Main Effect

The portion of output variance attributable to a single input parameter considered on its own, distinguished from its interaction effects with others.

Source: Saltelli et al. 2008

A main effect captures the influence a single input has on the output through its own variation, averaged over the others, and so measures its standalone importance. What it can miss is influence that the input exerts only in combination with others, its interaction effects, which do not appear in the main effect. An input with a modest main effect can still matter greatly if it interacts strongly, so relying on main effects alone can understate such a parameter. Both are needed for a full account. Saltelli and colleagues (2008) describe this.

Source: Saltelli et al. 2008

A main effect is measured by the first-order sensitivity index, calculated as the variance of the conditional expectation of the output given the input divided by the total output variance, which gives the share of variance explained by that input alone. It is estimated by Monte Carlo procedures that vary the input of interest while averaging over the others. The resulting fraction quantifies the input's individual contribution to output variability, excluding the extra effect that appears only through interaction with other inputs.

Source: Sobol 2001

A main effect is the output variance explained by an input on its own, while an interaction effect is the additional variance explained only when that input varies together with one or more others, beyond the sum of their individual main effects. So the main effect captures direct, individual influence, and the interaction effect captures joint influence. An input's total contribution is its main effect plus its interaction effects; a large gap between the two indicates that the input acts substantially through interactions rather than alone.

Source: Saltelli et al. 2008

Main effects are useful because they quantify how much each input individually contributes to output uncertainty, allowing inputs to be ranked for prioritisation, so that efforts to reduce uncertainty focus on those with the largest main effects. When main effects account for most of the output variance, the model behaves largely additively, simplifying interpretation. Comparing main effects with total effects also reveals the importance of interactions. Main effects thus support understanding which inputs drive the output and how simply the model responds to them.

Source: Saltelli et al. 2008

Relying on main effects alone can mislead when interactions are important, since an input with a small main effect may still be influential through interactions, which the main effect does not capture, and the main effects need not sum to the full output variance when interactions are present. Estimating main effects accurately can require many model runs. These limitations mean main effects are interpreted alongside total-effect indices, which include interactions, to avoid overlooking inputs that matter mainly through their joint action with others.

Source: Sobol 2001