f² Effect Sizes: Indirect and Total

[rjb285]

SmartPLS provides the output for f² direct effect sizes but not indirect or total. I've seen that the following equation can be used to calculate f² effect sizes:

f² = (R²_included - R²_excluded) / (1 - R²_included)

My questions are: 1) can the above equation be used to calculate f² indirect and total effect sizes, and if so, do any extra steps need to be done besides using the above equation? If both f² indirect and total cannot be calculated with the above equation, 2) how can one interpret the size of indirect and total effects with the SmartPLS output provided (e.g., the mean values obtained via bootstrapping)?

Thank you.

[jmbecker]

It is not possible to calculate the f² effect size for indirect or total effects as only directly associated constructs influence R², hence it makes only sense to remove directly associated constructs to assess the R² difference.

Something similar that is used in mediation analysis is the VAF (variance accounted for), but it is sometimes not very straigtforward to interpret if you have mixed (positive and negative) effects.

[rjb285]

Thanks for the reply.

A few follow-up questions:

1. I do have mediating variables that are either positively or negatively related to the endogenous (dependent) variable, so if you have any suggestions on how to interpret VAF values when this is the case, it would be very helpful?

2. Is there a way to calculate effect sizes of mediating variables as well, aside from variance accounted for?

Thanks again.

[jmbecker]

1. For competetive mediation the VAF is simply not useful.

2. Nothing that I know. If you find something somewhere, I would also be interested in the approach.