I'm looking for methodological advice on the undertaking described below. I tried to simplify as much as possible and hope its comprehensible this way - if not, please pardon my ignorance and shoot any question on points i might be missing.
Background of planned analysis in a nutshell:
I have observational data on probands who may choose to go "way1" oder "way2". I assume that way1/way2 affect probands' happiness in a different way and want to explain WHY they do. I assume way1/way2 differ between certain characteristics (observed variables A, B and C as well as unobserved covariates).
I have data on probands for different timepoints - before choosing way1/way2 and after the way is completed. Data includes happyness, way chosen, variables A B C and (some more) reasons for chosing between way1/way2.
I consider way2 a "treatment" with probands self-selecting into treatment-/controlgroup. I assume that self-selection is not randomized but biased by certain variables, with happiness amongst them (more happy people are more likely to choose way2). I want to estimate the treatment effect and analyse which portion of the treatment effect can be explained by A, B and C.
I used Propensity Score Matching to tackle self-selection-bias and estimate the average treatment effect on the treated. Results indicate that probands' who chose way2 are significantly more happy, while ~50% of this difference between control-/treatmentgroup after treatment could be attributed to self-selection into treatment. So I assume there is a treatment effect, meaning way1/way2 and their characteristics A B C should influence probands' happiness.
Now I want to sort of "decompose" the treatment effect into effects of self-selection as well as effects of A, B, C (and unobserved covariates that distinct between way1/way2): How much of a role do A B C play in increasing probands' happiness?
Any advice which method might be eligible for this kind of analysis?
Thanks alot Erik