Solved – Interpreting Mediation Output when ACME is stat. sig but ADE and Total are not

This should not happen if you use only one mediator in the model. If there are other mediators for a negative hidden away, they should reflect in the direct effect.

But there are certain conditions under which it would happen. Most likely, the IV weakly relates or has no relation to the DV in these conditions.

# first, some syntax for Sobel's test sobel <- function(mm, my) {   a <- coef(mm)["x"]   ase <- coef(summary(mm))["x", 2]    b <- coef(my)["m"]   bse <- coef(summary(my))["m", 2]    abse <- sqrt(a ^ 2 * bse ^ 2 + b ^ 2 * ase ^ 2)   # return ACME and z-test   c(acme = a * b, z = a * b / abse, p = (1 - pnorm(a * b / abse)) * 2) }  set.seed(899398) n <- 100 x <- rnorm(n) m <- rnorm(1) * x + rnorm(n) y <- rnorm(1) * m + rnorm(1) * x + rnorm(n)  coef(summary(lm(y ~ x)))["x", ] # total effect not stat sig   Estimate Std. Error    t value   Pr(>|t|)  0.2125229  0.1470346  1.4453944  0.1515374   coef(summary(mm <- lm(m ~ x)))["x", ] # IV affects MV   Estimate Std. Error    t value   Pr(>|t|)  0.25667463 0.10464021 2.45292550 0.01593713   coef(summary(my <- lm(y ~ m + x))) # Only MV significant for DV               Estimate Std. Error   t value     Pr(>|t|) (Intercept) -0.06147867 0.09632753 -0.6382253 5.248309e-01 m            1.08186228 0.09104230 11.8830723 1.241992e-20 x           -0.06516366 0.09716138 -0.6706745 5.040217e-01  sobel(mm, my) # returns ACME, z and z-test of ACME     acme.x        z.x        p.x  0.27768660 2.40227887 0.01629328  

The conditions OP described are all present here. This is one example of how it could happen. In reality, the relationships are probably way more complicated but it definitely is possible. If you have a not statistically significant total effect and the mediated effect is statistically significant in a one mediator model, I'd doubt any mediation was going on.

The way I found this example was by using a search for the right seed:

find <- FALSE tab <- 1:1e6 while (find == FALSE) {   seed <- sample(tab, 1)   set.seed(seed)   n <- 100   x <- rnorm(n)   m <- rnorm(1) * x + rnorm(n)   y <- rnorm(1) * m + rnorm(1) * x + rnorm(n)   te <- coef(summary(lm(y ~ x)))["x", 4]   mm <- lm(m ~ x)   dme <- coef(summary(my <- lm(y ~ m + x)))[c("m", "x"), 4]   me <- dme[1]; de <- dme[2]   ie <- sobel(mm, my)[3]   if (te > .15 & de > .15 & ie < .04) {     find <- TRUE   } } 

It is possible to expand the search function to store all such conditions and study the patterns ACME, ADE and ATE that produce the OP's situation.