Indirect effect for categorical mediator
Message/Author
 seonjoo lee posted on Thursday, August 11, 2016 - 11:11 am
I ran a mediation analysis of (X->M->Y) and X, M are binary and Y is continuous.
In this case, how can I compute indirect effect? Is it a*b?

Since the model is not linear for X ->M part, it's not clear how should I interpret the results.

How can I quantify % of mediation in this case??

Thank you.
 Linda K. Muthen posted on Thursday, August 11, 2016 - 11:30 am
Please see MODEL INDIRECT in the current user's guide on the website. It goes over these questions. The regression of m on x can be a probit regression or a logistic regression and the estimators can be WLSMV or ML. The interpretation will vary with the estimator. These topics are also covered in our book Regression and Mediation Analysis Using Mplus.
 seonjoo lee posted on Thursday, August 11, 2016 - 2:10 pm

In fact, I have to run two-level analysis due to the study design (with random intercept).

And I received the following error message: MODEL INDIRECT is not available for analysis with ALGORITHM=INTEGRATION.

Do you have any suggestion? Should I specify algorithm? If so, what should it be? Thank you.

ANALYSIS:
TYPE=TWOLEVEL; ESTIMATOR = ML;
 Linda K. Muthen posted on Thursday, August 11, 2016 - 4:12 pm
As a first step, read MODEL INDIRECT. If you can't use it, you can specify the ideas in MODEL CONSTRAINT.
 seonjoo lee posted on Tuesday, August 23, 2016 - 1:33 pm
Then, in the model constraint, should I use and interpret as the continuous mediator/outcome case? Note that M is categorical variable and Y is continuous in my case. Thank you.

MODEL:
%WITHIN%
Y ON M (b1);
Y ON X(cdash1);
M ON X (a1);
%BETWEEN%
Y;

MODEL CONSTRAINT:
PLOT(IND);
IND = a1*b1;
 Bengt O. Muthen posted on Tuesday, August 23, 2016 - 3:03 pm
If you specify WLSMV or Bayes with Mediator=Latent, the product formula is the correct indirect effect in the latent response variable conceptualization for the binary M.

On our Mediation page

http://www.statmodel.com/Mediation.shtml

the counterfactual papers discuss a more appropriate indirect effect based on recent causal inference literature. See the 2015 paper as well as our new book. This is automated in the current Mplus but only for single-level models. You can do it also using Model Constraint as shown in my 2011 paper but it is a long expression.

For multilevel models with random intercepts, the residual variance expressions going into these formulas need to be modified to take into account the between-level variances. This can be done using Model Constraint.