Sensitivity Analysis for Hierarchical models

Hello, i have a hierarchical model structure as follows:

Screenshot 2024-05-14 140636

obviously x contributes to the variance of y. But i want to find what percent of the variation is coming via r (function of x). Is this something i can get via ANCOVA?

Thanks a lot.

Dear Satyajeet

The question you ask has been addressed in the PhD thesis of Yann Caniou (2012) that you can download with this link. This is where ANCOVA with polynomial chaos expansions has been developed.
You can find ANCOVA indices in UQLab indeed.

Best regards

[1] Caniou, Y., 2012. Global sensitivity analysis for nested and multiscale models. PhD thesis, Université Blaise Pascal, Clermont-Ferrand.
[2] Sudret, B., Caniou, Y., 2013. Analysis of covariance (ANCOVA) using polynomial chaos expansions, in: Deodatis, G. (Ed.), Proc. 11th Int. Conf. Struct. Safety and Reliability (ICOSSAR’2013), New York, USA.