Moderated Mediation
Message/Author
 Michael Strambler posted on Tuesday, September 21, 2010 - 11:23 am
I am attempting to test a moderated mediation model where X->M->Y (all observed variables) is moderated by w, a binary variable (gender). I know how to examine this with a multiple group approach but am attempting the approach described in Preacher, Rucker & Hayes (2007) in Figure 2 model 5 where W influences paths a and b of the mediation chain.

With some help from Preacher & Hayes, I have modeled this as pasted below. However, all of the estimates SEs, ps, CIs are exactly the same for all of the paths with the exception of X->M and M->Y. This seems very odd to me. Can you point me to what I might be doing wrong? Thank you.

ANALYSIS: BOOTSTRAP = 1000;

MODEL:
M WITH MW;
M ON X (a1)
W XW (a3);
Y ON M (b1)
X W XW MW (b2);

MODEL CONSTRAINT:
NEW(eff1 eff2);
eff1=(a1+a3*1)*(b1+b2*1);
eff2=(a1+a3*2)*(b1+b2*2);
OUTPUT: CINTERVAL(bcbootstrap);
 Linda K. Muthen posted on Tuesday, September 21, 2010 - 2:18 pm
Can you send your input, data, output, and license number to support@statmodel.com.
 Linda K. Muthen posted on Tuesday, September 21, 2010 - 5:34 pm
I should have seen this earlier. The label b2 after x, w, ex, and mw holds all of those regression coefficients equal. It should be stated as:

Y ON M (b1)
X W XW
MW (b2);
 Michael Strambler posted on Tuesday, September 21, 2010 - 6:30 pm
Thank you. The results make much more sense now. Now it is only the M on W and M on MW results that are identical. Does it make sense that this would be the case? Might this be because the MW cross-product involves a binary variable (coded 1 & 2)?
 Linda K. Muthen posted on Tuesday, September 21, 2010 - 6:42 pm
I think you mean M on w and Xw. It is the same issue. The label needs to be on the next line.

M ON X (a1)
W
XW (a3);
 Michael Strambler posted on Tuesday, September 21, 2010 - 6:47 pm
Ah, yes. All looks well now. Thank you again for the help.
 Robert Wickham posted on Monday, November 01, 2010 - 8:52 am
Drs. Muthen,
I am attempting to fit a Moderated Mediation model with simple (single level) survey data. Specifically, I wish to examine the moderating influence of a dichotomous variable (Mod) effect coded (-1, +1) on the 'A', 'B', and 'Cprime' paths as seen in Edwards and Lambert (2007; Model H).
I realize that the multigroup function of Mplus may be used in this specific instance(e.g. a categorical moderator), however I would like to retain the more traditional 'cross product' approach for two reasons: 1) To replicate OLS estimates for all paths, 2) I am often interested in similar models with continuous moderators where multigroup analysis is not appropriate.
IV and Mod were centered prior to importing into Mplus, and product terms were created using a DEFINE statement.
I use the following code:

MODEL:
Med on Mod IV IVxMod; ! 'A' Path
Y on Mod IV IVxMod Med ModxMed; ! 'B' and 'Cprime' Paths

MODEL INDIRECT:
Y IND Med IV;

The resulting model has df = 1 and a significant ChiSq. Examination of RESIDUAL matrix suggests a notable covariance between Med and ModxMed.
Adding a covariance parameter results in a not-positive first-order derivative matrix.

I have run into this problem before in the past, and I have a hunch that it stems from the fact that Med is an endog variable.
Thanks
 Linda K. Muthen posted on Tuesday, November 02, 2010 - 10:21 am
If you obtain standard errors, the message most likely comes from the fact that the mean and the variance of your binary variable are not orthogonal. You can ignore the message if this is the case.
 Hong Deng posted on Thursday, May 10, 2012 - 8:10 pm
Dear Drs. Muthen,
I’m trying to test a moderated mediation model with nested data. Data for all my variables were collected from individual and the level of interest is individual too. Basically it is a 1-1-1 mediation model (x-m-y)with a level 1 moderator (w). It should be an easy one if my data isn’t nested in several clusters. Is it possible to test such a model in Mplus? How should I write my Syntax.
Thanks very much.
 Linda K. Muthen posted on Friday, May 11, 2012 - 10:20 am
Moderation can be handled by a multiple group analysis if the moderator is categorical or by creating an interaction term between the moderator and the variable being moderated. You can use TYPE=COMPLEX to take the non-independence of observations into account. Modify Example 3.11 and add CLUSTER to the VARIABLE command and TYPE=COMPLEX to the ANALYSIS command.
 Elizabeth Penela posted on Friday, May 25, 2012 - 2:48 pm
I am attempting to conduct a moderated mediation analysis where all variables are latent variables formed with continuous indicators. In my model, the independent variable (X) functions as a moderator of the b1 path (the path from the mediating variable to outcome). This model is illustrated in Preacher, Rucker & Hayes (2007) - Figure 2, Model 1.

I get an error message that says:
MODEL INDIRECT is not available for TYPE=RANDOM.

1. Is it possible to do moderated mediation with a latent interaction variable?

2. Any guidance as to how to generate syntax for this model would be greatly appreciated.

Best,
Elizabeth
 Bengt O. Muthen posted on Friday, May 25, 2012 - 3:03 pm
This type of model is discussed in Section 3 and Section 5 of

Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.

which is on our web site under Papers, Mediational Modeling. As stated in Section 3, Model Indirect cannot be used for this type of model. Section 5 shows how to define the direct and indirect effects instead using Model Constraint.
 Paula Ruttle posted on Thursday, August 30, 2012 - 12:17 pm
Dear Drs. Muthen,
I am currently running a moderated mediation model (X -> A -> Y with the pathway from A to Y being moderated by gender) using the following syntax:

Y on X;
A on X(Med1);
Y on A(Med2);

Y on Gender A*Gender;

MODEL CONSTRAINT:
NEW(Indir1);
Indir1=Med1*Med2;

This model revealed significant moderated mediation; however, correlations suggested that moderation could also be expected on the pathway between X and A. When I checked for moderation of this pathway it also revealed significant moderated mediation. I've been told that presenting a model with both moderated pathways is inappropriate and that I need to check to see which model is best; however I am unsure of how to do this. Do you have any advice or syntax for such a problem?

Many thanks in advance,
Paula
 Bengt O. Muthen posted on Friday, August 31, 2012 - 2:49 pm
I would suggest a 2-group analysis with gender as the grouping variable. You can then easily test if the two paths are the same or different across gender. I can't see why a model with both paths differing across gender would be inappropriate.
 Luisa Rossi posted on Thursday, October 25, 2012 - 4:32 am
Dear Drs Muthen,

I have been running some mediation analyses and found that the x-->y relationship was mediated by m.

I would now like to see if the a and b paths of the indirect models are different depending on whether respondents score high or low on a number of personality measures.

So far, I have used multiple group comparisons with difftest to assess this.

I am now thinking there may be a better way to do it but I am not sure. Can you help?

Thanks,
Luisa
 Linda K. Muthen posted on Thursday, October 25, 2012 - 9:57 am
Why are you dissatisfied with your approach? Is it because your moderator is continuous and you are categorizing it? See Example 3.18 in the Version 7 Mplus User's Guide on the website for another approach to moderated mediation.
 Luisa Rossi posted on Thursday, October 25, 2012 - 10:08 am
Hi Linda,

Thanks for the tip! I will look at the example. I am unsure whether multiple group comparison is the most effective way to look at moderated mediation or whether reviewers may criticize it.

Thanks again!
 Linda K. Muthen posted on Thursday, October 25, 2012 - 11:47 am
There are two ways to look at moderation. One is multiple group and the other to create an interaction variable.
 Luisa Rossi posted on Tuesday, October 30, 2012 - 7:03 am
Hi Linda,

I work with survey data so I had to impute my dataset to account of missing data.

I noticed that difftest cannot be used with imputed data so I am thinking about using the interaction variable approach.

The example you recommended above seems to be based on path analysis (?) as it is able to use the define option after the usevariable one.

I am working with latent variables so I first need to define them - however, mplus is not happy for me to use 'define' within the 'model' option.

What can I do?
 Linda K. Muthen posted on Tuesday, October 30, 2012 - 1:35 pm
With latent variables, you should use the XWITH option for interactions. DEFINE is for observed variables. You don't include it in the MODEL command but above or below it.
 Luisa Rossi posted on Wednesday, October 31, 2012 - 5:15 am
Thanks Linda!

AS I am interested in the potential moderating role of w on path a and b, I adapted the model 5 example in Preacher, Rucker, and Hayes (2007) but I used the XWITH command to obtain the two interaction terms

mw | m XWITH w;
xw | x XWITH w;

and included these interaction terms in the model as they suggest:

MODEL:
y on m (b1)
x
w
mw (b2)
xw;
m on x (a1)
w
xw (a3);

I find that there is no evidence for a moderating role of either mw or xw (Ps>.05).

However, when I had run the multiple group comparisons using w as the grouping variable I had found that it moderated path a (not b)...

I am slightly confused on why this might be... can you help? are the 2 approaches not 100% comparable?
 Linda K. Muthen posted on Wednesday, October 31, 2012 - 1:05 pm
These two approaches should yield identical results. Please send the two outputs and your license number to support@statmodel.com.
 C. Lechner posted on Monday, January 14, 2013 - 7:58 am
Dear Drs. Muthén,

I am testing a moderated mediation model where the moderator is a latent variable; i.e., there is a latent interaction using the XWITH command involved.
Because this requires TYPE=RANDOM, the STANDARDIZED output is not available in these analyses. However, I would like to report R-square values for my outcomes.
--> Is there any way to obtain R-square values for these analyses?

Many thanks in advance!
Clemens
 Linda K. Muthen posted on Monday, January 14, 2013 - 10:35 am
See the FAQ Latent Variable Interactions on the website.
 C. Lechner posted on Thursday, January 17, 2013 - 7:38 am
Thanks, Linda. I have a follow-up question:

Using the formulas provided in the FAQ, I programmed myself an Excel spreadsheet that calculates R-square, change in R-square, and standardized path coefficients. It reproduces the numbers from your example on p. 6 in the FAQ sheet perfectly well.

However, I wonder how one would generalize the equations from the FAQ sheet to include covariates. In my model (otherwise identical to Fig.2 on p.7), all three latent variables are regressed on a set of covariates. -> How do I get the total variances of the latent variables in this case?

My approach was to sum all the product terms of the squared regression weights and the variance of the respective predictor, plus the residual variance of the latent variable (which I get in the output). E.g., for a latent variable eta2, regressed on eta1 and covariates x1 and x2, where b1 to b3 denote regression coefficients and zeta2 the residual variance of eta2, the total variance would be obtained by computing:
Var(eta2) = b1^2 * Var(x1) + b2^2 * Var(x2)+ b3^2 * Var(eta1) + Var(zeta2).

However, this seems to systematically underestimate r-square.
-> Have I overlooked anything?
-> Is there any way to directly get the total variance of a latent variable that is regressed on a set of covariates in the Mplus output?
 Linda K. Muthen posted on Thursday, January 17, 2013 - 8:52 am
You need the variances of the two factors in the interaction. I think you are using the residual variances. If the variances are not available in TECH4, you will need to compute them.
 C. Lechner posted on Thursday, January 17, 2013 - 9:42 am
TECH4 is unavailable for TYPE = RANDOM. I tried to compute the variances of all latent variables in the way described above. Referring to the notation in Figure 2 in the FAQ sheet, extended by two covariates x1 and x2 for each latent variable, I compute

Var(eta1) = b11^2 * Var(x1) + b12^2 * Var(x2)+ ß^2 * Var(eta2) + Var(zeta1)

Var(eta2) = b21^2 * Var(x1) + b22^2 * Var(x2)+ Var(zeta2)

Var(eta3) = b31^2 * Var(x1) + b32^2 * Var(x2)+ ß1^2 * Var(eta1) + ß2^2 * Var(eta2) + 2*ß1*ß2*Cov(eta1,eta2)+ß3^2*Var(eta1*eta2) + Var(zeta3)

where eta1 is regressed on eta2 (coefficient ß), eta3 is regressed on eta1 (coefficient ß1), eta2 (coefficient ß2), and their interaction (coefficient ß3), all three latent are regressed on the covariates x1 and x2 (coefficients bij), zeta_i denote residual variances for the latent variables; and where Var(eta1*eta2) = Var(eta1)*Var(eta2)+[Cov(eta1,eta2)]^2 and Cov(eta1,eta2) = ß*Var(eta2).

-> Is this correct? There must be something missing. R-squares are substantially smaller than the ones Mplus computes for a model without interaction.
 Bengt O. Muthen posted on Thursday, January 17, 2013 - 5:29 pm
In your eta1 equation you have to express eta2 in terms of the x's so that eta1 is written as a function of these x's.

You also have to take into account that the x's are correlated and add a term like for the et1 equation:

2*Cov(x1, x2)*b11*b12.
 C. Lechner posted on Friday, January 18, 2013 - 1:04 am
Thanks you, Bengt – I think the covariance term is what I had overlooked. I'll add it and see whether the numbers add up to something that makes sense then.

As this involves a lot of manual computation when more covariates are involved, I wonder whether there is any easy workaround? E.g., could one simply estimate the factor variances in a measurement-part only model (without the covariates and structural paths) and use those as input for the calculations of standardized parameters and r-square in the final model?
I'm afraid that would bias the variance estimates, wouldn't it?
 Bengt O. Muthen posted on Friday, January 18, 2013 - 2:53 pm
It might be too approximate.
 ywang posted on Friday, March 29, 2013 - 12:49 pm
Dear Drs. Muthen:

I have a question about how to decide the signficance of the moderated medaition. M is a mediator and W is a moderator (gender, 0 and 1).

For the following input:
ANALYSIS: BOOTSTRAP = 1000;

MODEL:
M ON X (a1)
W
XW (a2);

Y ON M (b1)
X W XW
MW (b2);

MODEL CONSTRAINT:
NEW(eff1 eff2);
eff1=a1*b1;
eff2=(a1+a2)*(b1+b2);

Should we test the indirect effect of a2*b1 and a1*b2 in order to conclude the signficant moderated mediation?

Thank you very much in advance!
 Bengt O. Muthen posted on Friday, March 29, 2013 - 4:33 pm
Seems like you have set it up right. One thing you want to test is the difference between eff1 and eff2. To test significance of the moderation in the mediation, don't you want to test that a2*(b1+b2) is significant? Both the difference and this last term can be given NEW names so you get z-tests.
 Leslie Roos posted on Friday, May 03, 2013 - 1:54 pm
Hello!

I wanted to ask a question about a post from the first author on this post regarding a model he created from your 2007 Conditional Indirect Effects Paper, working from "Model 5". In line with the model, I am confused about the role of eff1 and eff2.

Having performed previous mediations with the eff1 = a*b, this makes sense to me based on the M ON (X & XW) and Y on (M & MW) paths. I am confused about the eff2 role of multiplying each by 2 -- what would this be representing?

Thank you!
Leslie

MODEL CONSTRAINT:
NEW(eff1 eff2);
eff1=(a1+a3*1)*(b1+b2*1);
eff2=(a1+a3*2)*(b1+b2*2);
OUTPUT: CINTERVAL(bcbootstrap);
 Bengt O. Muthen posted on Friday, May 03, 2013 - 5:06 pm
One and two standard deviations above the mean of zero for the moderator.
 Krista Highland posted on Thursday, May 30, 2013 - 10:13 am
Hello,

I am attempting to complete a moderated mediation in which my predictor and mediator variables are latent and I have a categorical and latent outcome. The format follows Preacher’s Model 5 in which the moderator impacts both paths a and b. The moderator variable has 4 categories (Black, White, Hispanic, Other). Would it be best to utilize the multiple group function, comparing all 4 racial groups together? Though, I am unsure of how to complete group comparisons from there. Or would it be better to run models with several dummy codes representing the moderator?
 Bengt O. Muthen posted on Thursday, May 30, 2013 - 10:21 am
I would suggest doing multiple-group analysis, letting the a and b paths vary.
 Yisheng Peng posted on Wednesday, July 10, 2013 - 9:47 am
I found most other researchers would calculate the critical ratios of differences(CRD) by dividing the difference between two estimates by an estimate of the standard error of the difference (Arbuckle, 2003). A CRD greater than 1.96 indicates that there was a significant difference between the two parameter estimates at p < 0.05.However, they usually do this in the Amos software. However, in the Mplus result part, I cannot find the standard error of the difference.

I am wondering how can you do this through the results provided by Mplus?
 Yisheng Peng posted on Wednesday, July 10, 2013 - 9:54 am
My question is, I want to do multi-group analysis to identify whether the path coefficients differ significantly between east and west. We compared the first model, which allows the structural paths to vary across cultures, with the second model, which constrains the structural
paths across cultures to be equal to examine the cultural differences.
All the other paths (i.e., factor loadings, error variances and structure covariances) were constrained to be equal. However, I found the factor loading are still different in the Mplus result part. Are there other things that need to be constrained equally?

By the way, do you have any sample code for me to do such a multiple group comparison of the mediation model?

Thanks.
 Linda K. Muthen posted on Thursday, July 11, 2013 - 2:19 pm
You can use MODEL TEST to do the CRD test. See the user's guide.

See the Topic 1 course handout on the website under multiple group analysis to see the inputs for testing for measurement invarinace.
 JOEL WONG posted on Tuesday, October 08, 2013 - 5:28 pm
I am attempting to test a first and second stage moderated mediation model. I have one predictor, one outcome, one mediator, and one moderator (W). W is hypothesized to moderate the relationship between the predictor and the mediator and the relationship between the mediator and the outcome.

This model is described as model 58 in Hayes' PROCESS manual -- see http://mres.gmu.edu/pmwiki/uploads/Main/process.pdf

Does anyone know the Mplus syntax for this model? Preacher et al. (2007) provides the Mplus syntax for several moderated mediation models, but it doesn't include this model. Thank you.
 Bengt O. Muthen posted on Tuesday, October 08, 2013 - 5:46 pm
UG ex 3.18 describes the case of a moderator Z that moderates the influence of the predictor X on M and X on Y. That involves creating X*Z in Define. A plot of the effects and their confidence bands are obtained by LOOP. So that's the first part of your question.

The second part is the moderation of the M->Y relationship. This calls for creating M*Z and regressing Y on it. LOOP could be used here as well.
 Krista Highland posted on Thursday, October 10, 2013 - 7:11 am
Hello,

Thank you for your previous suggestion in running my moderated mediation with 2 latent predictors, continuous mediator, and binary outcome. I have 4 groups, and have tested the model using the indirect command and bootstrapping (with BC confidence intervals). To compare the effect size of the indirect effects across groups. Would it be acceptable to examine whether the confidence intervals between groups overlaps as a means of testing for significant differences? Or is there a better way to test whether the effect sizes are significantly different (e.g. running a difftest where I constrain paths a and b and compare them to a non-constrained model)?

Also, when I run the mediation for the whole sample, the mediation is significant. However, when I run the mediation using multigroup, the indirect effect is no longer significant in any of my four groups. Would it be safe to say that this could be due to sample size issues (as, I have already established measurement invariance in my predictors)
 Linda K. Muthen posted on Friday, October 11, 2013 - 11:04 am
You should use DIFFTEST.

Yes, lower power could be the reason for this.
 Laura Baams posted on Tuesday, October 29, 2013 - 9:02 am
Hi,

I am running a bootstrap multigroup mediation model with observed variables. Two predictors (x1, x2), two mediators (m1, m2) and one outcome (y).
There are 5 groups for the multigroup part.

I have compared model fit of a model in which I constrain all paths to be equal across groups, and a model in which they are not equal, and variations of this.
The model with the best fit, is the one where groups 1 and 2 are constrained to be equal, and group 3 and 4 are constrained to be equal.

I need to report the standardized estimates, but these are not equal for groups 1 and 2, or 3 and 4, while the unstandardized estimates are.

From other posts I understand that Mplus does not constrain standardized estimates, does this mean I cannot report standardized estimates in this case?

Is there a way I can still obtain standardized estimates (that are equal across groups 1 and 2; and 3 and 4)?

Thanks so much!
 Linda K. Muthen posted on Tuesday, October 29, 2013 - 10:12 am
The standardized coefficients are standardized using different standard deviations for each group. This is why the coefficients are different. It is not because they are not constrained to be equal in the analysis.
 Patrícia Costa posted on Friday, January 31, 2014 - 2:47 am
Dear Drs Muthén,

I am running a moderated mediation model based on Preacher, Rucker & Hayes (2007) model 3: the path from mediator m to y is moderated by w.

The output shows that all paths are significant at p =.000.

However, the fit indexes are as follows:

AIC 195.379
BIC 221.996
Sample-Size Adjusted BIC 171.948

Chi-Square Test of Model Fit

Value 12.001
Degrees of Freedom 2
P-Value 0.0025

RMSEA

Estimate 0.358
90 Percent C.I. 0.182 0.565
Probability RMSEA <= .05 0.004

CFI 0.958
TLI 0.852

Chi-Square Test of Model Fit for the Baseline Model

Value 243.003
Degrees of Freedom 7
P-Value 0.0000

SRMR 0.311

Can I consider that my model is significant, relying on the significance of the paths?

Thank you for your input,
Patricia
 Linda K. Muthen posted on Friday, January 31, 2014 - 9:35 am
Model fit is not assessed using the significance of the model parameters. The fit statistics indicate that leaving out the two paths represented by the two degrees of freedom create a lack of fit.
 Hannah Lee posted on Sunday, March 30, 2014 - 2:17 pm
Hello,
I am trying to run a moderated mediation model (Similar to Model 2 as Hayes and Preacher 2007 shows).

The IV, Moderater are latent constructs and I am unable to use the MODEL INDIRECT with the latent interactions. So I referred to Muthen (2011) sections 3 and 5 using BOOTSTRAP=1000; and OUTPUT: cinterval(bootstrap);

But I keep getting the error message that bootstrap cannot be used with TYPE=RANDOM. How can I get the indirect/total effects?
====================================
ANALYSIS: TYPE = RANDOM;
bootstrap = 1000;
MODEL: x1 BY CPI1-CPI3;
x2 BY CPC1-CPC3;
w BY CCC1-CCC3;
m BY NPA1-NPA5;
d BY Perf1- Perf6;
x1xw | x1 XWITH w;
x2xw | x2 XWITH w;
d ON m (b1) x1 x2 w x1xw x2xw c1 c2;
m ON x1 (a1) x2 (a2) w x1xw (a3) x2xw (a4) c1 c2;

MODEL CONSTRAINT:
new (ind wmodval);
wmodval = -1;
ind=(a1+a3*wmodval)*b1;
ind=(a2+a4*wmodval)*b1;
OUTPUT: SAMPSTAT STAND;
cinterval(bootstrap);

*** ERROR in ANALYSIS command
BOOTSTRAP is not allowed with TYPE=RANDOM.
 Bengt O. Muthen posted on Sunday, March 30, 2014 - 4:55 pm
Drop the bootstrap request. If your sample size is not small it is unlikely that bootstrap SEs would be very different from regular ML SEs.
 Hannah Lee posted on Sunday, March 30, 2014 - 7:07 pm
Thank you, Dr. Muthen. Would N=201 sample size be sufficient?

Some of the t-values for the indirect effects come out to be borderline significant. I was wondering if this may be improved if I were able to bootstrap.
 Linda K. Muthen posted on Monday, March 31, 2014 - 8:05 am
I would not worry unless the sample size is less than 100.

I would be conservative as far as significance goes given that you are not doing a single test but several tests.
 CW posted on Tuesday, April 22, 2014 - 10:53 am
I have used the following syntax to test a moderated mediation model:

y ON m (b);
m ON x (gamma1)
z
xz (gamma2);

However, I am now realizing that this did not include a test of y on x, which seems like the typical c path in a mediation model. Can you explain to me why did is not present in this syntax, and is it necessary?

Thank you!
 Linda K. Muthen posted on Wednesday, April 23, 2014 - 10:22 am
Whether you include a direct effect in your model is up to you. Your research hypothesis should determine this.
 Alvin posted on Thursday, May 01, 2014 - 10:31 pm
Hi there, I estimated a moderated mediation model (similar to that of Hayes and Preacher). All looks good except I did not get fit statistics in my output, even though I did it without bootstrap. Can you advise? many thanks
Here's the relevant bit of the syntax:
Analysis:
Type = random;
ALGORITHM=INTEGRATION;
Model:
pte by conflict family witness access child;
adapt by safety bonds justice roles exist;
stress by basic health dispa safe;

whodas12 on pte (b1)
stress
stress on pte (a1)
Model constraint:
new (ind wmodval);
wmodval = -1;
ind=(a1+a3*wmodval)*b1;

Information Criteria

Akaike (AIC) 9305.490
Bayesian (BIC) 9484.270
Sample-Size Adjusted BIC 9319.462
(n* = (n + 2) / 24)
 Linda K. Muthen posted on Friday, May 02, 2014 - 9:15 am
Chi-square and related fit statistics are not available when means, variances, and covariances ore not sufficient statistics for model estimation. This is the case for numerical integration.
 Alvin posted on Friday, May 02, 2014 - 7:48 pm
Thanks very much Dr Muthen for the quick reply. I could not do it without numerical integration however. Is there a way to get fit statistics without using numerical integration. If not, how do I know if my model fits? In terms of interpreting the outcome, is it correct to say that the putative moderator did not moderate the mediating relationship between the IVs and DV, as the interaction product (ptexad) was not significant?
 Linda K. Muthen posted on Sunday, May 04, 2014 - 4:42 pm
When there are no absolute fit statistics, nested models can be tested using -2 times the loglikelihood difference which is distributed as chi-square. Non-nested models with the same set of dependent variables can be compared using BIC.

If the interaction is not significant, there is no moderation.
 Alvin  posted on Wednesday, May 07, 2014 - 1:27 am
Thanks. Another question is the output does not give standardized coefficients as this was not allowed under Type=random analysis .. Is there a way to obtain standardized estimates as I'm interested in the effect sizes
 Linda K. Muthen posted on Wednesday, May 07, 2014 - 11:02 am
Because the variance of y varies as a function of x with TYPE=RANDOM, we do not give standardized estimates.
 Alvin  posted on Wednesday, May 07, 2014 - 5:44 pm
Thanks Dr Muthen - it probably doesn't make sense then to standardize the estimates of the effect size, does it? Also, I notice boostrap can not be used to construct CIs in this case with a random-intercept-random-slope model. Why is that?
 Alvin  posted on Wednesday, May 07, 2014 - 6:06 pm
A further question Dr Muthen is, I notice in model 5 by Preacher et al, the value of w at which the conditional indirect effect of x is estimated is set to -1. Is this an accepted practice? The authors refer to the Johnson-Neyman (J-n) technique where a region of significance or a range of values of w is used in lieu of using arbitrary conditional values of w. Is this method used in analysis of moderated mediation models?
 Linda K. Muthen posted on Thursday, May 08, 2014 - 2:11 pm
The variance of y varies as a function of x for any random effect. In this case, standardization is not done.

If you add ALGORITHM=INTEGRATION; to the ANALYSIS command, I think you can use BOOTSTRAP.

-1 is probably one standard deviation below the mean. This is a common choice. See Example 3.18 where you can get a plot that shows a region of significance.
 Alvin  posted on Thursday, May 15, 2014 - 11:41 pm
Thanks Dr Muthen. I wanted to look at the significance level of a particular set of indirect paths (beta1 x beta2) in the mediation part of the moderated mediation model, as this path (beta2) dropped out (not significant) after building the moderators into the model. Of interest is whether this could be due to power issues (as I have a small sample size). In random-effect analysis however Mplus does not allow model-indirect command. Is there an alternative way to request estimates of indirect/direct effects in this case?
 Linda K. Muthen posted on Friday, May 16, 2014 - 10:00 am
See Slides 80-85 of the Topic 7 course handout on the website.
 Eric Thibodeau posted on Wednesday, June 25, 2014 - 12:41 pm
I have an environmental observed variable of maltreatment, one observed impulsivity mediator, and a latent antisocial variable as my outcome. I'm interested in using genotype as a moderator. The problem is my moderator (genotype) is categorical and my maltreatment variable is categorical (no maltreatment, emotional abuse, physical abuse). I understand that the common practice in SEM is to use multiple group comparisons.

This is my problem and confusion. Recent recommendations by GxE experts call for all covariates to be included as interaction terms in your model. For example, I will have race and age as covariates in my SEM (full partial). However, it's now recommended that you should also add "race x environment" and "age x environment" as covariate terms in addition to having them be "main effect" terms. The Age x environment term is easy to add as a covariate because age is continuous. Race is not so easy, because it's categorical. Thus I'm not sure how to "control" for these other moderation effects that include categorical variables. Do I just do a massive multiple group comparison?

I've considered dummy coding the categorical moderator variables, so that I can create interaction variables and add everything in one SEM rather than do many group comparisons. That way I can appropriately add covariates where I want (full partial). Is that bad practice? Any advice?
 Bengt O. Muthen posted on Wednesday, June 25, 2014 - 5:33 pm
Seems like (1) dummy coding categorical variables and creating interactions is a relatively simple way to go. (2) Multiple-group modeling is also fine, but you would either have to combine that with interaction terms or do groups as maltreatment x genotype (so 6 groups). Approach (1) allows only different regression effects while approach (2) also allows different (residual) variances for DVs.

You may want to ask this type of general modeling question on SEMNET.
 Alvin  posted on Monday, July 28, 2014 - 4:54 pm
Dear Dr Muthen, following a mediated moderation model, I ended up with unstandardized estimates. I was wondering since standardization isn't available in random-effect models, are there alternative ways for standardizing the estimated coefficients manually? I've previously obtained unstandardized estimates from a similar model but without interaction terms, and they look similar to the one with interaction effects. Does it make sense to obtain standardized effects in this case? this is a fair question that I anticipate reviewers may ask. Many thanks
 Bengt O. Muthen posted on Monday, July 28, 2014 - 5:26 pm
What are your Model command statements that give rise to a random effect model?
 Alvin  posted on Monday, July 28, 2014 - 5:34 pm
Here's the relevant bit of the syntax. The model was estimated using algorithm-integration. Many thanks

Model:
pte by conflict family witness access child;
adapt by safety bonds justice roles exist;
stress by basic health dispa safe;

whodas on pte (b1)
stress (c1)

stress on pte (a1)

whodas on dsmany;

Model constraint:
!plot(indirect);
!loop(mod,-1,2,0.1);
new (ind wmodval);
wmodval = -1;
ind=(a1+a3*wmodval)*(b1+b2*wmodval);

new(ac);
ac = a1*c1;
 Thorana Grether posted on Tuesday, July 29, 2014 - 4:14 am
Hi! I have problems when computing moderated mediation with 2 moderators (no problems if I run the analysis separately for each moderator):

MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -10455.691
THE ESTIMATED COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED. PROBLEM INVOLVING VARIABLE VBFS_1. THE CORRELATION BETWEEN VBFS_1 AND ZETA_2 IS 1.000
THE PROBLEM MAY BE RESOLVED BY SETTING ALGORITHM=EM AND MCONVERGENCE TO A LARGE VALUE.

Syntax for the analysis with 2 moderators.

analysis: type=random;

model:
wo_1 by … ;
gro_1 by … ;
vbf_1 by … ;
int1 | plum_1 XWITH vbf_1;
plum_1 on la_1 ze_1
wo_1 (a1)
gro_1 (a2)
vbf_1 (a3);
ze_2 on plum_1 (b1)
la_1 ze_1 int1;
int2 | plda_1 XWITH vbf_1;
plda_1 on la_1 ze_1
wo_1 (a4)
gro_1 (a5)
vbf_1 (a6);
leng_2 on plda_1 (b2)
la_1 ze_1 int2;

MODEL CONSTRAINT:
NEW (ind1 ind2 ind3 ind4 ind5 ind6);
ind1 = a1*b1;
ind2 = a2*b1;
ind3 = a3*b1;
ind4 = a4*b2;
ind5 = a5*b2;
ind6 = a6*b2;

Can you help me?

Thanks a lot.
 Linda K. Muthen posted on Tuesday, July 29, 2014 - 9:27 am
You should ask yourself why

THE CORRELATION BETWEEN VBFS_1 AND ZETA_2 IS 1.000

Two variables that correlate one cannot both be used in an analysis. They are not statistically distinguishable.
 Bengt O. Muthen posted on Tuesday, July 29, 2014 - 4:29 pm
Alvin - you are using XWITH. For standardization with XWITH, see our FAQ: Latent variable interactions.
 Alvin  posted on Tuesday, July 29, 2014 - 6:55 pm
Many thanks Dr Muthen. Can I just clarify, following the equations set out in your FAQ, in order to calculate the standardized coefficient of say beta1(direct effect) - beta1 by square root of V (n1) where V is the variance of latent factor 1 and n1 is ?
 Pieter Baay posted on Wednesday, July 30, 2014 - 12:10 am
Dear Linda,

I'm performing two moderated mediation analyses (one with observed categorical moderator, one with latent continuous mod) and I wonder which moderator value(s) to specify in the MODEL CONSTRAINT.
For the categorical moderator, I wrote:

X BY x1-x4;
M BY M1-M5;
Y BY Y1-Y8;
XM | X XWITH MOD;

Y ON M (a)
X;

M ON X (gamma1)
mod
XM (gamma2);

MODEL CONSTRAINT:
new(pinde pindeN test);
pinde = a*(gamma1+gamma2*1);
pindeN = a*(gamma1+gamma2*0);
test = pinde - pindeN;

Is this correct?
And what would this look like for a continuous, latent moderator?

In previous posts (e.g. by Hannah Lee and Alvin), a moderator value of -1 was specified. Could you please explain what the -1 represents (especially given their construction of latent variables)?

Thanks so much!
 annared posted on Wednesday, July 30, 2014 - 5:18 am
Dear Linda,
Thanks for your quick answer. If I use wo_1 instead of vbf_1 to build the interactions (int1 and int2) I get the same error message (i.e. that the correlation between wo_1 and ze_2 is 1.0). However, in both cases the correlation is not 1.0 when I run the analysis without int2. So I guess I have something wrong with my syntax?
Thank you!
 Bengt O. Muthen posted on Wednesday, July 30, 2014 - 3:35 pm
Alvin - are you referring to the bottom of page 7? Two lines from the bottom has Sqrt{V(eta_1)}, where eta_1 refers to Figure 2.
 Bengt O. Muthen posted on Wednesday, July 30, 2014 - 3:43 pm
Pieter - that input looks correct. For a latent moderator you have to use the estimated factor variance and look at two values such as 1 SD below vs 1 SD above the factor mean of zero.
 Bengt O. Muthen posted on Wednesday, July 30, 2014 - 3:45 pm
Annared - send your two outputs to support.
 Zaijia posted on Friday, August 01, 2014 - 8:17 pm
Should the result of indirect effects from Mplus be the same as PROCESS?
 Bengt O. Muthen posted on Saturday, August 02, 2014 - 2:55 pm
PROCESS(ORS) specified the hardware you the analysis uses and has nothing to do with estimated effects, only how long it will take to compute them.
 Zaijia posted on Saturday, August 02, 2014 - 7:31 pm
Hi, Dr. Muthen, thank you for your response. But I didn't mean the processor. I mean the Macro developed by Hayes for mediation analysis. Should the results from that macro be the same as Mplus?
 Bengt O. Muthen posted on Sunday, August 03, 2014 - 12:40 pm
I am not familiar with Hayes' macro. If M and Y are continuous and you use ML I would assume you get the same results.
 Zaijia posted on Sunday, August 03, 2014 - 1:08 pm
Yes, I found that when Y is dichotomous the results are different. Why does that happen? Another question is how to add interaction term into Mplus?For example, I have 2 dichotomous IV, one mediator, one DV and I want to test the moderated mediation effect, what will the syntax be like?
 Bengt O. Muthen posted on Sunday, August 03, 2014 - 2:00 pm
Question 1: Take a look at the paper on our website:

Muthén, B. & Asparouhov T. (2014). Causal effects in mediation modeling: An introduction with applications to latent variables. Forthcoming in Structural Equation Modeling.

Question 2: See the second bullet of our Mediation page

http://www.statmodel.com/Mediation.shtml
 Zaijia posted on Sunday, August 03, 2014 - 2:13 pm
That's really helpful!Thank you so much!
 Zaijia posted on Sunday, August 03, 2014 - 2:19 pm
What does this following syntax in your mediation page mean?

MODEL INDIRECT:
y MOD m z (-2 2 0.1) xz x;
 Linda K. Muthen posted on Sunday, August 03, 2014 - 2:22 pm
See the Version 7.2 Mplus Language Addendum on the website with the user's guide.
 Pieter Baay posted on Tuesday, August 05, 2014 - 12:14 am
Thank you for the suggestion to use + 1SD and -1SD above the factor mean of zero, based on the factor variance.

I've got two follow-up questions:
1) I think I should use the factor variance of the latent interaction effect rather than the factor variance of the moderator. Is this correct and if so, how can I obtain its value?

2) Is the mean of factors (such as XM) automatically set to zero or should I add a statement to do so? Or, alternatively, should I use the mean -/+ 1 SD as moderator values?

Thanks again for your help!
 Bengt O. Muthen posted on Tuesday, August 05, 2014 - 8:59 am
1) No. And, this value is not a parameter, so not available.

2) The mean of a latent variable interaction is not a parameter and should not be referred to. For moderator values, see the Latent Variable Interaction FAQ.
 Alvin  posted on Wednesday, August 06, 2014 - 10:41 pm
Many thanks Dr Muthen. Can I ask - my model is a probit model (with a categorical outcome variable, the others are continous) would it be possible to specific a logit model to derive ORs? Thanks v much for your help!
 Linda K. Muthen posted on Thursday, August 07, 2014 - 5:43 am
You can obtain a logistic model by using maximum likelihood estimation. WLSMV gives a probit model.
 Thomas Rigotti posted on Wednesday, August 13, 2014 - 2:32 am
I am working on a multilevel mediated moderation model. Technically that should be the same as a moderated mediation (like Model 2 in Preacher, Rucker & Hayes, 2007).
The indpendent (Intr) and dependent variable (Irri) in the model have been measured every day over five days (Level 1). Both the moderator (Age) and the mediator (WM) are traits (Level 2).
I know that a cross-level interaction usually is modelled by regressing the moderator on the random slope. But I need to treat the cross-level-interaction as a variable. Can I use the DEFINE-command for a cross-level-interaction, and what should I do with the random slope? Or maybe there is another solution?

USEVARIABLES ARE Intr Age WM Irri iact;
MISSING = All(-99);
CLUSTER IS id;
BETWEEN ARE Age WM;
DEFINE:
iact = Intr *Age;
ANALYSIS: TYPE IS TWOLEVEL RANDOM;
MODEL:
%WITHIN%
s | Irri ON Intr;
%BETWEEN%
Intr Age WM Irri;
Irri ON WM(b1)
Intr
Age
iact;

WM ON Intr(a1)
Age
iact(a3);

MODEL CONSTRAINT:
NEW (ind wmodval);
wmodval=10;
ind=(a1+a3*wmodval)*b1;

OUTPUT: TECH1 TECH8 CINTERVAL;

Your help is appreciated!
 Bengt O. Muthen posted on Wednesday, August 13, 2014 - 11:54 am
If you have

%within%
s | y on x;
%between%
y s on w;
s@0;

Fixing the residual variance s@0 is the same as working with an observed variable xw = x*w. You see this is you write out the formulas (or look at slide 45 of our Topic 7 handout). In practice you have to fix at a small value such as 0.01.
 Thomas Rigotti posted on Thursday, August 14, 2014 - 1:31 am
Thanks for your quick answer. I checked the handout, and the examples in the users guide, but still I am puzzled how to model the indirect effect between a cross-level-interaction (IV = Level 1, Mod = Level 2, DV = Level 1), and a Level 2 Mediator?
What I want to test is a mediated moderation.
 Shiny posted on Saturday, August 16, 2014 - 2:39 pm
I am testing a moderated Mediation model, with categorical DV. Moderator=mod. Mediators=m. I want to see how mod interacts with the IV (x) and influences the path a (similar to Preacher et al 2007 model 2)

The input in mplus is as follow:
USEVARIABLES ARE
x1 x2 x3 mod m1 m2 m3 y1 y2 y3 y4 y5;
CATEGORICAL =y4 y5;
ANALYSIS: TYPE = RANDOM;
MODEL:
xw BY x1 x2 x3;!IV
mw BY m1 m2 m3;! Mediator
y1w BY y1 y2;!DV1
y4 ON y3 (E); DV3 on DV2
y5 ON y1w(D);
y3 ON mw (C);
y1w ON mw(B);
mw ON xw (A);
Here starts with the moderator:
y3 y1w ON mod xwmod;! Regress dv1 2 on interaction and moderator
mw ON mod;! Regress mediator on moderator
xwmod | xw XWITH mod;
mw ON xwmod (A2);! Regress mediator on interaction
MODEL CONSTRAINT:
NEW(AB BD ABD wmodval AC CE ACE);
AB = (A+A2*wmodval)*B;
BD = B*D;
ABD = (A+A2*wmodval)*B*D;
wmodval =-1;
AC = (A+A2*wmodval)*C;
CE = C*E;
ACE = (A+A2*wmodval)*C*E;
OUTPUT: TECH1 CINTERVAL;

This Syntax is based on Preachers script. Is it correct? do i need to Regress the distal DVs (y4 y5)on moderator and interaction? Since bootstrap is not possible with Random, can I rely on the CI without Boot?! Thx!
 Bengt O. Muthen posted on Monday, August 18, 2014 - 2:00 pm
This looks correct. You may also want to use LOOP plotting (see our Mediation topic in the left column of the home page). I would regress y4 and y5 on moderator and interaction. Bootstrap is available with Random in Version 7.2.
 Shiny posted on Monday, August 18, 2014 - 3:30 pm
Thank you Dr. Muthen. I looked at the Output. before moderator was added, all Regression and indirect effects were significant. Adding interaction and moderator, neither interaction nor moderator and indirect effect significant. Does it mean there is no moderated Mediation effect?

The Mediation model:
Xw (latent variables) ----mw( latent mediator) -- y1w (latent) - y5 (categorical)
Xw ---mw --y3 --- y4 (binary)
Interaction is xw * mod, named as xwmod

Y4 ON Y3: estimate =0.594 p= 0.054
Y5 ON Y1w: 0.316 p=0.046
Y3 ON Mod(moderator):0.075 p= 0.310
y3 on Mw(mediator):-3.260 p=0.000
y3 on Xwmod(interaction):-0.027 p=0.503
Y1w ON mw (mediator) : -2.891 p=0.000
y1w on Xwmod(interaction) 0.022 p= 0.417
y1w on Mod(moderator): 0.105 p= 0.026
mw ON xw: 0.181 p= 0.004
mw on Xwmod: 0.006 p= 0.783
mw on mod:0.037 p= 0.110

estimate p
AB -0.506 0.032
BD -0.913 0.072
ABD -0.160 0.133
WMODVAL -1.000 1.000
AC -0.571 0.047
CE -1.937 0.088
ACE -0.339 0.167

Because I have categorical DV, by Default estimator is MLR, but bootstrap does not Support MLR. When I used WLSMV, then I cannot use Random. What can I do to get bootstrap function? Thx!
 Bengt O. Muthen posted on Tuesday, August 19, 2014 - 5:50 pm
It's a tricky situation. You have y4 binary and y5 categorical, which means that you need to carefully consider how indirect and direct effects are computed; see

Muthén, B. & Asparouhov T. (2014). Causal effects in mediation modeling: An introduction with applications to latent variables. Forthcoming in Structural Equation Modeling.

Your model is more complex because of the multiple indirect effects.

You may get away with considering the latent response variables y4* and y5* as the relevant DVs which is ok with MLR. I would not worry about bootstrapping unless your sample size is low. If your mod variable can be categorized you can use multiple-group modeling instead of XWITH and then do this using Bayes where no bootstrapping is ever needed.
 Shiny posted on Monday, August 25, 2014 - 2:08 pm
In your paper (page 8) it said: a*b effect is only valid for the underlying continuous latent response variable y*, not for the observed categorical outcome y itself. Does it mean I can not use MODEL CONSTRAINT and specify NEW (ab) and ab=axb, if I use original categorical y? Must binary y be converted into y*?
2. If so, how shall i modify in d original syntax?
Shall I write something like:
CATEGORICAL =y4 y5;
DEFINE y4 = y4* y5=y5*???
Then change the original path y4 (binary) on y3 into y4* on y3?

3. Can I use ANYLSIS: ESTIMATOR IS WLSMV AND BOOTSTRAP instead of bayes in multiple groups?

4. I did a multiple Group Analysis to test if the mediation effect differs across two Groups(Group H, Group L).

Input:
MODEL CONSTRAINT:
NEW(AHBHDH ALBLDL)
AHBHDH=AH*BH*DH;! Indirect effect in group H
ALBLDL = AL*BL*DL; !indirect effect in group L
DIFF = AHBHDH - ALBLDL;

Output
(Bootstrap 5000)
AHBHDH -0.531 -0.425 -0.376 -0.166 -0.030 -0.006 0.042
ALBLDL -0.320 -0.241 -0.199 -0.047 0.032 0.054 0.093
DIFF -11.874 -6.308 -4.536 -0.884 0.311 0.520 1.160

I can see in group H, there is an indirect effect at 95% CI, yet this indirect effect does not exist in group L. However the difference test includes 0. does the indirect effect differs across groups?
 Bengt O. Muthen posted on Monday, August 25, 2014 - 2:35 pm
2. You can still use a*b when the continuous latent response variable is considered the distal outcome.

3. Yes.

4. No. Think of it this way. You have 2 estimates and you have zero that you can line up as:

-0.166 -0.047 0

The value -0.166 is significantly smaller than zero but not significantly smaller than -0.047 because -0.047 is closer to -0.166 than zero is.
 Shiny posted on Monday, August 25, 2014 - 3:03 pm
Thank you very much for your prompt and helpful answer, Dr. Muthen. I Need a bit more Explanation of the 1st Point from your side. To simplify, let me just use a simple Mediation model(x-m-y). If I use a categorical y, what can I do in mplus to test Mediation? Use IND function but not the a*b? If I want to use a*b, according to your answer, it shall be y*? Would you be so Kind to give me a clue how to create y* in mplus? Thank you indeed!
 Shiny posted on Wednesday, August 27, 2014 - 12:37 pm
Dear Dr. Muthen,

could you pls tell me how to code y* (continuous latent Response variable) in mplus? I have an observable binary y (not latent). Shall i simply replace y with y*? I have not found related script.

Thank you for your help!
 Bengt O. Muthen posted on Wednesday, August 27, 2014 - 3:02 pm
You don't have to create y*. If you use WLSMV then a*b refers to the effect on y*. So all you have to do is use WLSMV.
 Shiny posted on Wednesday, August 27, 2014 - 3:18 pm
That is great to know, since I did use WLSMV already. Is the coefficient a probit Regression weight or a normal Regression weight (if this is a y*)? In multiple Group Analysis, can I do the same wald test or chi difference test, working with constrained or free Parameters of y*, like treating it as a continous variable, once WLSMV is specified?

Thank you very much for your helpful comment!
 Bengt O. Muthen posted on Wednesday, August 27, 2014 - 4:36 pm
Q1. a*b is a probit regression coefficient when you consider y to be the DV and it is a linear regression coefficient when you consider y* to be the DV; so the same coefficient plays two roles.

Q2. Yes
 Shiny posted on Wednesday, August 27, 2014 - 4:43 pm
Thank you for your answers, I really appreciate them!
 Winnie Yang posted on Tuesday, November 11, 2014 - 4:59 am
Dear Drs Muthen,
I am running a mediated moderation model. HP(X)->EP(M)->JS(Y). age as the moderator (W), HP, EP and JS are all latent variables, age is collected by asking participants to fill in their age ,so I believe that would be an observed variable.I have 4 questions below:
1. When creating a interaction variable, do I use XWITH command? I know that XWITH is suitable for latent variables only, while HP is a latent variable, Age is not. would XWITH still be right?
2. Assuming that I should use XWITH, I have the following syntax, do they look correct?
ANALYSIS:
estimator = ml;
type = random;
ALGORITHM=INTEGRATION;
MODEL:
HP BY HP101-HP106;
EP BY EP101 EP102 EP103 EP104R EP105 EP106R;
JS BY JS101-JS103;
HCPxAGE | HCP XWITH AGE;
JS ON EXP(B1)
HCP AGE HCPxAGE;
EXP ON HCP(A1)
AGE HCPxAGE (A3);
MODEL CONSTRAINT:
new(IND W);
W=-1;
IND=(A1+A3*W)*B1;
3. In terms of interpretation, if IND shows to be significant (p <.05), does that suggest then that W is a significant moderator? Or I would need to look at other areas for determination?
4. My model is actually more complicated than this. As a whole, I have 4 outcome variables and 2 independent variables and 2 mediators for each IV. Can I run it altogether then?Thanks!
 Bengt O. Muthen posted on Wednesday, November 12, 2014 - 6:11 pm
1. XWITH can be used for 2 latents or 1 latent and 1 observed.

2. Looks ok, but don't say

AGE HCPxAGE (A3);

because you can have only one parameter labeled per line.

3. Look at our website under Mediation (left margin of the home page)and you find the document

Loop plot for ex 3.18

Make sure you understand this before going on with your analyses. If needed, read the Preacher, Rucker Hayes article we refer to in the UG.

4. Only after you got the simpler models under your belt.
 Mirie Guerrier posted on Monday, January 19, 2015 - 1:50 pm
Hello,
I am running a sem model and want to test both moderation and mediation effects as follow
m = x w xw;
y = x m w xw mw;
Y: continuous;
M: dichotomous;
X and W both categorical (4 modalities each);
Using multi group I have an estimate (of X and M) for each category of W, although it s not clear to me how to proceed to test XW and MW (i guest i should compare estimates of X (and estimates of M) among the W'subgroups)? Could you please give me some insights?
Thank you
 Bengt O. Muthen posted on Monday, January 19, 2015 - 2:56 pm
With W as the grouping variable you want to test that the slopes of Y on M and M on X are the same across groups; that's testing the moderation. Make sure that the Y intercept is different across groups and that the M intercept is different across groups.

Note also that a dichotomous M calls for special considerations. See the paper on our website

Muthén, B. & Asparouhov T. (2014). Causal effects in mediation modeling: An introduction with applications to latent variables. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 12-23. DOI:10.1080/10705511.2014.935843

You may also/instead consider WLSMV estimation where M* instead of M is the relevant mediator (see my 2011 paper referred to in the paper above to explain this).
 Mirie Guerrier posted on Tuesday, January 20, 2015 - 11:12 am
thank you very much. Yes I want to test moderation effect. But I had a mistake in my previous post. Y is actually categorical (5 categories). As suggested I used the WLSMV estimator.

To test Y intercept I defined a restricted model in which the paths are constrained to be equal across the groups for X, M and W.
M on x w;
Y on m (1)
x (2)
w (3);
! As y is categorical I fixed each threshold as follow
[Y\$1@2 Y\$2@3 Y\$3@4 Y\$4@5];
1- I am not sure if the syntax is right?
2- should I only fix the Y intercept? Or both?

Then I used DIFFTEST to compare the unconstrained model and the restricted one.
Thank you
 Mirie Guerrier posted on Tuesday, January 20, 2015 - 1:51 pm
Sorry to post it twice it seems like it didnt work the first time.

thank you very much. Yes I want to test moderation effect. But I had a mistake in my previous post. Y is actually categorical (5 categories). As suggested I used the WLSMV estimator.

To test Y intercept I defined a restricted model in which the paths are constrained to be equal across the groups for X, M and W.
M on x w;
Y on m (1)
x (2)
w (3);
! As y is categorical I fixed each threshold as follow
[Y\$1@2 Y\$2@3 Y\$3@4 Y\$4@5];
1- I am not sure if the syntax is right?
2- should I only fix the Y intercept? Or both?

Then I used DIFFTEST to compare the unconstrained model and the restricted one.
Thank you
 Bengt O. Muthen posted on Tuesday, January 20, 2015 - 1:52 pm
I don't understand your setup. We talked about a multi-group analysis, grouping on W. But your input doesn't show that, nor any interactions with W. And I don't know why you fix the Y thresholds. I think the thresholds change across groups as the default so no need to mention them.
 Mirie Guerrier posted on Tuesday, January 20, 2015 - 2:19 pm
thank you
as i defined w as a grouping variable, i remove the interaction XW and MW in the equations. Obviously it was not the good thing to do.
I am not sure how to proceed to test "Y intercept and M intercept" across groups as suggested. could you please give me some more details

thanks again
 Mirie Guerrier posted on Tuesday, January 20, 2015 - 2:43 pm
hi,
here is my syntax :
usevariables are y x m w;
grouping is w (0=never 1=one 2=two 3=always) ;
categorical are m y;
Analysis:
type=mgroup;
difftest=deriv.dat; !from the unconstrained model ;
estimator=WLSMV;
model:
M on x w;
Y on m (1)
x (2)
w (3);
how could i improve it to

thank you
 Bengt O. Muthen posted on Tuesday, January 20, 2015 - 4:58 pm
When you have Grouping = w... you should not include w in the Model statements. See Topic 1 of our course on our website to get the basics. Ignore the intercepts for now.
 Riza Casidy posted on Wednesday, March 04, 2015 - 7:10 am
Hi

I am attempting to use the multiple group analysis in Mplus to test for moderated mediation with a categorical moderator, I would like to test whether an indirect effect differs between two subsamples (group a & group b). The IDV, DV, and MV are all latent, continuous variables

For each group, I requested the indirect effect by using the model constraint command.

GROUPING IS UNI (0=group a 1=group b);

MODEL:
PS by Q6_1 Q6_2 Q6_3;
SAT by Q8_1 Q8_2 Q8_3;
AO by Q18_1 Q18_2 Q18_3;
SAT ON PS;
PS ON AO;

MODEL DEAKIN:
PS by Q6_1 Q6_2 Q6_3;
SAT by Q8_1 Q8_2 Q8_3;
AO by Q18_1 Q18_2 Q18_3;
SAT ON PS (p1a);
PS ON AO (p2a);

MODEL CONSTRAINT:
NEW (ind_1);
Ind_1 = p1a*p2a;

MODEL UNIMELB:
PS by Q6_1 Q6_2 Q6_3;
SAT by Q8_1 Q8_2 Q8_3;
AO by Q18_1 Q18_2 Q18_3;
SAT ON PS (p1b);
PS ON AO (p2b);

MODEL CONSTRAINT:
NEW (ind_2);
Ind_2 = p1b*p2b;

MODEL CONSTRAINT:
NEW (diff);
diff = ind_1-ind_2;

Is my method above correct? Did I miss anything? Do I have to constrain the latent variable as well? How do I do that? I would like to be sure. Thank you.
 Bengt O. Muthen posted on Wednesday, March 04, 2015 - 2:39 pm
You also need to make sure you have a sufficient degree of measurement invariance across groups for your latent variable indicators.
 Yeshim Iqbal posted on Wednesday, April 15, 2015 - 8:39 pm
Hi there,

I'm trying to run the following model:

A --> B --> C

Where A-->B and B-->C are both moderated by D and

A = Categorical (3 different conditions)
B = Continuous (mediator)
C= Continuous (outcome)
D = Continuous (moderator)

Could you advise on what the input should be?

Thank you!
 Bengt O. Muthen posted on Thursday, April 16, 2015 - 8:30 am
Create products of variables (interactions) using DEFINE. Assuming 3 categories of A and therefore 2 dummy variables A1, A2:

A1D = A1*D;
A2D = A2*D;
BD = B*D;

and add B ON AD1, AD2 in the B regression and add C ON BD in the C regression.
 Jordan posted on Tuesday, April 21, 2015 - 8:28 pm
Hello,

I am attempting to run a moderated mediation model using SEM. I have been using the XWITH command to create the interaction term, and asking for indirect effect estimates using the MODEL CONSTRAINTS, as below. However, I do not know what to input for the question marks. I would like to see the indirect effect conditional upon the moderator at -1SD, mean, and +1SD; but since my moderator is latent, I'm not sure what to input.

I tried coding like this:
[moderator] (zmean);
moderator (zvar);

...and then simply inputting "zmean+sqrt(zvar)", for example to get +1SD.

...but the model wouldn't estimate the mean...so this doesn't appear to work.

Can you tell me what I should input in place of the question marks below if my moderator is latent and I"m using the XWITH command?

MODEL CONSTRAINT:
new (ind1-ind3);

ind1=(a1+a3*(?)) * b1;
ind2=(a1+a3*(?)) * b1;
ind3=(a1+a3*(?)) * b1;
 Bengt O. Muthen posted on Wednesday, April 22, 2015 - 2:03 pm
Unless you have multiple groups or time points, latent variables have mean zero. The SD is the square root of the model-estimated latent variable variance. Taken together, that gives you the ?
 Jordan posted on Wednesday, April 22, 2015 - 4:33 pm
Got it. Makes sense. Thanks for the help!
 claudia sacramento posted on Thursday, April 23, 2015 - 1:14 pm
Hi

I am testing a ML mediated moderation, first link moderated by a group (aggregated) var.

I might be mislabeling the coefficients. Assuming a1 is the relationship IV(x) to med(m); a2 mod(w) to med; a3 is the interaction on med; b1 is the m-y effect; cdash1 is the direct effect x-y; I run the model below but model constraint results suggest this is not right.

Also, is it ok to use the coefficients obtained in the between part of the model? I assumed so given that an L2 moderator can only influence the between level variance of an L1 variable...

Usevariables = x m w y;
Cluster = team ;
between = w ;
within = ;
Analysis:
Type = Twolevel random;
Estimator = ML;

MODEL:
%Within%
S|m ON x;
y ON m! SHOULD THIS BE (b1) instead?

%Between%
S ON w (a3);! CORRECT?
CTF ON w (a2);
[S] (a1);! CORRECT?
[y] (b0);
y ON m (b1) ;
y ON x (cdash1);

S WITH x;

MODEL CONSTRAINT:
NEW(LOW_w HIGH_w CIND_LO CIND_HI TOT_LO TOT_HI dif1 dif2);
LOW_W = 2.77;
HIGH_W = 3.74;

! cond ind
CIND_LO = a1*b1 + a3*b1*LOW_W;
CIND_HI = a1*b1 + a3*b1*HIGH_W;
dif1 = CIND_HI - CIND_LO;

! cond tot
TOT_LO = CIND_LO + cdash1;
TOT_HI = CIND_HI + cdash1;
dif2 = TOT_HI - TOT_LO;
 claudia sacramento posted on Thursday, April 23, 2015 - 1:17 pm
SORRY, in the post above, by CTF is meant 'm', so
%Between%
...
CTF ON w (a2);

%Between%
...
m ON w (a2);
 Bengt O. Muthen posted on Thursday, April 23, 2015 - 3:12 pm
One question is at which level you want the mediation - what does your research question say? If level-2 is the focus, why not say

%Within%
y on m x;
m on x;

%Between%
y on m (b1);
m on x (a1)
w(a2);
inter | x XWITH w;
m on inter (a3);

etc.
 claudia sacramento posted on Thursday, April 23, 2015 - 3:45 pm
Thank you for your very swift reply,

x is a level 1 var, w is level 2 var, so I was trying to examine the cross-level interaction, but in essence I would like to understand the underlying logic to model both between and within variance when testing for cross level interactions so i can best decide when one or the other is most suited

* In any case, I have tried to test the proposed syntax, but obtained the following error;
*** ERROR in MODEL command
Interactions declared on the between level require numerical integration.
Add ALGORITHM=INTEGRATION to the ANALYSIS command.

I have added this ALGORITHM=INTEGRATION, and obtained then the following error
*** ERROR in MODEL command
The XWITH option is not available for observed variable interactions. Use
the DEFINE command to create an interaction variable.
Problem with: INTER | X XWITH W
- what would you suggest?

* finally, in the syntax proposed, should the second line in the between read 'w on m (a2)'? Otherwise I am missing something.

Many thanks,
 Bengt O. Muthen posted on Thursday, April 23, 2015 - 5:04 pm
w (a2) is a continuation of the m on line above - look at the the semi colon.

For your question, send output to support.

See also slides 80-85 of our Topic 7 short course handout.
 claudia sacramento posted on Thursday, April 23, 2015 - 5:17 pm
apologies, had missed that absent ; in the previous line..
I have already gone through the slides and associated recorded video, as well as chapter 9 in the manual but am afraid i was still unable to figure this out - I have sent the material and license. Thank you very much,
claudia
 Pamela Allen posted on Wednesday, May 20, 2015 - 5:08 pm
Dr. Muthen,

I would like to test moderated mediation in which sex moderates the B path (asdom3-->fsdom3) in the mediation: group-->asdom3-->fsdom3. I also want the model to estimate the mediation hifreq2-->asdom3-->fsdom3. hifreq2, sex and group are binary. Indicators of latent variables are continuous. Is my desired model possible? If so, is adding MODEL CONSTRAINT commands for indirect effects to the existing model below (which only includes the interaction) the recommended syntax? Thank you.

CLASSES = c(2);
KNOWNCLASS IS c (group=0 group=1);

Model:
%overall%
asdom3 by as23_r as24_r as25_r as26_r as27_r as28_r;
fsdom3 by fs23_r fs24_r fs25_r fs26_r fs27_r fs28_r;
as23_r as24_r as25_r PWITH fs23_r fs24_r fs25_r;
as26_r as27_r as28_r PWITH fs26_r fs27_r fs28_r;

int | sex XWITH asdom3;
fsdom3 ON hifreq2 sex asdom3 int;
asdom3 ON hifreq2 sex;
sex with hifreq2;
[asdom3@0];
[fsdom3@0];

%c#2%
fsdom3 ON hifreq2 sex asdom3 int;
asdom3 ON hifreq2 sex;
sex with hifreq2;
[asdom3];
[fsdom3];
[as24_r fs27_r];
as23_r as24_r as25_r PWITH fs23_r fs24_r fs25_r;
as26_r as27_r as28_r PWITH fs26_r fs27_r fs28_r;

Analysis:
Type=Mixture Random;
Algorithm=integration;
 Bengt O. Muthen posted on Thursday, May 21, 2015 - 6:45 pm
I think it could be more easily done by creating a 4-class Knownclass c variable using the combination of group and sex. Then you have full control over how the slopes and intercepts should vary across those 4 categories.
 Pamela Allen posted on Thursday, May 21, 2015 - 9:05 pm
I am unsure how the indirect effect of group or sex should be tested in this recommended approach because once considered as a KNOWNCLASS variable, group and sex will not appear in the %overall% model syntax which seems necessary for MODEL CONSTRAINT to request the indirect effects. I am a beginner and do really appreciate the extra clarification. Thank you again.
 Bengt O. Muthen posted on Friday, May 22, 2015 - 5:37 pm
If you are a beginner, perhaps it is easier to not get into mixture Knownclass at all. Use XWITH to get "int" as you have done for the m->y moderation by sex, use sex as a binary x variable and use "group" as a binary x variable. Then you get your moderated indirect effect as usual:

a*b+g*a*z,

where a and b are the usual ones, g is the slope of fsdom3 regressed on int and z is the sex moderator (I hope I got that right; this is essentially Model 3 of Preacher et al, 2007).
 Pamela Allen posted on Tuesday, May 26, 2015 - 11:27 am
Thank you. Is this still viable if I am also interested in testing the sex X asdom3 interaction across groups (3 way interaction)? I don't know why my model below receives the new error "One or more variables have a variance greater than the maximum allowed of 1000000."

Model:
asdom3 by as23_r as24_r as25_r as26_r as27_r as28_r;
fsdom3 by fs23_r fs24_r fs25_r fs26_r fs27_r fs28_r;
as23_r as24_r as25_r PWITH fs23_r fs24_r fs25_r;
as26_r as27_r as28_r PWITH fs26_r fs27_r fs28_r;

sXas | sex XWITH asdom3;
sXasXg | group XWITH sXas;
fsdom3 ON hifreq2(Beta4);
fsdom3 ON sex (Beta2);
fsdom3 ON group (Beta5);
fsdom3 ON asdom3(Beta1);
fsdom3 ON sXas (beta3);
fsdom3 ON sXasXg(Beta6);
asdom3 ON hifreq2(gamma2);
asdom3 ON sex(gamma1);
asdom3 ON group(gamma3);

sex with hifreq2 group;
hifreq2 with group;

!Model constraint:
! NEW (INDhif INDg);
! INDhif=(gamma2*Beta1)+(gamma2*Beta3)...;
! INDg=....
 Bengt O. Muthen posted on Tuesday, May 26, 2015 - 2:40 pm
Please send output with this question to support.
 Dharmi Kapadia posted on Thursday, June 25, 2015 - 6:14 am
Hello,
I am doing a moderated mediation (code below) with categorical moderator (ethnicity) split into 5 dummy variables. CISRHigh is a binary mediator, anyserv is a binary outcome. WLMSV estimation is used. yw1 to yw5 (mediator*ethnic group) created under the DEFINE command.

Can you tell me how to test the difference between indirect effects using the model constraint command?

Thanks,
Dharmi

Analysis:
Type = RANDOM;

Model:
CISRhigh on positive;
CISRhigh on lacksupp;
CISRhigh on White;
CISRhigh on Irish;
CISRhigh on BlackCaribbean;
CISRhigh on Indian;

xw1 | lacksupp XWITH White;
xw2 | lacksupp XWITH Irish;
xw3 | lacksupp XWITH BlackCaribbean;
xw4 | lacksupp XWITH Bangladeshi;
xw5 | lacksupp XWITH Indian;

xw6 | positive XWITH White;
xw7 | positive XWITH Irish;
xw8 | positive XWITH BlackCaribbean;
xw9 | positive XWITH Bangladeshi;
xw10 | positive XWITH Indian;

CISRhigh on xw1;
CISRhigh on xw2;
CISRhigh on xw3;
CISRhigh on xw4;
CISRhigh on xw5;
CISRhigh on xw6;
CISRhigh on xw7;
CISRhigh on xw8;
CISRhigh on xw9;
CISRhigh on xw10;

anyserv on CISRhigh White Irish BlackCaribbean Bangladeshi Indian;

anyserv on yw1;
anyserv on yw2;
anyserv on yw3;
anyserv on yw4;
anyserv on yw5;
 Linda K. Muthen posted on Thursday, June 25, 2015 - 6:44 am
You label the parameters in the MODEL command, forexample:

Model:
CISRhigh on positive;
CISRhigh on lacksupp;
CISRhigh on White (p1);
CISRhigh on Irish (p2);
CISRhigh on BlackCaribbean;
CISRhigh on Indian;

and create a difference parameter in MODEL constraint:

MODEL CONSTRAINT:
NEW (diff);
diff = p1 - p2;
 Linda K. Muthen posted on Thursday, June 25, 2015 - 6:46 am
In your case, you would need to label the parameters involved in the indirect effects and create the two indirect effects in MODEL CONSTRAINT along with the difference parameter.
 Dharmi Kapadia posted on Friday, June 26, 2015 - 5:27 am
Thanks Linda - I have done that now.

However, I have just realised that I am using MLR estimation because WLSMV is not available when using XWITH for latent variable interactions.

Does this mean that I need to change my model setup because my mediator is binary? I have read the forum regarding binary mediator being treated differently when used as independent/ dependent variable when using MLR.

Thanks,
Dharmi
 Bengt O. Muthen posted on Saturday, June 27, 2015 - 4:02 pm
The combination of XWITH and a binary mediator is tricky:

- XWITH is only available for ML

- ML with a binary mediator needs to use the new counterfactually-defined direct and indirect effects

- the counterfactually-defined effect option is not available with XWITH (although it is available for latent variables)

I'm not sure what to suggest until we've generalized this.
 Lisa Hegelmaier posted on Tuesday, June 30, 2015 - 9:49 am
Dear Dr. Muthen,

I want to investigate if a mediation is moderated by a dichotomous variable (coded 0 and 1).
I opted for the multiple comparisons option and both the a- and b-path are significant for each group, with a moderation on the b-path.

As I am interested in indirect effects as well, I ran model 5 from Hayes (2007, Figure 2) with the syntax below.
My results indicate no a-path moderation and a b-path moderation which is in line with the multiple group comparison. However, both a1 and b1 are not significant anymore. This seems odd to me, as both analyses should yield in the same findings?

Many thanks for your help!

Model:
M ON X (a1);
W
XW (a3);
Y ON M (b1)
X W XW
MW(b2);

MODEL CONSTRAINT:

NEW(eff1 eff2 modval1 modval2);
modval1 = 0.00;
eff1=(a1+a3*modval1)*(b1+b2*modval1);
modval2 = 1.00;
eff2=(a1+a3*modval2)*(b1+b2*modval2);

output:
stand; cinterval (bcbootstrap);
 Dharmi Kapadia posted on Wednesday, July 01, 2015 - 1:16 am
Hello,

Thanks for the information. Do you think it is worth doing a multigroup mediation analysis instead? I haven't done multigroup analysis before, so I am unsure as to whether it would allow a CFA + mediation analysis (binary mediator) with WLSMV estimation.

Thanks,
Dharmi
 Joyce Weeland posted on Wednesday, July 01, 2015 - 1:26 pm
I ran into the same problem as posted above, in such that my mediated moderation using the syntax by Preacher and Hayes (binary moderator) seemingly yields different results than a multigroup approach. Could you point me in a direction where to search for the problem? I add the syntax underneath.

Thank you and kind regards,
Joyce

I S | mECBIis1@0 mECBIis2@1 mECBIis3@2;
I WITH S;
S ON Con;
MECBIIS1 ON I;
MECBIIS3@0;

Im Sm | M_NEGC1@0 M_NEGC2@1 M_NEGC3@2;
Im WITH Sm;
Sm ON Con (a1);

S ON Sm (b1);

M with Sm;
ConxM with Sm;

MxSm | Sm XWITH M;
S ON MxSm (b2);

MODEL CONSTRAINT:
new (ind wmodval);
wmodval = 1;
ind=a1*(b1+b2*wmodval);
 Bengt O. Muthen posted on Wednesday, July 01, 2015 - 5:09 pm
Lisa,

I don't know what you mean by "multiple comparisons". I thought you meant multiple group, but it doesn't seem like it.

Regarding a1, b1 significance, note that these are main effects and behave differently when you have the interaction.
 Bengt O. Muthen posted on Wednesday, July 01, 2015 - 5:12 pm
Dharmi,

WLSMV can do this, but the mediator will be the continuous latent response variable behind the binary observed variable.

Not sure how you think multiple-group replaces XWITH.
 Bengt O. Muthen posted on Wednesday, July 01, 2015 - 5:15 pm
Joyce,

Send the 2 outputs that you compare to support along with license number.
 Dharmi Kapadia posted on Wednesday, July 01, 2015 - 11:13 pm
Thanks Bengt.

At the moment, I am using XWITH for an interaction between latent variable and ethnic group for a moderated mediation. By using multigroup, I could get rid of this interaction in the moderated mediation and estimate a multigroup model instead.

Dharmi
 Linda K. Muthen posted on Thursday, July 02, 2015 - 11:52 am
It was not clear that one variable was categorical in the interaction. You can approach this as a multiple group analysis using ethnicity as the grouping variable.
 Shiko Ben-Menahem posted on Thursday, November 12, 2015 - 8:53 am
In the new MODEL INDIRECT language for moderated mediation you provide an example (3.18) for moderation of the X -> M path:

MODEL:
y ON m xz z;
m ON z xz x;

If the M -> Y path is moderated, would this be the correct model:

MODEL:
y ON m mz z;
m ON x;

or would it be:

MODEL:
y ON m mz z x;
m ON x;

Thanks!
 Bengt O. Muthen posted on Thursday, November 12, 2015 - 6:00 pm
In the new, October 2015, Version 7 User's Guide which is on our website, ex 3.18 has for your first model the more common approach

y ON m x z;
m ON x z xz;

and if you want to moderate the M->Y path I would say:

y ON m mz z x;
m ON x;

(in the last line you may want to add z in case it also influences m).
 Shiko Ben-Menahem posted on Thursday, November 12, 2015 - 8:32 pm
Many thanks!

A follow up question:

Release 7.4 handles ordinal mediators using the IND command but the moderated mediation approach in my previous question seems to not accept an ordinal M. Is there a workaround for moderated mediation with a categorical/ordinal mediator?
 Bengt O. Muthen posted on Friday, November 13, 2015 - 10:22 am
Yes, the counterfactual MOD is not yet available for ordinal mediator.

You would have to use WLSMV or Bayes viewing the mediator as a continuous latent response variable, not using MOD, but using Model Constraint in line with UG ex 3.18.
 Lawrence T. DeCarlo posted on Sunday, November 15, 2015 - 2:07 pm
Someone asked me for help recently with an example where they have a pure moderator of the relation between a predictor and a mediator. Let Y be the outcome, X be the predictor, M be the mediator, and Z the moderator. In my mind, if Z is a pure moderator of the relation between X and M, then the specification should be:

Y on X M;
M on X XZ;

However, in all the examples they found, like 3.18 in Mplus, as well as in Hayes (2015), Preacher et al. (2007), and Bengt's example above, the syntax is

Y on X M Z;
M on X Z XZ;

It seems like in this case, Z is not purely a moderator but also has direct effects on M and Y, although in some articles it is illustrated as simply being a pure moderator, so maybe I'm missing something.

Of course I don't want to steer this person wrong and I'm not really familiar with this literature, but am I correct to say that in the first example, Z is a pure moderator (between X and M) whereas in the second example it is a moderator with additional direct effects on M and Y?
 Bengt O. Muthen posted on Monday, November 16, 2015 - 3:03 pm
I don't think there are any firm rules here. The statement

M on X Z XZ;

uses the idea that if the interaction XZ is needed then the main effects X and Z should also be included. Perhaps that is often needed in practice in the sense that the effect of Z is significant.

Including Z in the statement

Y on X M Z;

is perhaps less convincing, but again Z may often be significant.
 Sam R  posted on Tuesday, December 01, 2015 - 8:37 am
Hi there,

I'm trying to test moderated mediation using the approach described in Preacher, Rucker & Hayes (2007) in Figure 2 model 2 so that I can test moderation in path A. My model is a manifest and the moderator is a binary 0/1 variable.

I'm a graduate student and still learning so bear with me, but I've done some searching on the forum before drafting syntax. My input is as follows:

usevariables = W_AG X_SCI M_S1 Y_Rat;
missing = all(999);
Grouping = W_AG (0=Low 1=High);

analysis: type = general;

model:

Y_Rat on M_S1(b1_Low);
Y_Rat on X_SCI;
M_S1 on X_SCI (b2_Low);

model constraint:

New (ind_Low);
ind_Low = b1_Low*b2_Low;

model:

Y_Rat on M_S1(b1_High);
Y_Rat on X_SCI;
M_S1 on X_SCI (b2_High);

model constraint:
New (ind_High);
ind_High = b1_High*b2_High;

model test:
ind_Low = ind_High;

Output: sampstat stdyx;

This input produces an error in model constraint command (label is ambiguous) for the label B1_Low-- I know this is likely an issue with where I've placed the parameter label but any input would be greatly appreciated -- Thank you for all of our work updating with these posts!
 Bengt O. Muthen posted on Tuesday, December 01, 2015 - 5:19 pm
I think the issue may be that you say

Model:

twice, whereas you should say

Model low:

Model high:

or follow UG ex 5.15.

Also, with a binary moderator you can do this more easily as a single-group analysis with a dummy covariate and using Define to create a product.
 Chan Chen posted on Tuesday, January 19, 2016 - 10:31 pm
Hi,
here is my moderated mediation model categorical dependent variable:

USEVARIABLES = x y m w mw;
CATEGORICAL = y;
DEFINE:
xw = x*w;

Analysis:
estimator = WLSMV;
BOOTSTRAP = 10000;

MODEL:
Y on M (b1);
Y on X (cdash);

M on X(a1);
M on W (a2);
M on XW (a3);

MODEL CONSTRAINT:

IND_LOWw = a1*b1 + a3*b1*LOW_W;
IND_MEDw = a1*b1 + a3*b1*MED_W;
IND_HIw = a1*b1 + a3*b1*HIGH_W;

TOT_LOWw = IND_LOWw + cdash;
TOT_MEDw = IND_MEDw + cdash;
TOT_HIw = IND_HIw + cdash;

PLOT(LOMOD MEDMOD HIMOD);
LOOP (XVAL, 0,8,0.1);
LODMOD = IND_LOWw*XVAL;
MEDMOD = IND_MEDw*XVAL;
HIMOD = IND_HIw*XVAL;
PLOT: TYPE = PLOT2;

OUTPUT:

Cinterval (bcbootstrap);

But the output showed an error as "Variances for categorical outcomes can only be specified using
PARAMETERIZATION=THETA with estimators WLS, WLSM, or WLSMV.”

As you could see in the model that I have identified the estimator as WLSMV;
why could the model not coverage?

Thank you!
 Linda K. Muthen posted on Wednesday, January 20, 2016 - 2:51 pm
Please send the output and your license number to support@statmodel.com.
 Bengt O. Muthen posted on Wednesday, January 20, 2016 - 7:22 pm
Note also that these effects are not the optimal ones for a binary Y. See instead the paper on our website:

Muthén, B. & Asparouhov, T. (2015). Causal effects in mediation modeling: An introduction with applications to latent variables. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 12-23. DOI:10.1080/10705511.2014.935843
 Chan Chen posted on Friday, January 22, 2016 - 7:26 am
thank you so much!
is it possible to model a moderated mediation model with categorical dependent variable. If so, is there any topic note or paper I could reference?
Thank you!
 Bengt O. Muthen posted on Friday, January 22, 2016 - 4:21 pm
Moderated mediation is described in that paper.
 Shiko Ben-Menahem posted on Friday, February 05, 2016 - 8:20 am
To clarify your earlier response (Bengt O. Muthen posted on Friday, November 13, 2015 - 10:22 am):

When you say use WLSMV or Bayes viewing the mediator as a continuous latent response variable, you mean not specifying the binary M as a categorical variable, correct?

Somehow, when M is included in the list of categorical variables using WLSMV (using TYPE=COMPLEX for clustered data) the mod med LOOP PLOT makes sense, but when treated as a continuous variable the resulting plot looks very strange.
 chan chen posted on Friday, February 05, 2016 - 8:41 am
Thanks Shiko Ben-Menahem,

I only specified Y as categorical variable, others are all continuous, and then I used WLSMV as the estimator since Y is categorical. My mediator is a continuous variable with 7 anchor point.
 Shiko Ben-Menahem posted on Friday, February 05, 2016 - 2:38 pm
Thanks, but the question was addressed to Dr. Muthén.
 Bengt O. Muthen posted on Friday, February 05, 2016 - 5:37 pm
You should specify M as categorical.
 Emma beuckels posted on Monday, February 22, 2016 - 2:48 am
Dear Dr. Muthen,

I wanted to investigate a moderated mediation by model 14 of hayes.

The total index of moderated mediation and the interaction(int1) appear to be non-significant. However, when I take a closer look to the conditional indirect effect, there are some significant specific conditional indirect effects. More specifically, the mediation effect is significant for a certain moderator value, but not for the other. Hence, I am wondering if I could still argue that some effects do present moderated mediation and discuss them?

Emma
 Bengt O. Muthen posted on Monday, February 22, 2016 - 5:49 pm
You can easily do that model in Mplus and get a moderation plot with confidence intervals that show you for which moderator values you have a significant effect.
 Margarita  posted on Thursday, February 25, 2016 - 6:36 am
Dear Prof. Muthén,

I am new to moderated mediation, and although I managed to run the analysis in Mplus I am not quite sure if I am interpreting the results correctly. Are you aware of any references about how to interpret the Mplus output?

Thank you
 Bengt O. Muthen posted on Thursday, February 25, 2016 - 7:37 am
The Mplus output for moderated mediation gives the usual results that are discussed in articles such as by Preacher and in books such as by Hayes.

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

FYI - the Mplus team is wrapping up a book on mediation so later this year you'll have more guidance.

If you have a specific question about the output, please ask.
 Margarita  posted on Thursday, February 25, 2016 - 3:22 pm
Prof. Muthén thank you for your reply. I look forward to the book.

I have a question, if you have the time. My understanding is that when the interaction terms are not statistically significant then we can conclude that there is not a moderation. Is that correct?

I get non-significant interactions but some of the conditional indirect effects are significant. Is such a discrepancy expected?

Thank you for your time
 Margarita  posted on Thursday, February 25, 2016 - 3:38 pm
Apologies for reposting, I thought it would save you some time.

Following my previous question, to be more precise, the bc confidence intervals showed that for some moderator values there is a significant effect. My question is, even though the interaction term was non-significant can I still conclude that for some moderator values there is actually an effect?

Thank you again
 Bengt O. Muthen posted on Thursday, February 25, 2016 - 6:33 pm
Yes, I think you can still conclude that for some moderator values there is an effect based on the CIs. The interaction term is often not significant due to low power unless the sample size is very big, so I think it can be dangerous to throw it out.
 Margarita  posted on Saturday, February 27, 2016 - 10:45 am
That's great, thank you. May I ask one last question: If the model fit is poor, in my case

x2 (9) = 2133.29, p < .001
CFI = .00
TLI = -1.73
RMSEA = .81 (.78-.84), p <.001

would you suggest still reporting the statistically significant effects? I really appreciate your help.
 Bengt O. Muthen posted on Sunday, February 28, 2016 - 4:06 pm
If you have moderation involving the mediator the usual tests of fit do not apply.

If you are not in that moderation case, the bad fit precludes interpreting the results.
 Michael Reichert posted on Tuesday, March 22, 2016 - 10:43 am
Dear Prof. Muthen,

maybe you can help me further with a question regarding model 14, as well? My data indicates a non-significant effect b2 between the moderating variable V and the outcome variable Y.

Indirect effects and interaction effects are all significant.

Is that mentioned non-significant effect a problem for my model?

Thanks for your help, best regards from Germany.
Michael
 Bengt O. Muthen posted on Tuesday, March 22, 2016 - 1:04 pm
Not a problem. The main effect of V on Y cannot be interpreted separately from the effect on Y by the M*V interaction.
 Johan Korhonen posted on Wednesday, March 23, 2016 - 2:35 am
Hello
I have some general questions regarding the indirect effects you obtain with the model indirect command:

1) To obtain reliable information on the significance of the indirect effects, do I have to specify a bootstrap analysis (under the analysis command) or can I interpret the p-values directly from the output without performing bootstrap analysis?

2) If bootstrapping is preferred and I use the MLR estimator in my analyses, should I re-run my model with ML so that I can examine the indirect effects under bootstrapping?

3) what exactly is the significance test for indirect effect based on?

All the best
Johan
 Bengt O. Muthen posted on Wednesday, March 23, 2016 - 9:26 am
You should use bootstrapping, for instance

Bootstrap = 1000;

and in the Output command you should say

Cinterval(bootstrap);

and then judge significance of the indirect effect by whether or not the bootstrap confidence interval covers zero or not.

Often, the symmetric confidence intervals from MLR are similar to the bootstrap intervals but it is better to go by the bootstrap intervals.
 Johan Korhonen posted on Wednesday, March 23, 2016 - 11:51 am

Johan
 Sarah Nowlin posted on Saturday, April 30, 2016 - 11:45 am
Hello,
I am trying to test for differences in indirect effects following the procedures described by Hayes in his 2015 MRB paper. The moderator is a categorical variable with only two levels. One of the covariates only varies within one of the two levels that makes up the moderator variable, but it is critical to control for that covariate in the group in which it does vary. How can you set up the model to avoid errors related to no variance but still get a statistical comparison of indirect effects across levels of the moderator. (specifically, if I include the main effect term AND the interaction term in the model, there is zero variance, but including only one or the other isn't a problem, but obviously not completely controlling for that covariate).
Thank you!
 Sarah Nowlin posted on Thursday, May 05, 2016 - 11:34 am
Hello (reposting),
I am trying to test for differences in indirect effects following the procedures described by Hayes in his 2015 MRB paper. The moderator is a categorical variable with only two levels. One of the covariates only varies within one of the two levels that makes up the moderator variable, but it is critical to control for that covariate in the group in which it does vary. How can you set up the model to avoid errors related to no variance but still get a statistical comparison of indirect effects across levels of the moderator. (specifically, if I include the main effect term AND the interaction term in the model, there is zero variance, but including only one or the other isn't a problem, but obviously not completely controlling for that covariate).
Thank you!
 Bengt O. Muthen posted on Thursday, May 05, 2016 - 6:53 pm
I think this is a good question for SEMNET.
 Eric Deemer posted on Thursday, May 12, 2016 - 12:07 pm
Hello,
I'm also trying to determine which values of a latent moderator I should use to test the significance of an indirect effect.

Dr. Muthen, in an April 2015 post you said,
"Unless you have multiple groups or time points, latent variables have mean zero. The SD is the square root of the model-estimated latent variable variance. Taken together, that gives you the ?"

Does this mean I could, say, do a 1-factor CFA of the latent moderator, estimate the residual variance, and subtract the residual variance from 1 to get the explained variance? Then take the square root of the latter to get the SD? Thank you.

Eric
 Bengt O. Muthen posted on Thursday, May 12, 2016 - 7:07 pm
No. Your 1-factor CFA gives an estimated factor variance. Take the sqrt of that to get the SD.
 Eric Deemer posted on Thursday, May 12, 2016 - 7:12 pm
Great, thanks so much.

Eric
 Gabriel van Beusekom posted on Tuesday, July 05, 2016 - 5:51 am
Dear Dr. Muthen

I am testing a longitudinal panelmodel (multigroup).

First I arrived a parsimonious unigroup model and than tested whether paths were similar between subgroups (males/females).

All testing of constraining went okay. However, if I constrain an indirect effect to be equal for subgroups, the results (xsquare and df)are similar to the model in which the indirect effect is freely estimated.

Does Mplus allow for testing of constraints for indirect effects?

I hope you have the time to answer this

Gabriël
 Bengt O. Muthen posted on Tuesday, July 05, 2016 - 6:01 pm
How do you constrain the indirect effect to be equal across groups?
 Gabriel van Beusekom posted on Wednesday, July 06, 2016 - 2:41 am
Dear Dr. Muthen

In my multigroup analyses, I first pasted the script of the unigroupmodel (containing constraints). Second i specified the grouping variable and than the models for both males and females.
Than i started comparing paths between the male and female models by placing constraints.

I gave the indirect effect in the model for males the same value (01) as in the model for females.

model indirect:
C_INT IND B_PV A_GNC (01);
C_EXT IND B_PV A_GNC;

C_INT IND B_GNC A_PV;
C_EXT IND B_GNC A_PV;

C_GNC IND B_PV A_INT;
C_GNC IND B_PV A_EXT;

C_PV IND B_GNC A_INT;
C_PV IND B_GNC A_EXT;
 Bengt O. Muthen posted on Wednesday, July 06, 2016 - 5:51 pm

model indirect:
C_INT IND B_PV A_GNC (01);

the label (01) that you give is ignored. You can't test that way.

You can use Model Constraint to express the indirect effect in each group and express the difference in indirect effects - that then gets a SE and thereby a z-test of the difference.
 Rick Borst posted on Wednesday, July 27, 2016 - 4:58 am
Dear Linda,

Is there a way to make a moderator under the DEFINE command that exists of two variables which still have to be made by a factoranalysis under the MODEL command?

Example: I want to make the variable under DEFINE: IndOrg = Org_rec*Ind_rec;

But I make Org_rec and Ind_rec under the MODEL command.

Now I receive the obvious error:
Undefined variable used in transformation:
ORG_REC
 Linda K. Muthen posted on Wednesday, July 27, 2016 - 6:30 am
The DEFINE command is for observed variables. Use the XWITH option for a latent variable interaction.
 Andrea Vocino posted on Monday, August 22, 2016 - 11:15 pm
Dear Linda & Bengt,

Just got the book Regression and Mediation Analysis Using Mplus but could not find the model I am working on.

I want to test a mediated moderation model using *latent variables* where the moderation effect is assessed via multigroup analysis as such variable is dichotomous.

How do I test the conditional indirect effects when I use multigroup analysis having latent variables assuming I have metric invariance?
 Bengt O. Muthen posted on Tuesday, August 23, 2016 - 11:21 am
You can piece that together from different parts of the book. The fact that the X, M, Y variables are latent does not complicate the setup. A latent mediator case is discussed in Section 8.6. Several types of moderated mediation is treated in Section 2.6 and multiple-group mediation analysis is treated in Section 3.6. The Section 3.6 analysis uses a binary X variable as the grouping variable but this is can be changed to the moderator being the binary grouping variable. Section 3.6 shows how interaction effects (which is what conditional indirect effects come from) are expressed in terms of slope non-equalities across the groups.
 Tor Neilands posted on Thursday, September 08, 2016 - 10:36 pm
VanderWeele in "A Unification of Mediation and Interaction: A 4-Way Decomposition", Epidemiology, 25(5), 749-761, 2014, describes a counterfactuals-based approach to decompose the total effect of exposure X on outcome Y via mediator M through four effects: CDE, reference interaction (Int_ref), mediated interaction (Int_med), and pure indirect effect PIE. A colleague is seeking my help to obtain these four effects from analysis we've run in Mplus for a continuous exposure, continuous mediator, and continuous outcome with the model specification containing an interaction of X with M in line with Case 3, Figure 4.1 in Muthen, Muthen, and Asparouhov, 2016, p. 204. Can you tell me how to obtain the four quantities described above using Mplus? (Could it be as simple as Mplus already producing these same effects under different names?) Thanks so much, Tor Neilands
 Bengt O. Muthen posted on Friday, September 09, 2016 - 4:16 pm
The 2015 VanderWeele book Explanation in Causal Inference discusses this in the context of a model with XM interaction on pages 377 and 378. Top of page 378 shows how to express the 4 effects in terms of model parameters and values of a continuous exposure (X) variable. This can be done in Model Constraint which also gives you SEs by the Delta method.
 Tor Neilands posted on Tuesday, September 13, 2016 - 6:43 pm
Thanks, Bengt! Using the book chapter you referenced plus the article I cited (both cover pretty much the same ground it seems), I was able to reverse-engineer Dr. VanderWeele's PROC NLMIXED SAS code from his article and book appendices into Mplus Model Constraint syntax as you suggested to compute the 4 decomposition effects based on the model parameters.

I am grand mean centering all covariates C to compute effects at the means of the covariates. I am less clear on the advisability of grand mean centering X and M in performing an analysis of this type. For a standard linear regression with interaction, centering both X and M yields more interpretable main effects and it appears to make the counterfactual effects easier to interpret in this analysis, too. However, are there any reasons why one should one not center either X or M in this analysis?

Thanks again and thanks, too, for setting up and being so attentive to Mplus Discussion - this is a tremendous resource for the research community.

Tor Neilands
 Bengt O. Muthen posted on Tuesday, September 13, 2016 - 6:52 pm
I am glad it worked out. If this is a common request perhaps we should add it automatically to the printing of our counterfactual effects. In the meantime, if you like, please send me your Mplus input so that we can create a FAQ on it.

I don't see a reason why one couldn't grand-mean center X and M.
 Tor Neilands posted on Wednesday, September 14, 2016 - 8:54 am
I just sent along the Mplus input and output where the results match results generated in SAS using Dr. VanderWeele's sample SAS code.

I very much like the idea of printing out these counterfactual effects in a future release of Mplus. I believe they add value and should not be too hard to obtain since most are a linear combination or, in the case of proportion mediated, ratios of effects or linear combinations of effects Mplus is already showing.

I'm glad there is no reason not to center X and M. Centering X is working well in my application. I am re-thinking centering M, though, because when I grand mean center M in my analysis, the interaction reference effect IntRef becomes zero and its coefficient is added to that of the CDE to alter the value of the CDE. Any further comments on this issue would be much appreciated.
 Bengt O. Muthen posted on Wednesday, September 14, 2016 - 4:59 pm
Thanks. I typically don't center M.
 Alexander Tokarev posted on Sunday, September 25, 2016 - 8:20 am
Dear Drs. Muthen,

I have a few questions about moderated mediation. I'm testing a model P->B->D, where P and B, and B and D paths are moderated by W; and B-> D path is moderated by Q; All variables are latent with ordinal indicators. The questions are:

1) I am trying to estimate the indirect effects at specific values of moderators (e.g.at -2 s.d and 2 s.d.). I am somewhat new to Mplus, so I was wondering if the code looks right?!
Model:
P BY Pcal1 Pcal2 Pcal3 Pcal4;
B BY Bwpb1 Bwpb2 Bwpb3 Bwpb4;
D BY D1 D2 D3 D4;

Q BY Rpca1 Rpca2 Rpca3r Rpca4r;

BW | B XWITH W;
PW | P XWITH W;
PQ | P XWITH Q;

P@1; B@1; D@1; W@1; Q@1;

D on B (b1);
B on P (a1);
B on PW (gamma1);
B on PQ (gamma2);
D on BW (gamma3);

MODEL CONSTRAINT: NEW(LowModM1M2 HighModM1M2);
LowModM1M2 = ((a1+gamma1*(-2)+gamma2*(-2))*((b1+gamma3*(-2));
HighModM1M2 = ((a1+gamma1*(2)+gamma2*(2))*((b1+gamma3*(2));

Thank you

Alex
 Bengt O. Muthen posted on Monday, September 26, 2016 - 12:43 pm
looks correct.
 Alexander Tokarev posted on Tuesday, September 27, 2016 - 4:54 am
Hi Bengt,

Thank you SO MUCH. I have just a few follow up questions please.

1) With TYPE = RANDOM; ALGORITHM = INTEGRATION; standardised coefficients are not available. Would that be correct to simply constrain variance of all latent variables to 1 (hence s.d.=1) to obtain standardised direct and indirect effect coefficients? If this is the case, should I also constrain latent means to be 0 as well?

2) Since the indicators are ordinal (measured on a 5 point-likert scale) but their respective latent variables are assumed to be continuous, if there a way to see how many data points are there associated with -2/2s.d. of each latent moderator variable in order to make a valid inference?! If e.g. it’s possible in Mplus to see distribution of a latent variable using percentiles? The reason I am asking this, is because ideally I want to avoid a situation that if I use e.g. -2/2s.d. mod values, but don't have enough data points to make valid inferences.

3) Is there actually a way to test if latent variables are indeed normally distributed or is it just an assumption?

4) I read in your new book on regression and mediation analysis in Mplus, that it is recommended to grandmean center moderator variables, would you recommend to grandmean center only moderators or all variables?

Thank you

Kind regards

Alex
 Bengt O. Muthen posted on Tuesday, September 27, 2016 - 12:13 pm
1) We have a FAQ

Latent variable interactions

that shows the formulas Mplus uses for standardization with XWITH.

If you fix factor variances at 1, this will refer to the residual variance for factors that are DVs, so this doesn't give standardized coefficients.

2) You can request Save = FS which means that you can look at factor scores.

3) No, there is not a good way to do this. You should view it as an assumption.

4) I am not sure I recommended that in the book - I wouldn't bother unless the interpretation needs it.
 Alexander Tokarev posted on Saturday, October 01, 2016 - 2:29 pm
Thank you very much for the clarification
 Alexander Tokarev posted on Monday, October 03, 2016 - 3:40 pm
Dear Bengt,

May I ask you a follow-up question regarding an earlier comment please.

My post: September 27, 2016 - 4:54 am
2) Since the indicators are ordinal (measured on a 5 point-likert scale) but their respective latent variable is assumed to be continuous, is there a way to see how many data points are there associated with -2/2s.d. of that latent moderator variable in order to make a valid inference?! If e.g. it’s possible in Mplus to see distribution of a latent variable using percentiles? The reason I am asking this, is because ideally I want to avoid a situation that if I use e.g. -2/2s.d. mod values, but don't have enough data points to make valid inferences.

2) You can request Save = FS which means that you can look at factor scores.

Per your suggestion, I have obtained factor scores. There are 4 columns corresponding to factor scores of each (ordinal) indicator. I am not exactly sure what to do now with the 4 factor-score columns in order to see how many data points are there associated with -2/2s.d. of a latent moderator variable? Do I need to combine the scores in some way or do something with each factor score column separately? I am sorry, if this is a very basic question.

Thanking you in advance
 Bengt O. Muthen posted on Monday, October 03, 2016 - 4:00 pm
We need to see your output - please send to Support along with your license number.
 Anika Schulz posted on Thursday, November 10, 2016 - 12:15 am
I ran a moderated mediation analysis with latent variables formed with continuous indicators (X -> M -> Y with the pathway from X to M being moderated by W). The conditional indirect effects for low and high levels of the moderator both turned out to be significant. However, their confidence intervals overlap. I was wondering which test I should use to find out if the slopes differ significantly from each other.

I used the following syntax (similar to Hayes’ model 7):

MODEL:
Y (b0);
Y ON M (b1);
Y ON X (cdash);
M (a0);
M ON X (a1);
M ON W (a2);
M ON XW (a3);

MODEL CONSTRAINT:
NEW(LOW_W HIGH_W
IND_LOWW IND_HIW);

LOW_W = -.72;
HIGH_W = .72;

IND_LOWW = a1*b1 + a3*b1*LOW_W;
IND_HIW = a1*b1 + a3*b1*HIGH_W;

OUTPUT:
CINTERVAL (BCBOOTSTRAP);

Thank you for your help.
 Bengt O. Muthen posted on Thursday, November 10, 2016 - 12:17 pm
The two effects are not independent so looking at the overlap in confidence intervals is not correct. Instead, express as a New parameter their difference.
 Roberto Guerra posted on Monday, December 05, 2016 - 7:09 pm
Hello all,

I am trying to conduct a power analysis (via monte carlo simulation on Mplus) to see how large a sample I would need to collect for a study. The hypothesized model is a moderated mediation model where the "b" path is moderated by a continuous variable

I was wondering if there was any guidance I could receive in the best way to do so via Mplus (either through resources or syntax - I have read previous preacher papers but still find myself having difficulty conducting such an analysis). I have seen some code above but some of the numbers that were included in the code confused me

Thank you all so much!
 Roberto Guerra posted on Monday, December 05, 2016 - 7:45 pm
To add to my question above, I have read over and tried to understand the
Thoemmes, MacKinnon, & Reiser (2010) paper on power analysis for complex mediational designs using monte carlo methods, and the Mplus syntax makes sense for a mediation model. Upon introducing the moderator on the b path, I no longer understand how to complete the code to run on Mplus

Thanks
 Bengt O. Muthen posted on Tuesday, December 06, 2016 - 12:25 pm
I think this book would be very helpful to you:

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

See especially chapters 2 and 3.
 Daniel Lee posted on Wednesday, January 18, 2017 - 5:22 pm
Hi Dr. Muthen,

I had a question regarding the Mplus code as seen in user manual (Example 3.18 Moderated-Mediation).

In your syntax, you did not include y on m x (the IV), but rather just y on m. When I ran with just y on m (and not: y on m x), the program did not yield any direct effects.

I'm wondering if the direct effects are there in the output and I'm just missing it, or if it is acceptable to estimate thee models without direct effects.

I only ask this as the "y on m" vs. a "y on m x model" reaps different results (e.g., effect sizes pr significance of predictors).
 Bengt O. Muthen posted on Wednesday, January 18, 2017 - 5:51 pm
I would use y on m x.
 sarah posted on Friday, February 03, 2017 - 9:39 am
My License number (STBML70008216)

Hy , in my PhD i collected data from 74 people for ten working days ( daily measures design : daily measures are nested in individuals) . i like to test a moderated mediation model with my multilevel data

CM=> independant variable=> mediator 1=>mediator 2=>performance ( DV) ( on the lower level( level1)
The moderator is on level ( it was measured once and moderate all the relationship between variables on the level 1)
Please i want to test such a multilevel moderated mediation model with Mplus ? can i have Mplus code ? please advice .thanks a lot for advance
 Bengt O. Muthen posted on Friday, February 03, 2017 - 5:54 pm
I believe you can do a suitable analysis in Mplus. But the question about which analysis is suitable is better asked on SEMNET.
 Saleh Moradi posted on Saturday, February 25, 2017 - 5:07 pm
Dear Drs Muthen,

I want to run a mediated moderation model with a Count Data as an outcome. i.e., X->M->Y and W as the moderator, moderating the path between X and M. X, M, W and Y are all latent variables. X, M, and W are continuous and Y is count. I have been advised to use Poisson regression with count data instead of OLS, or zero-inflated negative binomial regression for my specific case with lots of zeros. I have been searching for the most convenient platform to run this model. Is it possible to run this model in Mplus? If yes, can you possibly walk me through this, considering that I am a novice user of Mplus?
 Bengt O. Muthen posted on Sunday, February 26, 2017 - 9:23 am
Mediation with a count Y is described in Chapter 8 of our new book. Mplus provides the correct, counterfactually-defined direct and indirect effects for this case.

You say that Y is a count variable but you also say that it is a latent variable. Latent variables for X, W, and M is not an issue.
 AllisonG. posted on Tuesday, February 28, 2017 - 3:26 pm
I am doing moderated mediation model with a dichotomous IV - Race, latent mediator - Cognitive Health (composed of 3 cont variables), latent moderator - Social Health (composed of 3 cont variables), and a latent DV - Distress (composed of 2 cont variables).
First, I don't think my syntax accounts correctly for this model. Suggestions would be greatly appreciated.

DEFINE:
RaceSocH = Race*Social Health;

MODEL:
! Latent mediator
Optimism ON Cognitive Health;
Engagement ON Cognitive Health;
Pain Catastophizing ON Cognitive Health;
! Latent moderator
Social Support ON Social Health;
Resource Loss ON Social Health;
Social Undermining ON Social Health;
! Latent DV
Depression ON Distress;
PTSD ON Distress;

Cognitive Health ON Race;
Distress ON Cognitive Health Race;

Compared to other IVs, it seems odd to control for effects of Age, Education, Marital Status, or Health on Race. How do you recommend adding those as control variables? Thank you.
 Bengt O. Muthen posted on Wednesday, March 01, 2017 - 7:52 am
I think you should pose this question on SEMNET.
 An De Meester posted on Monday, April 10, 2017 - 7:12 am
Hello Dr. Muthen

I want to test a moderated mediation model with an observed IV (actual motor competence), 1 latent moderator (autonomous motivation), 2 latent mediators (perceived motor competence and competence satisfaction), and an observed DV (weekly time spent in organized sports).

As I'm using a combination of latent and observed variables, I'm not sure which commando for the analysis I should use. I want to use bootstrapping so I thought the analysis below might be correct but I'm not sure:

ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
BOOTSTRAP = 10000

Furthemore, as I have a latent moderator but an observed IV, I have doubts whether I need to use the XW | X XWITH W command or rather the XW = X*W for the interaction.

And finally, for the first mediator, I would use the following code:
Y ON M (b1);
M ON X (a1);
M ON W (a2);
M ON XW (a3);
Which code should I use for the second moderator?
Y ON M (b2);
M ON X (a4);
M ON W (a5);
M ON XW (a6);?

Thank you for any help you might be able to provide.

Kind regards
 Bengt O. Muthen posted on Monday, April 10, 2017 - 6:57 pm
Yes, use XWITH.

You have 2 mediators so use M1 and M2 (not the same M).
 An De Meester posted on Tuesday, April 11, 2017 - 12:04 am
Thank you!
 Nini Wu posted on Thursday, April 20, 2017 - 3:23 am
Hello£¬I am testing a path model A-B-C-D and there is direct effect from A to C and A to D . And I expected E £¨parent gender£©moderated the path from A to B, while F moderated the path from A to D £¨child gender£©.
below is my detailed syntax£¬could you point me to what I am wrong?
Define: AE=A*E;
AF=A*F;
Analysis:bootstrap=1000;
model:
B on A(a1)
E(a3)
AE(a2);
C on B (b1)
A;
D on C(c1)
A(d1)
F(d2)
AF(d3)£»
Model Constraint:
New(ind1 ind2 Zmodval);
Zmodval=1;
ind1=a1*b1*c1+a3*Zmodval*C1
ind2=d1+d3*Zmodval;
output:Cinterval(BCbootstrap);
For the output file, it displayed below:
*** WARNING in MODEL command
Variable is uncorrelated with all other variables: F
*** WARNING in MODEL command
Variable is uncorrelated with all other variables: AF
*** WARNING in MODEL command
At least one variable is uncorrelated with all other variables in the model.
Check that this is what is intended.
*** ERROR in MODEL CONSTRAINT command
Only one sign (=, > or <) is allowed for each statement. Problem with the
following statement starting with: IND1.
 Bengt O. Muthen posted on Friday, April 21, 2017 - 6:00 pm
 Anne Kuhn posted on Thursday, June 01, 2017 - 6:19 am
Hello,
for days im trying to figure out how to do the analysis for my model on SPSS model 7.

I have the following model:

X (two conditions that have been manipulated; one group had to read one story about specific informations of sustainable products; second group received only general information)
M (attitude - measured on a 7 point scale)
Y (buying intention - measured on a 7 point scale)
W (personal values a person has - 2 groups= high values and low values)

How can i do the test in Spss. Right now the problem is how to see the difference of both conditions in the output. I want to test the difference and i want to see that condition 1 which is the specific information is stronger than condition 2, but i have not been able to do this with model 7.

Best regards,
Anne
 Bengt O. Muthen posted on Thursday, June 01, 2017 - 4:28 pm
This is a forum for only Mplus questions.
 George Pro posted on Monday, July 24, 2017 - 12:16 pm
Hello world,

Looking for thoughts and critique.

Main outcome ('multi') has 3 levels. Focal predictor ('ethra') has 3 levels. The model is mediated by 'insur' and 'pover'. I'm also looking at ethra*femal.

How do I define a reference group for a categorical IV with KnownClass?

My code below generates this error:

Unknown class label: %ETHRA#1% %ETHRA#2% %ETHRA#5% FEMAL;

Usevariables are
femal ethra insur pover multi weigh xz;
Categorical are
insur pover;
Nominal is multi;
Classes is ethgp (3);
Knownclass is ethgp (ethra=1 ethra=2 ethra=5);
!Stratification = strat;
Weight = weigh;
Define:
xz = ethra*femal;
Analysis:
type = mixture;
Model:
%OVERALL%
multi#1 multi#2 on insur pover
xz (b)
%ethra#1% %ethra#2% %ethra#5% femal;
insur on %ethra#1% (reg1)
insur on %ethra#2% (reg2)
insur on %ethra#5% (reg3);
femal
xz (int1);
pover on %ethra#1% (reg4)
pover on %ethra#2% (reg5)
pover on %ethra#5% (reg6);
femal
xz (int2);
Model Constraint:
plot(indirect);
loop(mod,0,1,1);
indirect = b*(reg1 + reg2 + reg3 + reg4 + reg5 + reg 6 +
int1mod + int2*mod);
 Linda K. Muthen posted on Monday, July 24, 2017 - 1:42 pm
Please send the output and your license number to support@statmodel.com.
 steve posted on Thursday, July 27, 2017 - 3:00 am
Dear Professors,

I am trying to estimate a moderated mediation analysis following the example of case 3 as described in your book "Regression And Mediation Analysis Using Mplus". I have two short questions:

1) On page 115, Table 2.28: Does the estimate of .950 (Tot natural IE) refers to the conditional indirect effect when X = 7 (versus the mean 5)?

2) Accordingly, is it safe to substitute the values for x in the model indirect statement (Table 2.26, p.113) with any given values of interest, e.g., high values of x vs. low values of x; or is it mandatory that the two values in the statement need to reflect one standard deviation above the mean (x1) vs. the mean (x0)?

Thank you very much!
With kind regards
Steve
 ASIA RAFIQ posted on Monday, October 16, 2017 - 9:14 am
Hi!
I am a PhD scholar. currently working on Expatriates. i am having three IVS( X1, X2, X3) on Mediator (M) Two Dvs (Y1, Y2) and Two Moderators (W, V). W moderates at first levels X1W, X2W, X3W with M at first level and MV on both Y1 and Y2. i dont know how to write Mplus code with multiple Dvs and Ivs. i only know with single IV ans Dv. please help me in this regard. thank you in advance
 ASIA RAFIQ posted on Monday, October 16, 2017 - 9:31 am
Respected Professor!
I am a PhD scholar. currently working on Expatriates. i am having
three IVS( X1, X2, X3) on Mediator (M) Two Dvs (Y1, Y2) and Two
Moderators (W, V). W moderates at first levels X1W, X2W, X3W with M at
first level and MV on both Y1 and Y2. i dont know how to write Mplus
code with multiple Dvs and Ivs. i only know with single IV ans Dv.
 Bengt O. Muthen posted on Monday, October 16, 2017 - 10:34 am
For examples, look at the outputs at

http://www.statmodel.com/Mplus_Book_Tables.shtml
 Yuhan Zuo posted on Sunday, October 29, 2017 - 11:55 pm
Dear Muthen,

I am working on a mono-level moderated mediation model with non-independence problem. I use TYPE=COMPLEX to deal with the non-independence issue.However, BOOTSTRAPPING can not be used together with TYPE=COMPLEX, yet I need to get the BOOTSTRAPPING results of indirect effect (a*b) to test the moderated mediation model. Is there anyway I can get the BOOTSTRAPPING results when using TYPE=COMPLEX?
 Bengt O. Muthen posted on Monday, October 30, 2017 - 4:31 pm
If Type=Complex is due to clustering, you can do Type=Twolevel with Bayes to allow non-symmetric a*b CIs. Mplus does not have Bootstrapping for complex samples.
 Yuhan Zuo posted on Wednesday, November 01, 2017 - 1:54 am
Dear Muthen,

Although Mplus does not have Bootstrapping for complex samples, I want to know that if I can use Monte Carlo Method proposed by "Selig, J. P., & Preacher, K. J. (2008, June). Monte Carlo method for assessing mediation: An interactive tool for creating confidence intervals for indirect effects" to get the CI of the indirect effects when I use TYPE=COMPLEX to deal with my single level moderated mediation model with non-independence problem?

Thanks a lot again!
 Bengt O. Muthen posted on Thursday, November 02, 2017 - 2:59 pm
I doubt that the article's approach covers Type=Complex data; you can ask the authors.
 Jill Rabinowitz posted on Sunday, January 28, 2018 - 11:48 am
Hi there,

I am interested in testing whether a moderator moderates the relationship between an IV and a DV and whether a mediator mediates the relationship between the moderator and the DV (see specific variables below). I looked at example 3.18 in the users manual, but I can’t seem to figure out what my syntax should look like. Can you please help?

Mediator = dtotext2
IV = ZneighprobMR1
Moderator = zmfr1
DV = DSA1A3
covariates: icsex icethnic groupid

IDVARIABLE IS famid;
MISSING ARE ALL (999);
USEVARIABLES ARE icex icethnic groupid ZneighprobMR1 ZMFR1
mom1xflex1 dtotext2 DSA1A3;

ANALYSIS:
Type = general;
ESTIMATOR ML;
bootstrap = 5000;

MODEL:
DSA1A3 on dtotext2 (b) icex icethnic groupid ZneighprobMR1 ZMFR1; !model with just covariates

DSA1A3 on dtotext2 (b) icex icethnic groupid ZneighprobMR1 ZMFR1 mom1xflex1; !model with covariates and interaction term

dtotext2 on ZneighprobMR1 (gamma1); ! mediator regressed on moderator
???? (gamma2);

MODEL CONSTRAInT:
PLOT(indirect);
Loop(mod,-2, 2, .1);
indirect = b*(gamma1+gamma2*ZMFR1);

PLOT: TYPE = PLOT2;

OUTPUT:
stdyx;
CINT(bcbootstrap);
 Bengt O. Muthen posted on Sunday, January 28, 2018 - 11:57 am
Have a look at the chapter 1 and chapter 2 scripts for the examples in our book Regression and Mediation Analysis using Mplus shown at

http://www.statmodel.com/Mplus_Book_Tables.shtml
 Alison Goldstein posted on Saturday, February 03, 2018 - 3:20 pm
Hi,

I am running a model with moderated mediation with two mediators (the moderator is only moderating the relationship between the predictor and the first mediator). I currently am regressing the first mediator on the predictor, the first mediator on the interaction, and the first mediator on the moderator. My question is whether I should allow covariance between the predictor, the interaction term, and the moderator (where there is covariance between each of them) or should I constrain the covariances to 0?

Thank you,
Alison
 Bengt O. Muthen posted on Saturday, February 03, 2018 - 3:33 pm
No, don't mention parameters related to those 3 covariates - they are automatically correlated just like in regular regression.
 Brandon Goldstein posted on Thursday, February 15, 2018 - 2:14 pm
I think there maybe a mistake on the mplus website.

For model 3.18 the example download is:
MODEL: y ON m (b);
m ON x (gamma1)
z
xz (gamma2);

I believe this is not consistent with the mplus version 8 manual which has:
MODEL: y ON m (b)
x z;
m ON x (gamma1)
z
xz (gamma2);

The line x z; is missing from the example download.
 Bengt O. Muthen posted on Thursday, February 15, 2018 - 4:57 pm
Either model is fine but the Version 8 User's Guide setup is what I would recommend and is also what we are using in our mediation book.
 jb posted on Tuesday, February 20, 2018 - 2:11 am
Hello, I am extremely new to both SEM and MPlus so I was wondering if you could help me interpreting my output. All my variables are observed and all models fit very well. I have ran the following models with these findings:

Model 1 (basic mediation with only one mediator): M1 mediates the relationship between X and Y

Model 2: I added moderator W (dichotomous - high vs low value) on the "a" pathway of the mediation - significant moderation effect at the high value of the moderator

Model 3: I added to Model 2 another mediator in series (M2), so that now I have M1 and M2 in series, and W still moderating the IV-M1 ("a") path

I am finding a significant XW interaction. However all new/additional parameters are not significant except for the total effect of W at its high value.

I am struggling to interpret the results...
1- how do I understand if the serial mediation is significant, ie what do I need to look at?
2- is there a significant moderated mediation effect?
 Bengt O. Muthen posted on Tuesday, February 20, 2018 - 2:34 pm
This general analysis question is suitable for SEMNET.