How to measure marginal effect of interdependent variables on a binary outcome? My data represents observations on a possible sequences of events that may lead to a positive outcome (y).
Each event (A, B, C, D) is dependent on the previous event; for D to occur C must occur, for C to occur B must occur, for B to occur A must occur.
Some example rows to illustrate:




A
B
C
D
y




0
0
0
0
0


1
0
0
0
1


1
1
1
0
0


1
1
0
0
1


1
1
1
1
1




I'd like to measure the relative impact of each event on the probability of y. For example, I'd like to be able to make statements such as "Event B increase the probability by 10% compared to if only Event A occurs. However Event C only increases the probability by a further 1%".
I've considered using logistic regression. However, I have a concern that due to the inherent collinearity in the data the regression coefficients will not be reliable to infer from.
What possible methods could I use/explore?

It looks like a Bayesian problem. The probabilities of each event are not independent of one another, so logistic regression is unlikely to work since its underlying assumption is violated.
You can build a Bayesian network where each event A, B, C, D and y are nodes and use Expectation Maximization algorithm to estimate the probabilities of each event given the other ones.
Have a look to this blog post for a nice introduction of Bayesian Belief Network
