Regression-based Sensitivity Analysis Method

Currently, only one regression-based method is implemented in the SA Toolbox.

Regression

This method calculates first-order sensitivity indices by using a linear combination of polynomial functions fitted by a linear least-squares regression.

Explanation:
This method fits a linear (degree = 1) or polynomial (degree \(>\) 1) function between each input parameter and the output.
Polynomial regression allows the relationship to change direction – for example, to model U-shaped or S-shaped trends – and can therefore detect nonlinear relationships.
However, polynomial regression still assumes a specific functional form (a polynomial) and may not capture highly irregular or highly oscillating nonlinear or discontinuous relationships.
The SI are empirical estimates of the first-order effects. They are derived for each input parameter from the variance in the fitted output divided by the variance in the observed (original) output.

Implementation:
This method is implemented in Sensitivity Analysis → Setup → First-Order Effects → Regression.

User-specified software options:

Description	Data Type	Range	Default
Degree Controls the polynomial order used to approximate the relationship between each input parameter and the output. Behaviour Increasing degree gives more flexibility to the polynomial, and nonlinear relationships between input parameters and output might be captured better. As a consequence, the SI may increase. If degree is too high, overfitting may occur. As a consequence, the confidence intervals can widen, and the SI estimates may become unstable.	integer (positive)	not specified	2

Notes

Unsuitable entries, e.g. values outside the permitted or suitable range, will not trigger a warning message in the GUI.

Sampling methods:

Compatible with all sampling methods.
Assumes independent parameters.

References

Rabitz, Herschel; Alış, Ömer F. (1999): General foundations of high-dimensional model representations. In: J. Math. Chem. 25 (2‐3), 197–233.
Sudret, Bruno (2008): Global sensitivity analysis using polynomial chaos expansion. In: RESS 93(7), 964–979.