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Mplus Discussion > Structural Equation Modeling >
 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:

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 (

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

 Robert Archer posted on Friday, February 08, 2019 - 11:53 am
Good afternoon Dr. Bengt and Linda Muthen, I wanted to verify my understanding from this post. In order to calculate the percentage of the effect that is mediated by a specified model, the standardized "total indirect estimate" should be dived by the standardized "total estimate," correct?
Also, are there handouts that discuss the significance levels of the total effects versus total indirect effects? I would like to read up more on what this means. Thank you much for your time and any information that can be provided. Have a good weekend.
 Bengt O. Muthen posted on Saturday, February 09, 2019 - 11:13 am
This is a good general question for SEMNET.
 Robert Archer posted on Saturday, February 09, 2019 - 3:23 pm
Thank you much.
 Joanna Davies posted on Friday, May 22, 2020 - 8:27 am

im running a multiple mediation model with 2 exposures, 2 binary outcomes and 3 mediators.

From the model indirect output i get the 'total' effect and the 'specific indirect' effects

Can i report the proportion mediated by a specific path (specific indirect/total) as the % of the total effect mediated by m?

Are there any limitations on this interpretation because of my multiple mediators or the binary outcomes?

Is the 'total' effect reported the PNDE or the TNDE? and are the 'specific indirect' PNIE and TNIE?

Thank you.
 Bengt O. Muthen posted on Saturday, May 23, 2020 - 5:30 am
I don't see how you get the counterfactual effects that you mention in your case where you have 3 mediators - they are developed only for 1 mediator (although we have an article posted on our Mediation page that shows how to do it for multiple mediators). Send output to Support along with your license number.
 Joanna Davies posted on Saturday, May 23, 2020 - 7:45 am
Ok, thank you. I read the Nguyen 2015 paper. I see that a counterfactual interpretation with multiple mediation requires more thought.

Avoiding the counterfactual terms, is a simple effect decomposition possible with my model?

I want to say that the total effect of y on x is -0.127, and the specific indirect effect mediated by m is -0.044, therefore 34.6% of the total effect of x is mediated by m.

Is this interpretation/calculation of the decomposed effect only possible in the case of one mediator?

Many thanks
 Bengt O. Muthen posted on Monday, May 25, 2020 - 4:20 pm
That may be a good question for SEMNET.
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