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);
 wang ying posted on Wednesday, January 08, 2020 - 7:33 am
Dear Prof. Muthen,

I have a three-level model, in which X is at level 1, mediator M is at level 2, Y is at level 3, moderatore W is at level 3, and controls at all three levels. I have two questions. Thank you very much.

1. When testing hypotheses about M-Y, i.e., not including X, do we need to include M-Y at level 3, or only at level 2? i.e., we should use syntax 1 or syntax 2?

In this model, the independent variable is M, which is at level 2, so I assume that I can adopt Syntax 1; however, I'm not 100% sure because there are control variables at level 3.

In addition, if your suggestion is to use Syntax 2, then may I know whether I should use the coefficient of M-Y at level 2 or at level 3 or at both levels as evidence of this hypothesis? Thanks.

Syntax1:
%within%
Y on level 1 controls;
%between 2%
Y on M
level 2 controls;
%between 3%
Y on level 3 controls;

Syntax 2
%within%
Y on level 1 controls;
%between 2%
Y on M
level 2 controls;
%between 3%
Y on M
level 3 controls;

Due to the size limitation, I include the second question in another message.
 Bengt O. Muthen posted on Wednesday, January 08, 2020 - 10:56 am
I assume that when your model statements refer to variables called "level1", "level2", and "level3", you are referring to X variation on these 3 levels. I also assume that M varies also on level 3. If so, then syntax 2 is the closest but on level 3 you also want to regress M on "level3".
 wang ying posted on Friday, January 17, 2020 - 9:47 pm
Thanks, prof. Muthen. Sorry, I have a typo in the prior message. X should be at level 3 (i.e. firm level) while Y should be at level 1 (i.e., individual level). i.e., X has variance at level 3, M has variance at both level 2 and 3, and Y has variance at all the three levels. I adopt Syntax 2 (and add "M on level 3 controls" on level 3) to test the relationship between M and Y. Now, the coefficient of "Y on M" is not significant at level 2 (i.e. team level) while it is significant at level 3. May I know whether I should report both coefficients at level 2 and 3 or only report the coefficient at level 3? And if reporting both, how to justify the result supports the hypothesis that M is positively related to Y? Whether the insignificant coefficient at level 2 is an issue? Thank you very much.
 Bengt O. Muthen posted on Sunday, January 19, 2020 - 4:55 pm
Just report all that you've found.

I assume you are mostly interested in Level 3 because that's where you have X and where you have mediation.
 wang ying posted on Sunday, January 19, 2020 - 8:40 pm
Thanks, Prof. Muthen.