totaleffectindices

Totaleffectindices, or total effect indices, are a family of sensitivity measures used in global sensitivity analysis to quantify how much an input variable contributes to the variance of a model’s output, including all its interactions with other inputs. They provide a comprehensive assessment of an input’s influence beyond its isolated, direct effect.

In variance-based sensitivity analysis based on Sobol decomposition, the total effect index for an input i, often denoted S_Ti, represents the sum of all terms in the output variance that involve Xi, including all higher-order interactions with any combination of other inputs. Practically, S_Ti can be interpreted as the fraction of output variance that would remain if Xi were varied along with all interactions removed, or equivalently, the fraction of variance explained by Xi when considering every possible interaction.

Total effect indices are always nonnegative and typically lie between 0 and 1. They satisfy S_Ti ≥ S_i, where S_i is the first-order (main) effect index for Xi, reflecting that totals capture both direct and interactive contributions. High S_Ti values indicate that an input is influential not only on its own but also through interactions with other inputs, whereas low values suggest a minor overall impact.

Calculation of S_Ti relies on sampling-based estimators, such as those derived from Saltelli or Jansen methods, and requires a model to be evaluated across a designed set of input samples. These indices are widely used for model reduction, screening of inputs, and uncertainty quantification, helping to prioritize factors and understand nonlinearities and interactions in complex models.