Proportion mediated and mediated-to-direct ratio

For the single-mediator model M = i1 + a X, Y = i2 + cp X + b M, MacKinnon, Warsi and Dwyer (1995) define the proportion of the total effect that is mediated as \(ab / (c' + ab)\) and the ratio of the mediated to the nonmediated effect as \(ab / c'\). When the three path standard errors are supplied, first-order delta-method variances are returned. The core proportion is the same measure as PropMd (NIE over NIE plus NDE, with NIE = ab and NDE equal to the direct effect under the linear model) and is delegated to it rather than redefined. Variance forms: \(Var(PM) = (b^2 c'^2 s_a^2 + a^2 c'^2 s_b^2 + a^2 b^2 s_{c'}^2) / (c' + ab)^4\) and \(Var(ratio) = (b^2/c'^2) s_a^2 + (a^2/c'^2) s_b^2 + (a^2 b^2 / c'^4) s_{c'}^2\), the first-order (uncorrected) solutions in the same paper.

Usage

Propme(a, b, c_prime, se_a = NULL, se_b = NULL, se_c_prime = NULL)

Arguments

a

Path X to M.

b

Path M to Y adjusted for X.

c_prime

Direct effect X to Y adjusted for M.

se_a, se_b, se_c_prime

Optional standard errors of the paths.

Value

List with estimate, same_sign, indirect, total, ratio, method, and se, se_ratio when the standard errors are supplied.

References

MacKinnon, D. P., Warsi, G. and Dwyer, J. H. (1995), A simulation study of mediated effect measures, Multivariate Behavioral Research 30(1), 41-62, doi:10.1207/s15327906mbr3001_3; full text verified at https://pmc.ncbi.nlm.nih.gov/articles/PMC2821114/

Examples

Propme(a = 0.5, b = 0.4, c_prime = 0.3)[c("estimate", "indirect", "total", "ratio")]
#> $estimate
#> [1] 0.4
#> 
#> $indirect
#> [1] 0.2
#> 
#> $total
#> [1] 0.5
#> 
#> $ratio
#> [1] 0.6666667
#>