Coalitional effect in logistic regression and assessing explanarory variable contribution
I have a problem that could be described as logistic regression with all dichotomous variables: 1 response variable (DV) Y (I would call it later as a feature/violet star) and 5 explanatory variables (IVs) A, B, C, D and E (also binary).
What's most important, I'm trying to infer which IVs contribute the most to Y and preferably somehow assess quantitatively their severity (something like ranking predictors, variable selection, etc.)
Of course, before I sent this post, I've made some reconnaissance, but I'm not sure if articles I've found reflect my problem properly, because of it's strong cooperative nature. It's very similar to coalitional games and Shapley value, but I'm not sure whether I can use it in this particular case and also I would like not to "preach to the converted" and would rather use something proven and well-tried.
Could you have a look on the situation below and recommend some methods, articles, books, etc. how to infer which explanatory and to what extent contribute the most to response Y (feature/violet star).
Let's say, we have five different objects denoted as labelled balls: A, B, C, D, E creating some subsets and the single special feature of interest marked as violet star. If the star is filled, the feature is present in a specific set, whereas hollow star denotes its absence.
Any subset of these five objects (there're $2^5 - 1$ possible types of such nonempty subsets) can appear many times, sometimes with the feature being present and sometimes without it, as depicted below, where there're six instances of the full set and $\frac{2}{3}$ of them have the feature.
We can assume (if it's needed) there's always at least one instance of the full set with the feature present (for example the one marked with thicker red envelope).
For every of the $2^5 - 1$ possible nonempty subsets we have three values, e.g. 946
for (A, C, E):
* $F_{ACE}$ - number of all occurrences of subset (A, C, E) \textbf{with} the feature.
* $N_{ACE}$ - number of all occurrences of subset (A, C, E) \textbf{without} the feature.
* $T_{ACE} = F_{ACE} + N_{ACE}$ - simply total number of all appearances of subset (A, C, E).
The cardinalities of instances $T_X$ of every subset type $X$ can be different, but there's a very obvious and rather trivial rule that if $X \subset Y$ then $T_X \geq T_Y$. For example, $(A, C, E) \subset (A, B, C, D, E)$ thus $T_{ACE} \geq T_{ABCDE}$. That's because any instance of subset (A, B, C, D, E) is at the same time an instance of (A, C, E), but for narrower (A, C, E) we can have more instances.
In this description I use six instances for each subset type just bacause of limited space for pictures and those six instances are intended to reflect the overall proportion between instances having and lacking the feature.
Among all these $2^5 - 1$ types, some of them are more likeli to have the feature (for this particular subset/type, there're more instances with the feature than without it), whereas other types are more prone to lack it. Please look at two figures below and the following numbers:
$$ \frac{F_{ACE}}{T_{ACE}} = \frac{5}{6}, ~~ \frac{F_{BD}}{T_{BD}} = \frac{1}{6}, ~~ \frac{F_{ABCDE}}{T_{ABCDE}} = \frac{4}{6} ~\text{(the situation of the very first picture)} $$ A blatantly obvious property is that in my model the ratio $\frac{F}{T}$ is not monotonic (in neither direction) with respect to inclusion relationship.
And finally the most crucial property I would like to make my model had, is some kind of cooperative interaction between objects in subset, which is the last thing I'm going to describe beneath. 945