I have a dataset about university students and their educational success. I would like to investigate how student sex influences the chances of graduation, but sex correlates with many other predictors, like the topic of study. I thought about using propensity scores matching to deal with this entanglement, but here the casuality is the reverese of the typical propensity scores settings: the study topic cannot influences the students sex (my "treatment"). Is it still valid to use propensity score methods? Or should I use other technique? What other technique could I use? Most of the solutions to the multicolinearity problem is designed for the prediction, rather than the inference, like the principal component transformation, in which I would lost my original variable of interest.
If your "treatment" is sex and your "outcome" is educational success (perhaps measured by grades), then conditioning on anything on the causal path between sex and success in your analysis will create bias. As a result, the usual advice is not to use something like PSM for this, as these methods are meant for dealing with pre-treatment confounding variables.
The question of what you should do instead is a little trickier. I think it's unclear what precisely is meant by
how student sex influences the chances of graduation
There are a few ways to think about this question, and without clarifying the counterfactual you're thinking about it's hard to recommend a more specific course of analysis to help you answer it.
Edit: You've clarified that you "would like to show that the effect of sex is not fully explained by the effect of other variables I have access to". In this case, you are looking at how much of the causal effect of sex flows through a particular set of intermediate variables on the path to your outcome, and you are performing a mediation analysis. This paper explains a general view of mediation analysis, and it has an accompanying R package plus a Python equivalent.
$\begingroup$ I would like to show that the effect of sex is not fully explained by the effect of other variables I have access to. That's why matching looks promising to me, as it provides a logic of something like "the other variables being almost equal, the sex still influences the outcome". $\endgroup$ Feb 15, 2021 at 16:21
$\begingroup$ Got it - I've updated my answer to point you to some references and methods that you might find useful for that. $\endgroup$ Feb 15, 2021 at 17:00