the dyadwise interaction (before aggregation) is needed.

Best wishes

  Juergen

[Jingyi Sun]

Dear Prof. Lerner, 

Thank you for your reply. In my case, subrepetition (2,0) and closure are highly correlated. I think it's because the same events (e.g., three collaborators) generate both statistics. The repetition statistic contains both direct only and closed closure, and the closure statistic contains both indirectly only and closed closure. I think in the case of collaboration, it may be helpful to differentiate the three cases. 

Best regards,

Jingyi

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