Proportion of total effect mediated
Message/Author
 Jon Heron posted on Wednesday, August 03, 2011 - 8:25 am
Hi Bengt/Linda,

I have a simple mediation model in which X, M and Y are all binary. I am interested in the proportion of the effect from X to Y which is mediated through M. My Mplus model:

MODEL:
Y on X M; M on X;
model indirect: Y IND X;

gives a total effect of 0.386 and total indirect of 0.149, so I get a proportion of 0.149/0.386 = 38.6%

As I am aware of the issues regarding mediation involving binary variables, I have been attempting to replicate these figures using Stata (-binary_mediation- function) and also using the excel spreadsheet from Nathaniel Herr's website (http://nrherr.bol.ucla.edu/Mediation/logmed.html).

These are based on the same approach and both report that the proportion mediated is 22.9%

Now the stata/Herr approaches scale the a/b/c/c' parameters by ratios of SD's such that the indirect effect, and hence the proportion mediated, are derived from figures that bear little resemblance to the original regression models.

In contrast, the total effect in my Mplus analysis is clearly just the c-path were I just to regress Y on X. It seems that Mplus has a slightly different scaling routine such that the regression equation for M on X maintains it's residual variance of 1, whilst the equation for Y is scaled - presumably to render the parameter estimates comparable.
 Jon Heron posted on Wednesday, August 03, 2011 - 8:26 am
Is this slightly different approach enough to explain this rather large discrepancy?

thanks, Jon
 Linda K. Muthen posted on Wednesday, August 03, 2011 - 3:24 pm
The difference is likely because in Mplus m is treated as m*, the latent response variable underlying m, both as a dependent and independent variable.
 Jon Heron posted on Thursday, August 04, 2011 - 5:37 am
Oh I see, thanks that makes sense

Jon