How to calculate effect size Kappa Squared for multiple parallel mediators?

Question

I was using the function mediation() from the package MBESS to calculate κ² (kappa squared) as the effect size for a single mediator model. How can I calculate κ² for a multiple mediator model?

I'm aware of Process for SPSS and SAS, but would have to go through the process of installing either software and familiarizing myself with it, so I would prefer a solution for R. The Process FAQ states: "There are some ambitious folks translating some of the PROCESS models into R and Mplus code. You can find those online." Unfortunately I haven't yet been able to find any of that R code, or none that fits my model (with two parallel mediators), so I hope one of you can possibly help me.

Here's my model:

I didn't yet dare install MEDMOD, as I'm on a Mac.

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Edit.

Ha. I actually installed SPSS and Hayes' Process macro, only to find out that "κ² [is] available only in models with a single mediator" (Hayes, 2013, p. 432). Bummer. Have to read Preacher & Kelley (2011) again to see wether κ² only applies to single mediator models, and probably choose another effect size index.

Sources:

• Hayes, A. F. (2013). Introduction to Mediation, Moderation, and Conditional Process Analysis. New York: Guilford.
• Preacher, K. J., & Kelley, K. (2011). Effect size measures for mediarion models. Psychological Methods, 16, 93-115.

Answer 1

I regret to say that kappa-squared has some pretty big flaws, and its continued use probably does more harm than good. I no longer recommend it. Please see:

Wen, Z., & Fan, X. (2015). Monotonicity of effect sizes: Questioning kappa-squared as mediation effect size measure. Psychological Methods, 20, 193-203.