Binary Mediators and ML PreviousNext
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 Jon Heron posted on Wednesday, March 28, 2012 - 1:37 am
Hi Bengt/Linda

As you know, the model indirect command can only be used with WLSMV when working with a binary mediator.

With ML, the mediator is treated as a dummy variable in it's role as an independent variable - does this mean that multiplying the paths to derive an indirect effect is invalid due to scaling and constrained residual variances?

many thanks, Jon
 Linda K. Muthen posted on Wednesday, March 28, 2012 - 10:23 am

The reason you can't use a product indirect effect with ML and a binary mediator is that the mediator is treated as a latent response variable when it is a dependent variable and an observed variable when it is an independent variable.
 Xu, Man posted on Thursday, March 29, 2012 - 7:19 am
I read in other threads that when logit link is used, its latent response variable that is the dependent and independent variable. Is it valid t to calculate the mediationo use the NEW in this context?
 Linda K. Muthen posted on Thursday, March 29, 2012 - 10:26 am
A product indirect effect is not valid for maximum likelihood in Mplus for the logit link or the probit link when the mediator is binary.
 Xu, Man posted on Thursday, March 29, 2012 - 10:44 am
Actually the mediator in my case would be ordinal, not binary (sorry I did not realise the centre of discussion is binary being different from ordinal here). I remember under some specification it was possible to request INDIRECT with an ordinal meditor so I just assume it would be valid to calculate the mediation with probit link.
 Xu, Man posted on Thursday, March 29, 2012 - 10:49 am
Sorry, in my previous previous post, I meant for when probit link is used, it is the latent response variable of the mediator that was used as depedent and independent, hence I thought it would be OK to calculate the product of regression coefficients in this case.
 Linda K. Muthen posted on Thursday, March 29, 2012 - 4:19 pm
An ordinal mediator is treated as a continuous variable. If you can use MODEL INDIRECT, you can compute the indirect effect as a product.
 Jon Heron posted on Monday, April 02, 2012 - 8:00 am
Hi Linda

slightly delayed thanks for your response to my initial question.

Looks like I have a few more options to play with.
 Jon Heron posted on Tuesday, April 03, 2012 - 7:42 am
Bit of an update, with no obvious questions inserted.

[1] Bayes estimation (uses probit link) and gives results similar to probit/ML when using "mediator=observed;", and results similar to probit/WLSMV when using "mediator=latent;". That's good.

[2] I had hoped I might be able to rig up some post-estimation parameters using model-constraint so that I can re-scale the logit/ML output (e.g. using David Kenny's equations: but I'm unable to refer to the variance of the dependent variables in the models, ditto the parameter SE's, using Mplus labelling.

Logit/ML/rescaling has some benefits such as sticking with OR's which are more readily interpretable. Stata's binary-mediation function will run this automatically and also permit the use of bootstrapping, but this only works for rather simple models. Looks like I'll be sticking with probit/WLSMV in Mplus and taking the hit in terms of losing my beloved odds ratios.
 Bengt O. Muthen posted on Tuesday, April 03, 2012 - 9:17 am
I assume you are considering a binary mediator M and perhaps also a binary outcome Y.

[1] That's right.

[2] The research that the Kenny note refers to is largely outdated now. Instead you should take a look at

Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.

which is on our web site together with Mplus scripts. This paper goes through new causal effect literature and shows how you should define indirect and direct effects with categorical and other variables. It implies that you can stay with ML-logit and odds as you desired.
 Jon Heron posted on Tuesday, April 03, 2012 - 10:38 am
Yes, just binary M for now.

Thanks for the ref :-)
 Xu, Man posted on Wednesday, April 04, 2012 - 4:29 am
Dear Linda,

My case is a more complicated situation so it would not be possible to get mediation output from MODEL INDIRECT. I test the mediation effect from an ordinal mediator with the slope and intercept of a growth curve as outcome variables.

Few things in the model that I think might be useful to present here are

I think in this case latent response variable is used instead of the observed ordinal variable, so I thought maybe I could apply the simple calculation for mediation effect with MODEL CONSTRAINT. Is this valid to do?

Thank you!
 Xu, Man posted on Wednesday, April 04, 2012 - 5:07 am
Or maybe I can never calculate a valid mediation effect because estimator is mlr instead of weighted least square in this case?

I have to specify TYPE=RANDOM in order to get the model run with TSCORE option.
 Linda K. Muthen posted on Wednesday, April 04, 2012 - 1:29 pm
If you are using MLR and have an ordinal mediator that is listed on the CATEGORICAL list, you cannot create an indirect effect as a product. Instead you would need to create it according to the formulas in the following paper:

Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.
 Ewan Carr posted on Friday, June 22, 2012 - 3:07 pm
Further to the above:

I have a two-level model, with a continuous outcome, and a binary mediator (full specification below).

I'm testing a 2-1-1 mediation pathway — a level-2 variable is mediated by a level-1 variable.

Some questions:

1) Should I list the binary mediator on the CATEGORICAL list (My guess: yes)?

2) Should/can I test the between-level indirect effect using MODEL CONSTRAINT?

3) Is MEDIATOR = LATENT the default in Mplus? Based on the above reference, it seems the best option here.

I'm using Bayesian estimation for this model.

Many thanks in advance!



y ON m;


m ON x (a);
y ON m (b);
y ON x;


 Bengt O. Muthen posted on Friday, June 22, 2012 - 8:30 pm
Yes, Yes, and Yes.
 Ewan Carr posted on Saturday, June 23, 2012 - 3:05 am
Great, thanks for the quick response.

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