Two-level 2-2-1: total and indirect e...
Message/Author
 Lucia posted on Wednesday, June 01, 2016 - 2:14 am
Hi!
I have a couple of questions about a two-level 2-2-1 mediation model, with random intercepts and cluster-robust standard errors.

The data are hierarchical (three-levels) and the main variables are the following:
*outcome (y) at level 1 = unordered categorical (nominal) with 3 categories

*mediator (m) at level 2 = binary

*predictor of interest (x1) at level 2 = categorical recoded into 2 dummies (x1_2 x1_3) and x_3 is the dummy of interest

1) Is it possible to estimate the indirect and total effects if the mediator (level 2) and the outcome (level 1) are measured at different levels and have different non-normal distributions (binomial and multinomial)?

2) If yes, how do we interpret the exponential of the indirect and total effects?
 Bengt O. Muthen posted on Wednesday, June 01, 2016 - 10:17 am
1) I think so. But how to express these effects correctly using counterfactuals may be a research topic - I don't recall having seen it expressed.

2) That's a later question, after the effects have been defined.

Counterfactual effects consider expectations which corresponds to probability Y=1 for a binary outcome Y. I recommend dichotomizing the outcome in two ways for two different analyses. An effect from a level 2 variable to a level 1 variable goes via the random intercept for the level 1 variable.
 Lucia posted on Tuesday, June 14, 2016 - 9:21 am

I have another question.

I dichotomized the output in two ways (y_1 and y_2) but the error indicates:
*** MODEL INDIRECT is not available for TYPE=TWOLEVEL with ALGORITHM=INTEGRATION.

My code is :
....
ANALYSIS: TYPE=COMPLEX TWOLEVEL;

MODEL:
%BETWEEN%
y_1 ON m ;
m ON x1_2 x1_3;

MODEL INDIRECT:
y2_1 IND x1_2;
y2_1 IND x1_3;

If the Numerical integration is required for the "COMPLEX TWOLEVEL" analysis, what's wrong with my code?

Thanks!
 Linda K. Muthen posted on Tuesday, June 14, 2016 - 9:22 am
 Robert Allen King posted on Monday, October 24, 2016 - 12:37 pm
Hello

I want to run a multiple mediated model and I am running into estimation issues. My guess is that I have done something wrong, but I wanted to make sure my code was right before I started diving deeper into causes.

Thank you for the help!
Robert

USEVARIABLES ARE
ID X
Y M1
M2
;
MISSING IS *;
CLUSTER = ID;
BETWEEN ARE M1 X;
ANALYSIS: TYPE = TWOLEVEL RANDOM;

MODEL:
%WITHIN% !INDIVIDUAL LEVEL
Y;
%BETWEEN% !GROUP LEVEL
M1 ON X (A1);
Y ON M1 (B1);
M2 ON X (A2);
Y ON M2 (B2);
Y ON X;

MODEL CONSTRAINT:
NEW (AB1
AB2);
AB1=A1*B1;
AB2=A2*B2;
OUTPUT: TECH1 TECH8 CINTERVAL;
 Bengt O. Muthen posted on Monday, October 24, 2016 - 3:07 pm
Should M2 also be put on the Between list?

Otherwise, I see no error.
 Robert Allen King posted on Tuesday, October 25, 2016 - 12:23 pm
Thank you for the help!
 Andrew Li posted on Tuesday, August 22, 2017 - 11:32 am
Dear Dr. Muthen,
I have a 2-2-1 model (x-m-y) model with the first path moderated by a level-2 moderator w. I also have a level-1 control C1 and a level-2 control C2. Would you please take a look at the code below and let me know if it is correct? Thank you.
missing = all(-999);
usevariables = a1 x m y w c1 c2 inter;
cluster = a1;
between = x m w c2 inter;
Within = c1;
define:
standardize x w;
inter = x * w;
analysis: type = twolevel random;
model:
%within%
y c1;
y on c1;
%between%
x m y w c2 inter;
m on
x (p1)
w
inter (p2);
y on
x
w
inter
m (b) c2;
model constraint:
new (ind1 ind2 wmo1 wmo2);
wmo1 = 1; !1 SD of the moderator W
wmo2 = -1; !-1 SD of the moderator W
ind1 = (p1+p2*wmo1)*b;
ind2 = (p1+p2*wmo2)*b;
output: tech1 tech8 cinterval;
 Bengt O. Muthen posted on Tuesday, August 22, 2017 - 6:06 pm
A quick look says that it seems alright - but don't rely on me; instead, check the literature.

And you can't have

m(b) c2;

You should say

m(b)

c2;
 Brittany Tokasey posted on Monday, March 30, 2020 - 7:31 am
Hello,

I have a cross-classified 2(A)-2(A)-1 two-level mediation model I'd like to run. I have some idea of what the input should look like based on Luo (2017), but wanted to verify that it’s correct.

These data are from an experiment where participants made trait ratings for different target women. Every target had two photos - one where she was high in performed femininity (PF) and one where she was low in PF. PF is the IV and the trait ratings were the outcome variable (y). Each participant only saw a quarter of the full set of targets. Therefore, each trait rating is crossed with target (Target) and participant (Subj). The mediator (m) is a different trait rating taken from a pilot study. I believe the input should look like this:

VARIABLE: NAMES = Target Subj PF y m ;
CLUSTER = Target Subj;
WITHIN = PF;
ANALYSIS: TYPE = CROSSCLASSIFIED;
ESTIMATOR = BAYES; PROCESSORS = 2;
MODEL: %WITHIN%
y ON PF; y ON m (b);
m ON PF (a);
%BETWEEN Target%
y ON m;
%BETWEEN Subj%
y ON m;
MODEL CONSTRAINT:
New (indn);
indn = a*b;

In general, does this look correct and more specifically, should any of the between slopes be included in the indirect effect? Thank you in advance for your time!
 Bengt O. Muthen posted on Monday, March 30, 2020 - 4:17 pm
Looks ok but I don't see why you say it is a 2(A)-2(A)-1 model. The IV and the mediator are not 2(A) variables but seem to vary also on the Within level the way you write the model.
 Brittany Tokasey posted on Tuesday, April 14, 2020 - 11:45 am
Hi Dr. Muthen,

Thank you for your response! The 2()-2()-1 naming convention is somewhat new to me so I apologize for any confusion that may have caused. The IV and mediator definitely do vary within participants and within target women.

After running this syntax, I have a couple other questions I’m hoping you could answer for me. One is how Mplus estimates the a path from the IV to the mediator. Is it still using a multilevel model? I ask because my datafile has the same values for the mediator repeated many times. Because the mediator is the average trait rating for a photo, that average rating shows up in every row where participants made a response for that photo. In the a path model, when the mediator is the DV, there’s really no longer a random effect of participant then. So does Mplus analyze the a path using a regression?

Other programs I’ve used to run multilevel models (R, HLM7) break the output into “fixed” and “random” effects. So my second question is what would be considered the equivalents for both effects in the Mplus output?

Thank you again for your help!
 Bengt O. Muthen posted on Wednesday, April 15, 2020 - 3:54 pm
Are you saying that your mediator is a Between-level variable?

The mixed effect model (fixed and random effects) is equivalent to the twolevel model that you specify in Mplus. Random effects are variables and have their parameters (means, variances, and relations to other variables) estimated on the Between level.
 Brittany Tokasey posted on Thursday, April 16, 2020 - 9:14 am
Hi Dr. Muthen,

Thank you for getting back to me! I believe the mediator varies both within and between. Let’s say that the DV is perceived intelligence and the mediator is how likable the person in the photo is, on average. All targets have two photos – one where she is wearing makeup and one where she isn’t. We’ve been treating target woman as one factor and participant as the other factor. In addition to makeup, each photo of each woman has a rating of how likable they are. So a portion of the datafile could look like this:
Participant Target Woman Makeup Likable (mediator) Intelligence
1 A Yes 3 5
2 A No 4 4
3 A Yes 3 6
4 A No 4 3
1 B No 6 7
2 B Yes 5 6
3 B No 6 5
4 B Yes 5 7

continued...
 Brittany Tokasey posted on Thursday, April 16, 2020 - 9:14 am
...
Makeup varies both within participants (all participants see some photos with makeup, some without) and within target women (all target women have a with makeup photo and a without). The mediator also varies within participants (participants see photos with different likable ratings) and within target women (each target woman has a different likable rating for each of her photos). I believe the mediator is also considered to vary between target women because each set of photos has different ratings. Additionally, each participant saw a different combination of photos, so I think the likable ratings are considered to vary between participants.

When focusing just on the a path in the mediation model from makeup to likable, it seems that just the target woman, makeup, and likable columns from above are needed to run that model. It seems to me that the model for the a path would then only have a random effect of target woman (and not participant). But there’s of course a lot more than 4 participants in the full dataset, so the same likable rating is repeated many times for each photo, making me wonder if the model is just regressing likable on makeup, not using a mixed effects model.

Thank you!
 Bengt O. Muthen posted on Friday, April 17, 2020 - 6:25 am
I think these questions are more suitable for SEMNET.
 Karim posted on Wednesday, October 14, 2020 - 1:11 am
Dear Dr. Muthen,

I am testing a 2-2-1 model with a level 2 W moderating the 2-1 path (second stage moderation). Could you please take a look at the code below and let me know if it is correct? Thank you very much!
USEVARIABLE = x m y w mw ;
CLUSTER IS ID
BETWEEN = x m w mw ;
DEFINE:
Center x m w (grandmean) ;
mw = m * w ;
ANALYSIS: TYPE IS TWOLEVEL ;
ESTIMATOR = BAYES;
MODEL:
%WITHIN%
y ;
%BETWEEN%
y m x mw ;
y on m (b1)
w (b2)
mw (b3)
x ;
m on x (a1);
MODEL CONSTRAINT:
new(ind_low ind_hi);
ind_low=(b1-b3*SD)*a1;
ind_hi=(b1+b3*SD)*a1;
 Bengt O. Muthen posted on Wednesday, October 14, 2020 - 4:09 pm
That looks correct, replacing SD with the value.