# Sensitivity Analysis for Hierarchical models

**URL:** <https://uqworld.org/t/sensitivity-analysis-for-hierarchical-models/3638>\
**Category:** Community Q&A and How To\
**Created:** [May 14, 2024, 12:08pm UTC](https://uqworld.org/t/sensitivity-analysis-for-hierarchical-models/3638 "2024-05-14T12:08:10Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Satyajeet\_Bhonsale](https://uqworld.org/user_avatar/uqworld.org/satyajeet_bhonsale/32/1699_2.png) [@Satyajeet\_Bhonsale](https://uqworld.org/u/Satyajeet_Bhonsale)\
**Post date:** [May 14, 2024, 12:08pm UTC](https://uqworld.org/t/sensitivity-analysis-for-hierarchical-models/3638/1 "2024-05-14T12:08:10Z")

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Hello, i have a hierarchical model structure as follows:

![Screenshot 2024-05-14 140636](https://uqworld.org/uploads/default/original/2X/c/cbd960720506530ea8f673aa7883f31268d572af.png)

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.

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**Author:** ![bsudret](https://uqworld.org/user_avatar/uqworld.org/bsudret/32/224_2.png) [@bsudret](https://uqworld.org/u/bsudret)\
**Post date:** [May 16, 2024, 8:54am UTC](https://uqworld.org/t/sensitivity-analysis-for-hierarchical-models/3638/2 "2024-05-16T08:54:58Z")

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Dear Satyajeet

The question you ask has been addressed in the PhD thesis of Yann Caniou (2012) that you can download with this [link](https://sudret.ibk.ethz.ch/research/publications/doctoralTheses/y--caniou.html). This is where ANCOVA with polynomial chaos expansions has been developed.  
You can find ANCOVA indices in UQLab indeed.

Best regards  
Bruno

**References**  
[1] Caniou, Y., 2012. [Global sensitivity analysis for nested and multiscale models](https://ethz.ch/content/dam/ethz/special-interest/baug/ibk/risk-safety-and-uncertainty-dam/publications/doctoral-theses/ThesisCaniou.pdf). PhD thesis, Université Blaise Pascal, Clermont-Ferrand.  
[2] Sudret, B., Caniou, Y., 2013. [Analysis of covariance (ANCOVA) using polynomial chaos expansions](https://www.research-collection.ethz.ch/bitstream/handle/20.500.11850/78972/eth-8010-01.pdf), in: Deodatis, G. (Ed.), Proc. 11th Int. Conf. Struct. Safety and Reliability (ICOSSAR’2013), New York, USA.