Mediation in a 3-level model
Message/Author
 Necati Ertekin posted on Tuesday, April 24, 2018 - 9:34 am
Dear MPlus community,

I am interested in a mediation analysis (both direct and indirect effects) for a 3-level multilevel model in which (1) the predictors are continuous and can be at each level, (2) the mediator is continuous and level-1, and (3) the outcome variable is binary and level-1.

While I am not 100% sure, example 9.21 in the User's Guide seems to address this type of mediation. If so, could you also please provide a citation for the methodology that example 9.21 is using?

Thanks,
 Bengt O. Muthen posted on Wednesday, April 25, 2018 - 10:12 am
Yes, the UG ex 9.21 is relevant here. It uses Bayesian estimation and the methodology for that is described in the papers on our website:

Asparouhov, T. & Muthén, B. (2010). Bayesian analysis of latent variable models using Mplus. Technical Report. Version 4. Click here to view Mplus inputs, data, and outputs used in this paper.

Asparouhov, T. & Muthén, B. (2010). Bayesian analysis using Mplus: Technical implementation. Technical Report. Version 3.

Note also that the indirect and direct effects in this case refer to the Y* outcome, that is, the continuous latent response variable for the binary Y outcome. "Counterfactual" direct and indirect effects for Y have not yet been developed for this multilevel case (see our book for definition of counterfactual effects).
 dummyvariable123 posted on Wednesday, August 22, 2018 - 11:24 am
Dear Dr. Muthen,

I am trying to examine a 3-level mediation: mediator and outcome at L2, predictor at L3.

%within%
y;
%BETWEEN id%
y;
y ON mediator(b);
%BETWEEN classroom%
y;
y ON x(c);
mediator ON x(a);

MODEL CONSTRAINT:
indirect = a*b;
direct = c;
total = c+a*b;

The output gives an error message informing that my mediator has variation within a cluster for one or more L3 clusters. How should I change the syntax when the mediator has variation at both L2 and L3?

Thank you
 Bengt O. Muthen posted on Wednesday, August 22, 2018 - 4:40 pm
See the V8 UG page 634.

Also, don't you want

y ON mediator (b);

 dummyvariable123 posted on Thursday, August 23, 2018 - 1:53 am
Thank you for your guidance. I still have some problems:

1. Following the UG, I specified:
between = Mediator;
between = (classroom) X;
While keeping the syntax above.

I got an error message:
"Unrestricted x-variables for analysis with TYPE=THREELEVEL must be a variable on only one level. The following variable cannot exist on more than one level: Mediator."

2. If I have "Y ON mediator" on L3 instead of L2, this leads to a conclusion "X predicts classroom level of Mediator, which in turn predicts classroom level of Y". Is that correct?
I am more interested in testing whether "X predicts between-person level of Mediator, which in turn predicts between-person level of Y". Shouldn't Mediator be on L2 to test this?
 Bengt O. Muthen posted on Thursday, August 23, 2018 - 6:28 pm
 dummyvariable123 posted on Sunday, August 26, 2018 - 10:51 am
Dear Dr. Muthen,

I want to test if L3 (classrooms) predictor "X" affects L2 (persons) outcome "Y" via the mediator "M" that has variations at L2 and at L3.

I created 2 variables representing the level-specific parts of the mediator M: "L2M" and "L3M".

Is my syntax for such mediation model correct?:

within = time;
between = (persons) L2M (classrooms) L3M X;

MODEL:
%within%
Y;
Y ON time;

%BETWEEN persons%
Y;
Y ON L2M (b1);

%BETWEEN classrooms%
Y;
Y ON X;
L3M ON X (a);
Y ON L3M (b2);

MODEL CONSTRAINT:
indirect = (a*b1)+(a*b1*b2);
 Bengt O. Muthen posted on Monday, August 27, 2018 - 1:43 pm
Looks fine, but I think the indirect effect will be

a*(b1+b2);