Moderated mediation two-level model PreviousNext
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 Antje Schmitt posted on Monday, October 27, 2008 - 1:00 pm
We did an Experience Sampling study and collected data (events, emotions, work engagement) from 55 people twice a day for nine working days (repeated measures design: daily measures are nested in individuals). We like to test a moderated mediation model with:
Daily events --> triggering emotional experiences (mediator) --> influencing work engagement (DV) (Lower Level Mediation). The moderators are on Level 2 (they were measured once).
Is it possible to test such a multilevel moderated mediation model with Mplus and how could I perform the analyis? Thanks a lot in advance!
 Kristopher J. Preacher posted on Monday, October 27, 2008 - 3:21 pm
Yes, it is possible. Bauer, Preacher, & Gil (2006, pp. 153-158) address this model. We have code in SAS, SPSS, and HLM for lower-level mediation models with the potential for moderation by level-2 predictors (see quantpsy.org), but it is also easy to do in Mplus. Here is Mplus code that yields the same output:

TITLE: 1-1-1 model from BPG article
DATA: FILE IS bpg_example_data.dat;
VARIABLE: NAMES ARE id x m y;
CLUSTER IS id;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
MODEL:
%WITHIN%
sa | m ON x;
sb | y ON m;
sc | y ON x;
m y;
%BETWEEN%
sa sb sc m y;
sa WITH sb(cab);
sa WITH sc m y;
sb WITH sc m y;
sc WITH m y;
m WITH y;
[sa](sa); [sb](sb); [sc](sc);
MODEL CONSTRAINT:
NEW(ind);
ind=sa*sb+cab; ! indirect effect
OUTPUT: TECH1 TECH8;

Bauer et al. use a parametric bootstrap to obtain a CI for the indirect effect. A modification of the R code here can be used to achieve the same goal using Mplus output. Ex.11.11 in the Mplus Users Guide will also be helpful.

Bauer, D. J., Preacher, K. J., & Gil, K. M. (2006). Conceptualizing and testing random indirect effects and moderated mediation in multilevel models: New procedures and recommendations. Psychological Methods, 11, 142-163.
 Antje Schmitt posted on Wednesday, October 29, 2008 - 10:02 am
Thanks a lot! Especially the Mplus code was very helpful.
 Jeffrey Kahn posted on Wednesday, November 16, 2011 - 2:52 pm
I have a 2-1-1 mediation model based on a diary study. Event rumination mediates the relation between attachment anxiety and event disclosure. Attachment avoidance is a level 2 covariate predicting event disclosure. Event intensity is a moderator of the b path between event rumination and event disclosure.

My Mplus code is based on Preacher, Zypher, and Zang (2010):

TITLE: Moderated mediation model
DATA: FILE IS data.dat;
VARIABLE: NAMES ARE code ev_int ev_disc
ev_rumin attavoid attanx;
USEVARIABLES ARE code ev_int
ev_disc ev_rumin attavoid attanx;
BETWEEN IS attanx attavoid;
CLUSTER IS code;
ANALYSIS: TYPE IS TWOLEVEL RANDOM;
MODEL: %WITHIN%
ev_rumin ev_disc;
sb | ev_disc ON ev_rumin;
%BETWEEN%
attanx ev_rumin ev_disc attavoid;
ev_rumin ON attanx(a);
ev_disc ON ev_rumin(bb);
ev_disc ON attanx attavoid;
sb WITH attanx ev_rumin ev_disc
attavoid;
[sb](bw);
MODEL CONSTRAINT:
NEW(b indb);
b=bb+bw;
indb=a*b;
OUTPUT:
TECH1 TECH8 CINTERVAL;

Did I handle the attavoid covariate properly? Also, how do I integrate the moderating effect of ev_int? Thanks.
 Bengt O. Muthen posted on Wednesday, November 16, 2011 - 9:20 pm
aatavoid is an observed between-level covariate so I wouldn't mention its variance as you do. If it predicts sb I would add that ON statement instead of WITH.

As for the moderator, first see if the sb variance is significant or if a fixed slope can be used. Generally speaking, with a continuous moderator, use Define to create the interaction.
 Jeffrey Kahn posted on Friday, November 18, 2011 - 5:05 pm
Thank you, Bengt.

The sb variance is significant. I would like to see if ev_int (a level 1 variable) can predict the variance in sb. My intuition was to add the following statement in the %BETWEEN% section:

sb ON ev_int;

However, from your above comment it seems that I should use DEFINE to create an interaction term:

DEFINE: interact=ev_int*ev_rum;

Would I then include the following statement in the %BETWEEN% section?

ev_disc ON ev_rumin(bb) ev_int interact;

If it helps, my model can be viewed at:
http://my.ilstu.edu/~jhkahn/Multilevel%20moderated%20mediation.gif
 Bengt O. Muthen posted on Saturday, November 19, 2011 - 12:13 am
With a significant sb slope your model specification in your first message gives an interaction between the within-level part of ev_rumin and the between-level part of ev_disc. This, I think, is the moderation you talked about in your first message.

See also slide 45 of our Topic 7 short course handout.
 Yan Liu posted on Monday, April 30, 2012 - 5:46 pm
Hi, Bengt

I am conducting some anlayses using the multilevel mediation models based on SEM framework introduced by Preacher, Zyphur, and Zhang (2010). I also read the paper "constructing covariates in multilevel regression" by Asparouhov and you (2007).I like this new approach a lot.

However, I found that the model doesn't run for ordinal categorical outcome variable. I wonder if there is a way for me to use this approach for categorical outcome.

The model I used has two outcomes (PAHome & PESch), one mediator (Enjoy) and one predictor (TT). The syntax is attached as follows.

USEVARIABLES = ideal-individ Enjoy PESch PAHome;
CATEGORICAL = PESch;
CLUSTER IS classid;
MISSING = ALL(999);

ANALYSIS:TYPE = TWOLEVEL;
MODEL:
%WITHIN%
TTw BY ideal-individ;
Enjoy ON TTw (aw);
PAHome ON Enjoy (b1w);
PAHome ON TTw;
PESch ON Enjoy (b2w);
PESch ON TTw;

%BETWEEN%
TTb BY ideal-individ;
Enjoy ON TTb (ab);
PAHome ON Enjoy (b1b);
PAHome ON TTb;
PESch ON Enjoy (b2b);
PESch ON TTb;
 Linda K. Muthen posted on Tuesday, May 01, 2012 - 4:28 pm
Please send your output and license number to support@statmodel.com.
 Yan Liu posted on Thursday, May 03, 2012 - 10:44 pm
Hi, Linda

Thank you for your reply. I tried WLSMV estimator, then the model worked fine. Do you think if this is appropriate?

If it is, I have further questions. First, as far as I know full information ML can handle missing data. Here I used WLSMV, how are the missing data handled using this estimator?

Second, for my data set 20% missing on the mediator and two outcome variables. The missing values depend on gender and the predictor(a latent variable with four indictors). Is my understanding correct that I should include gender as a covariate to control for the gender differences on missingness (for both mediator and outcome variables)?

Can I use gender as a moderator? I tried to create an interaction between gender and the predictor (latent variable), but it didn't work. Is there a way to do it?

Thanks.
Yan
 Linda K. Muthen posted on Saturday, May 05, 2012 - 5:49 pm
See the following technical appendix on the website:

Weighted Least Squares Estimation with Missing Data

Yes, you should include gender as a covariate. You can use the XWITH option to create an interaction between a latent an observed variable.
 Yan Liu posted on Thursday, May 10, 2012 - 12:19 am
Hi, Linda

Thank you so much!
So WLS estimator still uses FIML to treat missing values. What is the default for deleting missing values? I noticed the number of observations in the output is the same as the covariate, gender.

I tried the interaction between "gender" and the latent predictor "TTw", but it seems WLSMV doesn't run for this moderated mediational model. The error message is "WLSMV is not allowed with TYPE=RANDOM". So do we have to use MLR estimator?

Hence, I changed estimator to MLR, but it seems that the model didn't run if the outcome, "PESch", is defined as categorical. The error message is as follows.

Observed variable on the right-hand side of a between-level ON statement must be a BETWEEN variable. Problem with: ENJOY

I also tried to define the outcome "PESch" as a continuous variable, but it doesn't work well. If I have to treat outcome variables as continuous to run moderated mediational models, what strategies would you recommend? Thanks a lot!

Here is part of my Mplus syntax.
ANALYSIS:TYPE = TWOLEVEL RANDOM;
MODEL:
%WITHIN%
TTw BY ideal-individ;
sexTT| sex XWITH TTw;
Enjoy ON TTw (aw);
Enjoy ON sex sexTT;
PAHome ON Enjoy (b1w);
PAHome ON TTw sex sexTT;
PESch ON Enjoy (b2w);
PESch ON TTw sex sexTT;
 Linda K. Muthen posted on Thursday, May 10, 2012 - 5:24 pm
Missing data handling is not done in the same way for weighted least squares and maximum likelihood. Weighted least squares is described in the technical appendix I referred you to. Maximum likelihood is described in the Little and Rubin book cited in the user's guide.

Missing data theory applies to dependent variables. Observations with missing data on one or more independent variables are not included in the analysis.

Put a factor behind joy, for example,

f BY enjoy@1; enjoy@0;

use f instead of enjoy as the covariate.
 Yan Liu posted on Wednesday, May 16, 2012 - 6:27 pm
Hi, Linda

Followed your suggestion, I put a factor behind enjoy, but it seems the model didn't work. Could you please take a look and see if my model is specified correctly. Thanks a lot!
Yan

ANALYSIS: TYPE = TWOLEVEL RANDOM;

MODEL:
%WITHIN%
TTw BY ideal-individ;
sexTT| sex XWITH TTw;
fw BY enjoy@1; enjoy@0;
fw ON TTw (aw);
fw ON sex sexTT;
PAHome ON fw (b1w);
PAHome ON TTw sexTT;
PESch ON fw (b2w);
PESch ON TTw sexTT;

%BETWEEN%
TTb BY ideal-individ;
fb BY enjoy@1; enjoy@0;
fb ON TTb (ab);
PAHome ON fb (b1b);
PAHome ON TTb;
PESch ON fb (b2b);
PESch ON TTb;
ideal-individ@0;


Here is the error message.
THE ESTIMATED WITHIN COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED.
THE VARIANCE OF TTW APPROACHES 0. FIX THIS VARIANCE AND THE CORRESPONDING COVARIANCES TO 0, DECREASE THE MINIMUM VARIANCE, OR SPECIFY THE VARIABLE AS A BETWEEN VARIABLE.
 Bengt O. Muthen posted on Thursday, May 17, 2012 - 12:55 am
The message says that the variance of ttw approaches zero. To investigate why, you could simplify the model to only include the ttw and ttb factors, that is, using only the variables ideal-individ. If that does not show the same problem, then add variables into that model. Step-wise model building is always recommended.
 Ari Malka posted on Saturday, June 09, 2012 - 10:39 pm
Hello,

We are testing a model wherein we have military personnel nested within teams. Each team also has a group of leaders (and a group of subordinates). We have hypothesized a moderated-mediation model wherein Leadership Team Cohesion --> Subordinate Team Cohesion --> Team Performance. We also hypothesized two first stage moderators: (1) subordinate level of agreement on the extent to which their leadership team forms a cohesive unit and (2) racioethnic similarity between the leadership and subordinate teams (in the same larger team). We want to use moderated-mediation wherein all variables are at level 2 and wherein all variables are at level 1 (except the moderators) all in the same model. In other words, we want to have 6 latent variables (3 team level and 3 individual level). Is this possible?
 Linda K. Muthen posted on Sunday, June 10, 2012 - 9:41 pm
Yes, you can have a model with 3 team-level and 3 individual-level latent variables.
 ari malka posted on Saturday, June 30, 2012 - 6:00 pm
Hi Linda,

Thanks for the response above (regarding the model with leadership team cohesion). I am having trouble figuring out the code for mediation (both levels 1 and 2)and the code for the two moderators. Would it help to see my model? What is the best way for me to show it to you? Any help would be greatly appreciated!!

Ari
 ari malka posted on Saturday, June 30, 2012 - 6:01 pm
So far, this is my code:

VARIABLE:
NAMES ARE Cluster ClusSize Rank SubTeam Gender Race Age TeamEff1
TeamEff2 TeamEff3 TeamEff4 TeamCoh1 TeamCoh2 TeamCoh3 TeamCoh4
LeadCoh1 LeadCoh2 LeadCoh3 LeadCoh4 RaceSim rwgTCun rwgLCun;
USEVARIABLES ARE ClusSize Rank SubTeam Gender Race Age TeamEff1
TeamEff2 TeamEff3 TeamEff4 TeamCoh1 TeamCoh2 TeamCoh3 TeamCoh4
LeadCoh1 LeadCoh2 LeadCoh3 LeadCoh4 RaceSim rwgTCun rwgLCun Cluster;
MISSING ARE ALL (999);
CLUSTER IS Cluster;

ANALYSIS:
TYPE IS TWOLEVEL;
ESTIMATOR IS MLM;
ITERATIONS = 1000;
CONVERGENCE = 0.000001;

Model:
%Within%
LTCi by LeadCoh1@1 LeadCoh2 LeadCoh3 LeadCoh4;
TCi by TeamCoh1@1 TeamCoh2 TeamCoh3 TeamCoh4;
TPi by TeamEff1@1 TeamEff2 TeamEff3 TeamEff4;
TCi on LTCi;
TPi on TCi;

%Between%
LTCg by LeadCoh1@1 LeadCoh2 LeadCoh3 LeadCoh4;
TCg by TeamCoh1@1 TeamCoh2 TeamCoh3 TeamCoh4;
TPg by TeamEff1@1 TeamEff2 TeamEff3 TeamEff4;
TCg on LTCg;
TPg on TCg;

OUTPUT: SAMPSTAT RESIDUAL STANDARDIZED CINTERVAL TECH3 TECH4;
SAVEDATA:
FILE IS Diss Data for Mplus 6.22;
FORMAT IS FREE;
RECORDLENGTH = 1000;
 Linda K. Muthen posted on Sunday, July 01, 2012 - 4:49 pm
This looks okay.

Please limit posts to one window.
 baozhenzhou posted on Saturday, February 01, 2014 - 2:23 am
Hello! We want to test a moderated mediation model just like the model 5 in the following paper (when the a and b paths are both moderated by w):
Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42, 185-227.
Our model is perceived school climate (x) --> deviant peers affiliation (m) --> delinquency(y). The moderator is effortful control (w). Given we were analyzing clustered data (students are nested within 10 schools). Is it possible to test such a multilevel moderated mediation model with Mplus and how could I perform the analyis? Thanks a lot in advance!
 Linda K. Muthen posted on Saturday, February 01, 2014 - 8:12 pm
Ten schools is too few for multilevel modeling. You need at least 20 and many would suggest 30-50. Instead create nine dummy variables and use those as covariates to control for non-independence of observations.
 baozhenzhou posted on Sunday, February 02, 2014 - 12:32 am
Linda, thanks for your help! The Mplus User's Guide has a description of how to refer the levels of a nominal dependent variables in the MODEL command but no description of how to create dummy variables for independent in the DEFINE command. I have searched the Mplus Discussion for the answers and found the following example. But I still can't understand how to write the syntax for the dummy variables of 10 schools? Could you help me? Thanks a lot!

DEFINE;
white = 0;
if (raceth eq 1) then white = 1;
black = 0;
if (raceth eq 2) then black = 1;
etc.
 Linda K. Muthen posted on Sunday, February 02, 2014 - 4:22 pm
The above DEFINE command is how you would create dummy variables. You should create k-1 dummy variables where k is the number of categories.
 baozhenzhou posted on Sunday, February 02, 2014 - 11:48 pm
Thanks, Linda. Followed your suggestion, this is my code to define nine dummy variables for ten schools(sc).
DEFINE:
sc1 = sc == 1;
sc2 = sc == 2;
sc3 = sc == 3;
sc4 = sc == 4;
sc5 = sc == 5;
sc6 = sc == 6;
sc7 = sc == 7;
sc8 = sc == 8;
sc9 = sc == 9;
Did I handle the dummy variables properly? Thank you very much!
 Linda K. Muthen posted on Monday, February 03, 2014 - 4:38 pm
This does not look correct. You should have a cluster variable that takes on the values of 1 through 10.

DEFINE:
sc1=0;
if cluster == 1 then sc1 = 1;
sc2=0;
if cluster == 2 then sc2 = 1;
ETC.
 luk bruyneel posted on Friday, February 07, 2014 - 7:02 am
Hello,

After a succesful multilevel mediation model (2-2-1), I'm looking for moderated mediation, using the Mplus codes that come with Preacher, Rucker and Hayes (2007) 'Addressing moderated mediation hypotheses'. I used model 2, where the a path is moderated by w (first stage moderation):

MODEL:
%WITHIN%
y on l;

%BETWEEN%
y on m (b1)
x
w
xw;
m on x (a1)
w
xw (a3);
MODEL CONSTRAINT:
new (ind wmodval);
wmodval = -1;
ind=(a1+a3*wmodval)*b1;

Your help would be appreciated in the complete and correct interpretation of the findings:
- m is significant to y, x/w/xw are not
- x and w are significant to m, xw is not
- significant indirect effect
 Bengt O. Muthen posted on Friday, February 07, 2014 - 7:53 pm
There is no significant moderation, but the indirect effect is significant.
 luk bruyneel posted on Friday, February 07, 2014 - 8:01 pm
Thanks for your reply!
-So if xw were significant to m, there would be significant moderation?
-Since x is not significant to y, there is full mediation?
 Bengt O. Muthen posted on Friday, February 07, 2014 - 8:02 pm
Right.
 luk bruyneel posted on Sunday, February 16, 2014 - 7:48 am
In the above multilevel moderated mediation model with a categorical outcome, Mplus automatically uses Bayesian estimation. In a previous post in the 'CFA with Bayesian estimation' forum you mentioned that PPC for multilevel models has not been implemented yet.
Is there a way to assess model fit here then?
 Linda K. Muthen posted on Sunday, February 16, 2014 - 5:14 pm
This has not yet been developed. So there is no way to assess fit.
 luk bruyneel posted on Sunday, February 23, 2014 - 8:02 am
Thanks for your reply! In my 2-2-1 model, I want to combine moderated mediation and simple mediation for another variable in the same model. Is the following model correct? Are there any problems known with such model, except that model fit cannot be assessed?

%BETWEEN%
!moderated mediation
y on m (b1)
x1
w
x1w;
m on x1 (a1)
w
x1w (a3);

!mediation
y on x2;
m on x2(a);


MODEL CONSTRAINT:
new (ind1 ind2 wmodval);
wmodval = 0.125;
ind1=(a1+a3*wmodval)*b1;
ind2=a*b1;
 Bengt O. Muthen posted on Tuesday, February 25, 2014 - 7:45 pm
I don't see a problem. Note that you can use the LOOP option (see UG ex 3.18).
 annebell yang posted on Monday, May 12, 2014 - 10:24 pm
Hi Dr. Muthen,
I am wondering if mplus can test two moderators at different stages at the sometime, like model 21 in Hayes' new book "PROCESS". Basically, I want to test a model like this:
x-->m-->y(y1, y2, y3),
the relation between x and m is moderated by moderator 1, and m-->Y relation is moderated by moderator2. In addition, I also have multiple dependent variables.

Moreover, these y1, y2, y3 are measured by team leaders (all other variables are individual level), so I want to control for team level variance, so I specify a two-level model,just no independent variables in level 2.

So my questions are
1 can mplus test such a model? because I could use PROCESS macro in spss to test this moderated mediation, but PROCESS does not have multilevel functions. and it can only test one dv at a time.

2 if mplus can, can I use indirect to test the moderated mediation? Do I need to test each dv at a time? But can I use indirect to test two moderators at the same time?

Thank you very much in advance for your reply!


annebell
 annebell yang posted on Monday, May 12, 2014 - 10:42 pm
Dear Dr. Muthen,
I also have another model I am not quite sure.
The model is a moderated mediation,
x-->m(m1, m2, m3)-->Y(Y1, Y2, Y3), and the relation between x and m is moderated by a Moderator. All These variables are individual level, except for Y is measured by team leader, so i want to control for team level variance, but no IVs in team level. I have three mediators, and three dependent variables.


I have used Bayes iterations, and the moderation is significant. However, if I just use regular iterations, the results are not significant. My question is what is the difference between the two? Which results should I use?



Thank you a lot!

annebell
 Bengt O. Muthen posted on Tuesday, May 13, 2014 - 11:38 am
This is possible in Mplus, but you have to study up on what it means. It is straightforward to do two-level moderated mediation in Mplus. In your case you just add a between part for the y variables by mentioning their variances. If Bayes gives significance and ML doesn't it can mean that the distribution of the estimate is not symmetric/normal. In this case Bayes is preferrable (bootstrap is an alternative for ML, but doesn't exist yet for two-level).
 Yan Liu posted on Monday, August 18, 2014 - 1:10 am
Dear Dr. Muthen

I am trying a 2-1-1 multilevel moderated mediational model. However, I always got a error message to ask me to define cluster, which I have included (teacher's id). Could you please take a look at my Mplus syntax? Thanks a lot!
(w=moderator, x=predictor,m=mediator, Sex=covariate, y1& y2=outcome)

DEFINE: xw=x*w;
USEVARIABLES ARE x Sex w m y1 y2 tchid xw;

MISSING=ALL(999);
CLUSTER = tchid;
BETWEEN= x xw;

ANALYSIS: TYPE = TWOLEVEL RANDOM;
STARTS=500;
STITERATIONS=500;

MODEL:
%WITHIN%
m y1 y2;
y1 ON Sex m;
y2 ON Sex m;

%BETWEEN%
x m y1 y2;
mom ON Sex
w
x (a1)
xw (a2);
y1 ON Sex
x
xw
w
m (b1);
y2 ON Sex
x
xw
w
m (b2);
MODEL CONSTRAINT:
NEW(ind1 ind2 wmodval);
wmodval=-1;
ind1=(a1+a2*wmodval)*b1;
ind2=(a1b+a2*wmodval)*b2;

*** ERROR in VARIABLE command
TYPE=TWOLEVEL requires specification for the CLUSTER option.
 Kristopher J. Preacher posted on Monday, August 18, 2014 - 1:34 am
Currently you have CLUSTER=tchid in the DEFINE section. You may want to move the command "DEFINE: xw=x*w;" outside the VARIABLE section.
 Yan Liu posted on Monday, August 18, 2014 - 2:57 am
Dear Dr. Preacher,

Thank you so much! It works!

I have one more question. I saw that wmodval is defined as -1 in an example (model 2) you provided in your paper (Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated Mediation hypotheses: Theory, methods, and prescriptions.)

What is this wmodval? How should we give the value to it?

Thanks!
Yan
 Kristopher J. Preacher posted on Monday, August 18, 2014 - 5:11 am
wmodval is any value of the moderator at which you wish to estimate the effect of x on y. It could be the moderator's mean, the minimum or maximum, 1SD above the mean, etc. -- anything. You should look into the LOOP command in Mplus; it makes probing interaction effects easier.
 Carolyn CL posted on Monday, August 25, 2014 - 3:15 pm
I have one dependent level-1 variable(y), one level-1 independent variable(z), one level-1 mediator(m1), two level-2 mediators(m2_1, m2_2), and two level-1 controls(age and sex). I include both cross-level indirect pathways (1-1-1, 1-2-1, 2-2-1) and mediated moderation (interactions):

USEVARIABLES ARE ID y z m1 m2_1 m2_2 age sex zXm1 m2_1Xm2_2 zXm2_1 m1Xm2_2;
CLUSTER = ID;
BETWEEN = m2_1 m2_2 m2_1Xm2_2;
DEFINE:
zXm1 = z*m1;
m2_1Xm2_2= m2_1*m2_2;
zXm2_1= z*m2_1;
m1Xm2_2= m1*m2_2;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
MODEL:
%WITHIN%
y z m1 zXm1;
y ON z m1 zXm1 age sex;
m1 ON z age sex;
%BETWEEN%
y z m1 m2_1 m2_2 zXm1 m2_1Xm2_2 zXm2_1 m1Xm2_2;
y ON z(a);
y ON m1(b);
y ON m2_2(c);
y ON m2_1(d);
y ON age sex zXm1 m2_1Xm2_2 zXm2_1;
y ON m1Xm2_2(j);
m1 ON z(e);
m1 ON m2_2(f);
m1 ON m2_1(g);
m1 ON age sex;
m2_2 ON m2_1(h);
m2_1 ON z(i);
m1 WITH m1Xm2_2;
MODEL CONSTRAINT:
NEW(INDgb INDfb INDeb INDsf xmodval);
INDgb=g*b;
INDfb=f*b;
INDeb=e*b;
xmodval = 1;
INDsf=f+(b+j*xmodval);

Can you confirm that a sig coefficient for the m1Xm2_2(j) suggests a moderated mediated effect, but not an indirect effect (given non-sig INDfb term)?
 Kristopher J. Preacher posted on Monday, August 25, 2014 - 9:18 pm
In your model, a significant j coefficient suggests a significant interaction between m1 and m2_2 in the 'between' model, not moderated mediation, and not an indirect effect. Also, instead of:

INDsf=f+(b+j*xmodval);

I think you mean:

INDsf=f*(b+j*xmodval);

...which is the conditional indirect effect of m2_2 on y through m1, at the point where m2_2 = 1.
 Carolyn CL posted on Monday, August 25, 2014 - 9:54 pm
Thank you for this.

A few follow up questions, if I may:
1) What can I make of a sig interaction, but no sig indirect or conditional indirect effects?
2) The estimated direct and indirect paths reflect unconflated estimates of within and between effects, with random intercepts?
3) Because I have very small cluster sizes (80% N =1, 20% N = 2-5), the within level of the model has very little power?
 Kristopher J. Preacher posted on Tuesday, August 26, 2014 - 10:08 pm
1) A n.s. indirect effect means that there is no evidence that the indirect effect departs from zero. A n.s. conditional indirect effect means that the effect in question does not detectably differ from zero at the chosen value of xmodval (but it might at others). The interaction's significance pertains only to the two interacting variables, and does not necessarily reflect the presence or absence of moderated mediation. We discuss how to quantify and test for the presence of moderated mediation for some models, including this one, in Appx. A of this paper (see Scenario 1). In your case, you can obtain a CI for f*j. If the CI excludes zero, that is evidence for moderated mediation.

2) You have no within effect of m2_2 on m1, only a between effect (f). There are both within and between effects of m1 on y, and only a between effect of the interaction term m1Xm2_2 (j). j is a strictly between effect, so all effects of interest are at the between level, and occur among level-2 variables and the random intercepts for the level-1 variables.

3) It is difficult to say without knowing more about your design and your expected effects. You can run a power analysis in Mplus, but because you already have the data it is probably too late to glean anything useful from a power analysis.
 Carolyn CL posted on Wednesday, August 27, 2014 - 7:06 pm
Many thanks for this.

To be clear, the model now includes:

Y ON m1Xm2_2(j) !interaction effect
INDfb = f*b !indirect effect effect of m2_2 on Y through m1
INDsf = f*(b+j*xmodval) !conditional indirect effect of m2_2 on Y, where effect through m1 depends on value of m2_2
INDjf = f*j !moderated mediation effect where strength of indirect effect of m2_2 on Y through m1 is moderated by m1
 Kristopher J. Preacher posted on Wednesday, August 27, 2014 - 8:27 pm
That looks right to me.
 Carolyn CL posted on Wednesday, September 03, 2014 - 2:59 pm
Dear Dr. Preacher,

I would like to obtain predicted values for the significant interaction term in my model.

I am unsure as to how to proceed in the MSEM framework and was hoping you would be able to provide me with a reference or formula to obtain predicted (fitted) values of y given specified values of x, and specified values for the interaction term.
 Kristopher J. Preacher posted on Thursday, September 04, 2014 - 7:07 pm
I am not sure how to do that with Mplus. It sounds like you want to compute predicted y-values given your equation with interactions. If so, that can be done using methods developed for regular regression models, perhaps using a spreadsheet.
 Carolyn CL posted on Friday, September 05, 2014 - 6:37 pm
Thanks for this.

In the end, given that there were no sig. conditional indirect effects nor moderated mediated effects, we decided to simply estimate the interaction term.

However, I noticed that inclusion of the interaction term (m1Xm2_2) changes the direction of the m2_2 direct effect on y (without the interaction term B = -.09, ns; with the interaction term B = .19,ns).

1) Is this likely a result of adjusting for the interaction term, or should I be concerned about potential multicollinearity?

I also noticed that in fig. A (Model 1) in Preacher, Rucker & Hayes (2007) it appears as though the interaction term (xm) is allowed to correlate with both x and m, but the syntax for Model 1 in the appendix only specifies a correlation between xm and m.

(2) Should only a correlation between xm and m be specified when estimating an interaction term?

I ask in part because my coefficients (size) and their significance level change in somewhat meaningful ways depending on whether I specify a correlation between xm and m, or include an additional correlation between xm and x.
 Kristopher J. Preacher posted on Friday, September 05, 2014 - 10:31 pm
1a. The coefficient has a different interpretation after including the product, and thus a different value. Prior to adding the product, c is the effect of m2_2 holding constant m1 (and all other predictors). After adding the product, c is the effect of m2_2 where m1 = 0 (holding constant all other predictors).

1b, 2. The code is outdated. I would add the covariance. Otherwise you risk introducing misfit. xm and m will almost certainly be correlated, and fixing this parameter to 0 can induce bias.
 Carolyn CL posted on Monday, September 08, 2014 - 1:20 pm
1) To be clear, when you say 'I would add the covariance', you mean 'xm WITH m' and 'xm WITH x'?

2) Also, should I be concerned that when I run the model as a multiple linear regression (in SPSS) and include the interaction term (m1Xm2_2) I get a VIF > 5 for the m2_2 coefficient?

3) My understanding is that the traditional approach taken to deal with multicollinearity induced by interaction terms is to mean center variables before creating the product term, but that the MSEM approach does not require centering of variables. Is this correct?
 Kristopher J. Preacher posted on Monday, September 08, 2014 - 2:59 pm
1. Yes. Or more simply, 'xm WITH m x'.

2, 3. These sound more like regression-related questions than Mplus-specific issues. But in general, centering has no effect on estimates or tests of interaction effects. You might pursue this topic on the SEMNET listserv.
 Yan Liu posted on Saturday, September 13, 2014 - 2:17 pm
Dear Dr. Preacher,

I conducted a multilevel moderated mediational model.
MODEL:
%WITHIN%
m y1 y2;
y1 ON Sex m;
y2 ON Sex m;

%BETWEEN%
x m y1 y2;
mom ON Sex
w
x (a1)
xw (a2);
y1 ON Sex
x
xw
w
m (b1);
y2 ON Sex
x
xw
w
m (b2);

The model is terminated normally. However, my model fit is bad. Do you think it's because my model doesn't fit the data well or because of cluster size or other issues?
Thanks a lot!

Model fit:
Chi-Square Test of Model Fit Value 636.624
Degrees of Freedom 7
P-Value 0.0000

RMSEA Estimate 0.286

CFI 0.677
TLI -0.244

SRMR
Value for Within 0.235
Value for Between 0.021
 Kristopher J. Preacher posted on Saturday, September 13, 2014 - 5:31 pm
It is probably because there are 7 parameters constrained to zero in your model, and some of these are not reasonable in light of the data.

This is not a software-specific question. You might get better help on a general listserv like SEMNET.
 Johanna Seiz posted on Tuesday, November 11, 2014 - 8:56 am
I am trying to calculate a multilevel mediated moderation (analogous to model 2 in Preacher, Rucker & Hayes, 2007)where a third variable (Level 2) affects path a (Mediation is lower level). I wanted to build my models gradually, so I started off calculating my 1-1-1 mediation using Preachers' syntax from the top of this post.

Yet I keep on getting the following error message:

*** FATAL ERROR
THERE IS NOT ENOUGH MEMORY SPACE TO RUN THE PROGRAM ON THE CURRENT
INPUT FILE. THE ANALYSIS REQUIRES 5 DIMENSIONS OF INTEGRATION RESULTING
IN A TOTAL OF 0.75938E+06 INTEGRATION POINTS. THIS MAY BE THE CAUSE
OF THE MEMORY SHORTAGE. YOU CAN TRY TO REDUCE THE NUMBER OF DIMENSIONS
OF INTEGRATION OR THE NUMBER OF INTEGRATION POINTS.

Is there anything I can do about this?
I also tried to specify sa and sc as random, only keeping sb fixed (following my hypotheses),

sa | m ON x;
y ON m(sb);
sc | y ON x;

(rest of the syntax being equal)

yet somehow MPLUS does not recognize sb in this way.

*** ERROR in MODEL command
Unknown variable(s) in a WITH statement: SB

What did I do wrong?
Your help would be very much appreciated!
 Linda K. Muthen posted on Tuesday, November 11, 2014 - 10:34 am
You can try using INTEGRATION=MONTECARLO (5000); Five dimensions of integration is computationally heavy. You may want to try the random effects one at a time and estimate them as fixed if the variances are not significant.

To change

sb | y ON m;

to a fixed effect, say

y ON m;
 Yan Liu posted on Tuesday, November 11, 2014 - 11:02 am
Dear Dr. Muthen,
I am trying a 2-1-1 multilevel moderated mediational model. My outcome is a count variable (minutes of phyical activities) with a long tail.

If the outcome is treated as continuous, the model works, but the model fit is bad. However, the model won't run if the outcome is treated as count. Could you please give me some advice?
Thanks!
Yan

(note. x=predictor, y=outcome, mod=moderator,med=mediator)
USEVARIABLES ARE x covariate mod med y tchid x_mod;
CLUSTER = tchid;
BETWEEN= x ;
COUNT ARE y (nb);

DEFINE:
x_mod = x*mod;

ANALYSIS: TYPE = TWOLEVEL RANDOM;
STARTS=500;
STITERATIONS=100;
ALGORITHM = INTEGRATION;
INTEGRATION =GAUSSHERMITE;
MCONVERGENCE = 0.01;
MODEL:
%WITHIN%
Y ON covariate
med;

%BETWEEN%
med ON covariate
mod
x (a1)
x_mod (a2);
y ON covariate
x
mod
x_mod
med (b1);

MODEL CONSTRAINT:
NEW(ind1 mod);
mod=-1;
ind1=(a1+a2*mod)*b1;
 Linda K. Muthen posted on Tuesday, November 11, 2014 - 7:26 pm
Please send the output and your license number to support@statmodel.com.
 Johanna Seiz posted on Wednesday, November 12, 2014 - 6:48 am
Dear Linda,

thank you for the quick reply. If I use Montecarlo Integration (as you suggested), I always receive the error:

*** FATAL ERROR
THIS MODEL CAN BE DONE ONLY WITH MONTECARLO INTEGRATION.

..which I really don't understand, as I used it.

Concerning the fixed effects, when I specify them as you suggested, how can I calculate the Model constraints/indirect effect if I do not give a label to the slope? (as it is a 1-1-1 Mediation?)


Thanks again!
 Linda K. Muthen posted on Wednesday, November 12, 2014 - 11:47 am
Please send the output and your license number to support@statmodel.com.

You can label the slope if you want to. If you have a problem with that, send the output.
 Samantha Paustian-Underdahl posted on Thursday, January 15, 2015 - 11:52 am
I am testing a ML moderated mediation with the mediation model at level 1 and the moderator at level 2. The level 2 moderator is categorical. Will Mplus allow me to dummy code this variable and include dummy variables as level 2 moderator?
 Bengt O. Muthen posted on Thursday, January 15, 2015 - 1:50 pm
Yes.
 Cassie Suh posted on Tuesday, February 10, 2015 - 5:51 am
Hello! I am trying to do a 1-1-1 multilevel mediation with a level 2 moderator that impacts path a (model2 moderated mediation)

The code I wrote so far is:
(m<-y, h <-m, q <-x, u<-w, and b,c,d,e are level 1 control variables)
Variable:
Names are
a b c d e f g h i j k l m n o p q r s t u;
Missing are all (-99);
usevariables are a b c d e h m q u;
Cluster is a;
Within are b c d e;
Between are u;
Analysis:
Type=Twolevel random;
Model:
%WITHIN%
sa | h(m) ON q(x) b c d e;
sb | m(y) ON q(x) b c d e;
sc | m(y) ON h(m);
h m;
%BETWEEN%
sa sb h m q;
[sa](a1);
[sc](b1);
m ON u(w);
h ON u(w);
sa ON u(w)(a3);
sb ON u(w);
MODEL CONSTRAINT:
NEW(ind1 ind2 ind3);
ind1= b1*(a1+a3*(-2.66));
ind2= b1*(a1+a3*(0);
ind3= b1*(a1+a3*2.66);
Output: cinterval;

It runs without problems but I'm not sure if its correct(especially the control variables part).
Also, if it is correct, do the significant results of SA ON U
tell me that there is a moderated mediation?
Or as the CI results for IND1 IND2 IND3 all include 0 is there no interaction effect?
Thank you.
 Cassie Suh posted on Tuesday, February 10, 2015 - 12:22 pm
Hello again, I wanted to revise my question but I couldn't find an edit or delete function so I'm just adding on to above. I'm sorry for not being able to make it into one post.

Along with wanting to know if the code in the above post is correct,
again, assuming that the code above is correct, if SB ON U(interaction) is significant then I have read that there is moderated mediation. Is this correct?

However, I have also read that looking that the conditional indirect effects per group, the CI intervals for some groups should include 0 while others do not(interpretation of PROCESS results).
What does it mean if, as mentioned above, there is a significant interaction effect but
1) all the CI include 0s
2) all the CI don't include 0 and IND1, IND2 and IND3 are all significant.

In other words, I would like to know how to interpret the results to see if there is indeed the effect I'm looking for.

Thank you very much in advance.
 Bengt O. Muthen posted on Tuesday, February 10, 2015 - 5:59 pm
Your input

%WITHIN%
sa | h(m) ON q(x) b c d e;
sb | m(y) ON q(x) b c d e;
sc | m(y) ON h(m);

is not correct. You can have only one slope on the right of the bar (|) so e.g.

sa | h on q;

And I don't know what the parenthetical x, m, y refer to - are they labels? Only one label before ; can be used.

Also, your notation

m<-y, h <-m, q <-x, u<-w

is unclear to me - do you really mean for y to influence m, for instance? Mediation modeling uses

x->m->y

(typically going from left to right as I show).

Let's straighten this out first.
 Cassie Suh posted on Wednesday, February 11, 2015 - 7:34 am
oh, i see that it could be confusing, i only used the <- and () signs so that you could better follow what i named my variables.
For instance, i only meant the q was what i named my x variable, m my y variable and so on. i know that () and stuff aren't used in mplus and the arrows have nothinf to do with my model.

Therefore, excluding that
i would say
sa | h on q
h on b c d e?

what about my other questions?

thank you!
 Bengt O. Muthen posted on Wednesday, February 11, 2015 - 2:46 pm
Please send your output to Support and explain exactly what you are asking about in the output.
 Lieke ten Brummelhuis posted on Wednesday, April 08, 2015 - 6:13 pm
I have the exact same question as this thread started with (Antje Schmitt, Oct 27 2008).

I have a 1-1-1 mediation model moderated by a level 2 variable (first stage moderation). I'm trying to find out three things:

1) How to estimate the mediation model in Mplus. I usually use the indirect model (IND) for this. Is this ok to use in a two-level model?

2) I don't understand the syntax dr. Preacher gave as answer to the first post (to test the moderated mediation model). More specifically, where is the moderator variable in this syntax? Or, is the interaction effect estimated by using random slopes? If so, how do I know the random slopes are caused by my moderator?

3) If I have a binary variable for the level 2 moderator, is is possible to use multi-group analysis and compare the mediation models between two groups? Or is this not an optimal solution?

Thank you!
 Bengt O. Muthen posted on Thursday, April 09, 2015 - 12:24 am
1) Yes.

2) See the handout and video for our Topic 7 short course, slides 67-85.

3) It is a good solution.
 Lieke ten Brummelhuis posted on Saturday, April 11, 2015 - 5:17 pm
Thank you for your quick reply Bengt. I watched the video in which you go over the syntax briefly. Just to make sure I understand it correctly: this syntax is just to estimate the 1-1-1 mediation model and will show if the indirect effect varies on the between level, right? Because if there is no variance on level two, there is no need to explain this variance with a level 2 variable. I just ran the syntax separately for four x variables and the variances of sa, sb, sc and the indirect effect are all not significant except for one (sa for one x). Can I then conclude that the mediated model does not vary between groups? Thank you!
 Bengt O. Muthen posted on Sunday, April 12, 2015 - 11:38 pm
When you say "group" in your last sentence, do you mean "cluster/level-2 units"?
 Lieke ten Brummelhuis posted on Monday, April 20, 2015 - 6:51 pm
I think I should have said, "can I then conclude that the mediated model does not vary between level-2 units".

The level 2 units are persons (we have five days clustered in persons). We'd like to know if the mediation model differs between persons with and without children, so that is a level-2 variable. That's why I said groups, referring to people with children as group 1 and people without children as group 2. But I guess I can only say that the mediation model does not vary between people, which indirectly means it also does not vary between people with and without children. Is that correct?
 Bengt O. Muthen posted on Tuesday, April 21, 2015 - 12:06 am
Right.
 Dan R. posted on Wednesday, May 20, 2015 - 2:10 pm
If I have a level 1 mediation model, but the mediator is best described as a moderation (i.e., mediator variable * dummy coded condition), what is the best way to include the main effects in the within level?

For example:
M*C ON X;
Y ON M*C;
Y ON X;

1) I presume I should also include Y ON M and Y ON C, no?

2) If the main effects are included at the within level, should the moderation M*C and Y be the only variables with between level variance?

If any articles or information comes to mind regarding this unique 'moderated effect as a mediator' situation, I'd love to read further. Thank you for your help!
 Bengt O. Muthen posted on Wednesday, May 20, 2015 - 5:39 pm
I think what you are saying is that you want the regression slope of Y on M to be different for (moderated by) different values of C. Then you say

y on x m c mc;
m on x;

There may be substantive reason to regress m not only on x, but also on c.

Note that the inclusion of the mc interaction variable throws off the chi-square testing and it should be ignored. See Preacher et al.'s (2007 Model 3.
 Tao Yang posted on Tuesday, June 02, 2015 - 9:34 pm
Hello, I have a 2-1-1 model with a level-1 moderator for the first-stage mediation. x was measured at level-2. m,y,and w(moderator) were measured at level-1 and had variance at level-2. If I understand correctly, the moderated mediation would operate at level-2 so I computed level-2 mean of w as the moderator. Below is my syntax.

VARIABLE:
NAMES = y x m w w_mean clus; !w_mean is level 2 mean of w
USEVARIABLE = y x m w_mean xw;
BETWEEN = x w_mean xw;
CLUSTER = clus;
MISSING = .;

DEFINE:
CENTER x w_mean (GRANDMEAN);
xw = x * w_mean;

ANALYSIS:
TYPE = TWOLEVEL;

MODEL:
%WITHIN% ! no hypothesis at within level

%BETWEEN%
y ON m (b)
x (cp)
w_mean
xw;

m ON x (a1)
w_mean
xw (a3);

MODEL CONSTRAINT:
NEW(ind_l ind_h tot_l tot_h);
! between-level conditional indirect effect and total effect
ind_l = b*(a1+a3*-2);! suppose -1SD of w_mean is -2
ind_h = b*(a1+a3*2); ! suppose +1SD of w_mean is 2
tot_l = cp+ind_l;
tot_h = cp_ind_h;

Can I have your suggestion on:
(1) Was model specification and conditional indirect effect correct?
(2) Was it necessary to have "y ON w_mean xw" under %BETWEEN%?

Thanks!!
 Bengt O. Muthen posted on Wednesday, June 03, 2015 - 12:32 am
1. The Between looks fine, but you want to make sure that m, y and w are allowed to at least correlate on Within. And if you have
m-> y on Between, why wouldn't that hold also on Within?

2. It sounds like your main focus was on moderating the x-> path, but often that moderator and its interaction also influence y. I don't think it is always substantively necessary to include that, but practically speaking it may be a good idea.
 Tao Yang posted on Wednesday, June 03, 2015 - 4:52 am
Thank you, Bengt! This is very helpful! I realized that m, y and w also had variances on another level-2 cluster. So x was on level-2b. m, y, and w on level-1 and had variances on level-2a and level-2b. My focus was w moderating the first stage of the 2-1-1 mediation on level-2b. Syntax below.

VARIABLE:
NAMES = y x m w w_mean2a w_mean2b level2a level2b;
! w is original value
! w_mean2a is mean w on level2a
! w_mean2b is mean w on level2b
USEVARIABLE = y x m w_mean2a w_mean2b w_c xw;
CLUSTER = level2b level2a;
WITHIN = w_c;
BETWEEN = (level2a) w_mean2a (level2b) x w_mean2b xw;

DEFINE:
w_c = w - w_mean2a - w_mean2b;
xw = x * w_mean2b;

ANALYSIS:
TYPE = CROSSCLASSIFIED;

MODEL:
%WITHIN%
y ON m; ! m -> y holds on Within
w_c WITH m y;

%BETWEEN level2a%
y ON m; ! m -> y holds on level2a
w_mean2a WITH m y;

%BETWEEN level2b%
y ON m (b)
x (cp)
w_mean2b
xw;

m ON x (a1)
w_mean2b
xw (a3);

(1) Does %BETWEEN level2b% portion look right?

(2) To correlate w, m, and y on Within and Level2a, I decomposed w into mean on level-2a, mean on level-2b, and w on Within. Is it the right approach in cross-classified data? Okay to compute w on Within as "w - w_mean2a - w_mean2b"?

Thanks!!
 Bengt O. Muthen posted on Wednesday, June 03, 2015 - 6:48 pm
Looks reasonable.
 Tao Yang posted on Thursday, June 04, 2015 - 12:33 pm
Thank you, Bengt!
 tom norton posted on Thursday, August 06, 2015 - 5:12 am
Hi Bengt

I'm attempting to run a level-1 mediation with two level-2 moderators. W moderates the X-M path only, and V moderates the M-Y path only:

VARIABLE: NAMES = ID X M W V Y;
USEVARIABLES = ID X M W V Y;
CLUSTER IS ID;
MISSING ARE ALL(-99);
BETWEEN ARE W V;
WITHIN ARE X;

ANALYSIS:
TYPE = TWOLEVEL RANDOM;
ALGORITHM = INTEGRATION;
INTEGRATION = MONTECARLO;
MITERATIONS = 1000;

MODEL:
%WITHIN%
X M Y;
sa | M ON X;
sb | Y ON M;
sc | Y ON X;

%BETWEEN%
sa sb sc M Y;
sa WITH sc M Y;
sa WITH sb(cab);
sb WITH sc M Y;
sc WITH M Y;
Y ON V (b2);
M ON W (a2);
sa ON W (a3);
sb ON V (b3);
[sa](sa);
[sb](sb);
[sc](sc);

OUTPUT:
TECH1 TECH8 CINTERVAL;

I am confronted with the error message:

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-ZERO DERIVATIVE OF THE OBSERVED-DATA LOGLIKELIHOOD.
THE MCONVERGENCE CRITERION OF THE EM ALGORITHM IS NOT FULFILLED. CHECK YOUR STARTING VALUES OR INCREASE THE NUMBER OF MITERATIONS.

Would you suggest increasing the MITERATIONS further, or making changes elsewhere?

Regards

Tom Norton
 Linda K. Muthen posted on Thursday, August 06, 2015 - 1:02 pm
I would try the suggestion of increasing the number of MITERATIONS as a first step. The default is 500.
 tom norton posted on Monday, August 10, 2015 - 12:07 am
Hi Linda, I increased the number of MITERATIONS to 2000, and received the following error message:

THE MODEL ESTIMATION DID NOT TERMINATE
NORMALLY DUE TO A CHANGE IN THE
LOGLIKELIHOOD DURING THE LAST E STEP.

AN INSUFFICENT NUMBER OF E STEP ITERATIONS MAY
HAVE BEEN USED. INCREASE
THE NUMBER OF MITERATIONS OR INCREASE THE
MCONVERGENCE VALUE. ESTIMATES
CANNOT BE TRUSTED.

SLOW CONVERGENCE DUE TO PARAMETER 20.
THE LOGLIKELIHOOD DERIVATIVE FOR THIS PARAMETER IS 0.14395229D+00.

What would you suggest as a next step?
 Bengt O. Muthen posted on Monday, August 10, 2015 - 1:16 am
Try

integration = montecarlo(5000);

Ask for tech8 and make sure you don't have negative abs changes which would point to poor precision. Also look to see how many dimensions of integration you have - the more you have, the more integration points you need.

Alternatively, you can introduce one random slope at a time and see if it is needed, that is, if it really has a substantial variance; most don't.
 tom norton posted on Wednesday, August 12, 2015 - 6:55 am
Hi Bengt, I ran the model with montecarlo(5000) and 2000 MITERATIONS with the following message:

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-ZERO DERIVATIVE OF THE OBSERVED-DATA LOGLIKELIHOOD.

THE MCONVERGENCE CRITERION OF THE EM ALGORITHM IS NOT FULFILLED. CHECK YOUR STARTING VALUES OR INCREASE THE NUMBER OF MITERATIONS. ESTIMATES CANNOT BE TRUSTED. THE LOGLIKELIHOOD DERIVATIVE FOR THE FOLLOWING PARAMETER IS -0.31927547D+00: Parameter 14, %BETWEEN%: SA

I found negative abs changes for approx 1600 MITERATIONS
 Bengt O. Muthen posted on Wednesday, August 12, 2015 - 10:49 pm
If you don't have more than say 4 dimensions you can stay with the default integ = 15 and get good precision without neg abs changes.
 Milica Lazic posted on Sunday, August 16, 2015 - 12:58 pm
Dear Dr(s) Muthen,

I have 1-1-1 multilevel mediation model, with moderator on level 2. Also, I need a model with nonlinear moderator.Is it possible to test such a multilevel model with Mplus and how could I perform the analyis?

I created this sintax:

TITLE: two level nonlinear moderated mediation;
Data: file is C:/NJ.txt;
Variable: names = id y x m w;
Usevariables = id y x m w xw z xz;

WITHIN = x m;
BETWEEN = w z;
CLUSTER = id;

DEFINE:
xw=x*w;
z=w*w;
xz=z*x; !nonlinear interaction

Analysis:
TYPE= TWOLEVEL RANDOM;
ESTIMATOR=MLR;
ALGORITHM=INTEGRATION;

Model:
%WITHIN%
m ON x(aw); ! regress m on x, call the slope "aw"
y ON m(bw); ! regress y on m, call the slope "bw"
y ON x; ! regress y on x
y ON m x;
s | m ON x;

%BETWEEN%
m w xw z xz;
s ON w
s ON xw;
s ON z;
s ON xz;

MODEL CONSTRAINT:
NEW(indw);
indw=aw*bw;

Output:sampstat stdyx TECH1 TECH8 CINTERVAL;


Thanks a lot in advance!
 Linda K. Muthen posted on Sunday, August 16, 2015 - 3:56 pm
Are you asking about a nominal moderator or a nominal mediator. In your support question you say a nominal mediator.
 Milica Lazic posted on Sunday, August 16, 2015 - 4:05 pm
Dear Linda,

I am asking about nonlinear (squared) moderator.
 Bengt O. Muthen posted on Sunday, August 16, 2015 - 4:52 pm
You regress s on that squared moderator on Between.
 Milica Lazic posted on Monday, August 17, 2015 - 2:32 pm
I want to know does this look correct?

Thank you.
 Bengt O. Muthen posted on Tuesday, August 18, 2015 - 12:46 am
I see s on z; on between, so that looks correct for capturing a quadratic effect of your between-level variable w.

But you also have s ON xw; The xw variable has variation on both within and between, but you don't include it on within so I worry that no variance for xw is estimated on within. If you don't want to deal with xw on within you can create a cluster mean version of x and then create xw and work with it on between only.
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