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 David R lewis posted on Tuesday, February 17, 2015 - 6:19 pm
Do you have a sample input file for Latent Moderated SEM?

I have a moderated mediation model where the moderator (V) is an exogenous latent variable. The mediator (M) is also an exogenous latent variable. The DV (Y) is an observed continuous variable.

I would like to model the moderation between M and Y or between X and M. One complication is that X is an unordered categorical variable (2 dummy variables representing three values)

What can you suggest?
 Bengt O. Muthen posted on Wednesday, February 18, 2015 - 8:19 am
You have input in the FAQ Latent variable interaction LOOP plot.

Moderation modeling with latent variables and dummy Xs may be more easily done via multiple-group modeling (3 groups in your case) where key parameters vary across the groups. But you can use XWITH also for interactions between latents and dummies.

Modeling the moderation between M and Y requires extra care as shown in Model 1 of Preacher, Rucker, Hayes (2007) in MBR.
 David R lewis posted on Wednesday, February 18, 2015 - 12:55 pm
Thank you for the prompt and helpful reply.

From Preacher, Rucker, Hayes (2007), I want Model 2 and Model 3. Previously, I used "Define: MV = M * V with continuous observed variables. Now "Define" does not work before "Model" since M and V are latent variables created by "BY".

I can only get XWITH to work for "Type = Random; Algorithm = Integration;", no bootstrapping or fit stats. Is there a better alternative? I appreciate your assistance.

MODEL:
Variety BY Variety1 Variety2 Variety3; !(M)
Expertis BY Chooser1 Chooser2 Chooser3; !(W)
SelfDet BY SelfDet1 SelfDet2 SelfDet3 SelfDet4;
PrefID BY Manchk1 ManChk2 ManChk3;
Inter| Expertis XWITH Variety; !(M * W)
Variety ON Cat_0 Cat_U (a1); !(a1 or M on X1 and X2)
Satisf1 ON Cat_0 Cat_U !(c' or Y on X! and X2)
Variety (b1)
Expertis !(b2)
Inter (b3)
SelfDet
PrefID;
!Expertis WITH Variety;
!Inter WITH Variety;
MODEL CONSTRAINT:
PLOT(Indirect);
LOOP(Expert,-2,2,0.1);
Indirect=a1*(b1+b3*Expert); !(Y = a1(b1+b3W))
!MODEL INDIRECT:
!Cat_0 IND Variety Satisf1;
!Cat_U IND Variety Satisf1;
 Linda K. Muthen posted on Wednesday, February 18, 2015 - 2:32 pm
XWITH is required for interactions between latent variables.
 David R lewis posted on Thursday, February 19, 2015 - 10:54 am
Thanks Linda,

I see that the User Guide explains that. I was hoping for an alternative.

I have a working model, output and plots but I see that the model fit statistics are limited with MLR.

The plot of indirect effect against values of the moderator shows confidence intervals, that always include 0 so I can interpret that as meaning that the the null H of "zero indirect effect regardless of the level of the moderator" cannot be rejected. Still I was wondering if you could direct me to a source that would explain how to interpret the output.

Thanks

David
 Bengt O. Muthen posted on Thursday, February 19, 2015 - 2:50 pm
Yes, with XWITH fit statistics have not been developed in the literature. You can check significance of the interaction and compare models using BIC.

You are interpreting the moderator plot correctly. Which part of the output are you uncertain about? Regarding XWITH the 2 latent variable interaction FAQs is all we have at this point.
 David R lewis posted on Thursday, February 19, 2015 - 4:11 pm
Thank you.

I was hoping for a means to calculate p values of the conditional indirect effect over a range of values of the moderator and then apply the Johnson-Neyman technique.

If not, I will rely on the confidence intervals.

Best regards,

David
 Bengt O. Muthen posted on Friday, February 20, 2015 - 11:26 am
What is it you need beyond the confidence interval plot? That gives you the region of significance discussed in Figure 3 of Preacher, Rucker, Hayes (2007).

If you express the indirect effects in Model Constraint, you get p-values for them.
 David R lewis posted on Sunday, February 22, 2015 - 11:48 am
Hi Bengt,

When I use "Model Indirect:" in the constraints section I receive the following error message: "MODEL INDIRECT is not available for TYPE=RANDOM."

The model is one of conditional indirect effects (models 2 or 3 in PRH 2007) where the moderator and mediator are both continuous latent variables with 3 indicators each.

Your suggestions are appreciated.

David
 Bengt O. Muthen posted on Sunday, February 22, 2015 - 1:41 pm
You have to use Model Constraint, where you express the indirect effects using parameter labels given in the Model command.
 David R Lewis posted on Monday, February 23, 2015 - 6:03 pm
Hi Bengt,

One of the interaction variables is latent so I use XWITH and Type=Random.

I receive the error message "*** ERROR
MODEL INDIRECT is not available for TYPE=RANDOM.

MODEL:

Variety BY Variety1 Variety2 Variety3; !(M)
Expertis BY Chooser1 Chooser2 Chooser3; !(W)
Inter| NumCat_3 XWITH Expertis; !(X * W)
Variety ON NumCat_3 (a1)!(M on X1)
Expertis (a2) !(M on W)
Inter (a3); !(M on XW)
Satisf1 ON NumCat_3 (c)
Variety (b1); !(Y on X, M)

MODEL CONSTRAINT:
PLOT(Indirect);
LOOP(Expert,0,7,0.1);
Indirect=(a1+a3*Expert)*b1;!(a1+a3W)b1

MODEL INDIRECT:
NumCat_3 IND Satisf1

Do you have any suggestions?

Thanks

David
 Bengt O. Muthen posted on Tuesday, February 24, 2015 - 5:50 am
You have to express the indirect effect in Model Constraint in this case.
 David R Lewis posted on Tuesday, February 24, 2015 - 10:40 am
Dear Bengt,

I'm afraid I don't understand what you mean.

How would I modify my input?

Please let me know,

Thanks,

David
 Linda K. Muthen posted on Tuesday, February 24, 2015 - 10:53 am
You would label the parameters involved in the indirect effect in the MODEL command and specify the indirect effect as a new parameter in MODEL CONSTRAINT.
 David R Lewis posted on Tuesday, February 24, 2015 - 2:00 pm
I believe I have done that it the input code provided earlier. What am I missing?
 Bengt O. Muthen posted on Wednesday, February 25, 2015 - 1:08 pm
Your input says:

MODEL CONSTRAINT:
PLOT(Indirect);
LOOP(Expert,0,7,0.1);
Indirect=(a1+a3*Expert)*b1;!(a1+a3W)b1

MODEL INDIRECT:
NumCat_3 IND Satisf1


It should say:

MODEL CONSTRAINT:
PLOT(Indirect);
LOOP(Expert,0,7,0.1);
Indirect=(a1+a3*Expert)*b1;!(a1+a3W)b1
 David R Lewis posted on Thursday, February 26, 2015 - 8:04 am
Thank you for all of your help you have been very responsive and helpful. MPlus is awesome.

I have the analysis I needed including the CI, plot and plot data.

As well as being SEM rather than regression and modelling latent variables, with the LOOP, MPlus is superior to running Process regressions many times with transformed IV and Moderator values as suggested in Spiller et al. JMR 2013. As an enhancement I was hoping for p-values over the range of values of the moderator in the loop plot.

Also, it looks like there's no way to get bootstrap CI. Please confirm
1. With Latent moderators, I have to use XWITH
2. With XWITH, I must use Type=Random
3. With Type=Random, Bootstrap is currently unavailable.

Thanks again for all of your help.
 S.Arunachalam posted on Friday, March 20, 2015 - 5:09 am
Respected Prof. Muthen:

The new 'model indirect' way of plotting causal effect is not providing any plot graphs.

model indirect:
p MOD np mc (-.5 .5 .1) eomc eo;
plot:type = plot2;

p.s.: I have installed version 7.3.
 Bengt O. Muthen posted on Friday, March 20, 2015 - 11:37 am
That should work - see slide 39 of my handout and video from the 2014 Psychometric Society short course.

If this doesn't help, send input, output, data, and license number to support@statmodel.com.
 S.Arunachalam posted on Friday, March 20, 2015 - 7:04 pm
Dear Prof. Muthen. I have sent you an email. Thanks a lot !
 Eric Deemer posted on Friday, May 13, 2016 - 9:07 am
Hello,
When I run the input below I get the following error message: "A parameter label has been redeclared in MODEL CONSTRAINT. Problem with: IND". Do I need to provide another label for the plot command? Here is my input:

MODEL: sse by smq12 smq21 smq24 smq28 smq29;
pap by agq2 agq4 agq8;
procp by passp1-passp3;
anx by smq4 smq6 smq13 smq14 smq18;
procp on gpa gender;
procp on anx (b);
anx on sse
pap (a);
procp on pap;
interact | sse xwith pap;
anx on interact(c);
sse pap anx;

model constraint:
new(ind wmodval);
wmodval=.444;!+1SD sse
ind=(a+c*wmodval)*b;
plot(ind);
loop(sse,-.444,.444,0.01);

Thank you,
Eric
 Linda K. Muthen posted on Friday, May 13, 2016 - 1:26 pm
Remove the IND parameter from the NEW statement and move the PLOT statement up before the assignment statement involving IND.

model constraint:
new(wmodval);
wmodval=.444;!+1SD sse
plot(ind);
ind=(a+c*wmodval)*b;
loop(sse,-.444,.444,0.01);
 Nini Wu posted on Monday, August 20, 2018 - 12:35 am
Hi, Dr Muthen,
I have the following questions regarding lms. Could you please give me some suggestions?
I would like to test a latent moderated mediation model-----W moderated the direct effect of X on Y and M to Y. And M is a latent variable, which is a mediator. I have the following questions, could you please give me some suggestions£¿

1. Should all the variables including DV be standardized?
2. Below are the basic codes in mplus. I would like to see the indirect effects of M to Y at different levels of W (e.g., +1SD, 0, -1SD) and plot the region of significance. Are the codes right?(All the variables are assumed standardized)
Define: int1=x*w;
M by m1,m2,m3;
M on X(a1);
Y on M(b1);
Y on X(d);
Y on W;
Y on int1;
INT2 | M xwith W;
Y on int2(b2);
Model constraint:
New(modhigh modlow modmean indhigh indmean indlow);
modhigh=+1;
modmean=0;
modlow=-1;
indhigh=a1*b1+a1*b2*high;
indmean=a1*b1+a1*b2*mean;
indlow=a1*b1+a1*b2*low;
plot(indirect);
loop(modval,-3,3,0.2);
indirect=a1*b1+a1*b2*modval;

3. How to write the mplus code about the effects of M to Y at different levels of W(e.g., +1SD, 0, -1SD) and the plot?

Thank you very much and look forward to your reply.
 Bengt O. Muthen posted on Monday, August 20, 2018 - 11:30 am
You are missing some terms. You want to include and label

M ON int1;

Y ON int1;

The indirect and direct effects in this case are given in our RMA book, Section 4.5.3, starting on page 206.

See also pages 91-94.
 Nini Wu posted on Tuesday, August 21, 2018 - 7:59 pm
Thank you so much for the valuable feedback.


I am sorry that I don't have your RMA book now. Would you mind letting me know if the e-copy of the book is available?

If not, could you please give me an example of the mplus codes for the third questions in my previous post?

Thanks a lot£¡
 Bengt O. Muthen posted on Wednesday, August 22, 2018 - 4:46 pm
Q1: No

Q2: I'm afraid the expression is too long for me to check and type in right now. You can find it also in Hayes' book and perhaps in Preacher's articles.
 Andrea Maloof posted on Wednesday, October 24, 2018 - 1:40 am
Hi - I am modeling a 3-way interaction using XWITH. This model includes 3 latent variables and 1 manifest variable. My manifest variable is made up of participant scores (due to the instrument being proprietary, I could not have access to individual items, and only have access to total scores). When modeling my manifest variable, I am modeling it like a latent factor with a single indicator, and am setting the error variance.

1. Is this the correct way to model the manifest variable?


2. If not, what is the correct way?
 Andrea Maloof posted on Wednesday, October 24, 2018 - 1:53 am
To clarify, my IV is the manifest variable, and my moderators and DV are latent variables.
 Bengt O. Muthen posted on Wednesday, October 24, 2018 - 5:32 pm
Don't put a factor behind a single indicator unless you know its reliability.
 Ghufran Ahmad posted on Wednesday, January 09, 2019 - 12:34 am
Hi,

Please describe how to model a latent moderator variable which has two correlated factors?

I am implementing the procedure of Sardeshmukh and Vandenberg 2017 ORM (model a: first stage moderation) for testing a moderated mediation model.

Thanks.
 Bengt O. Muthen posted on Wednesday, January 09, 2019 - 5:06 pm
When you say that you have "a latent moderator variable which has two correlated factors" - do you mean that you have 2 moderator variables?
 Ghufran Ahmad posted on Wednesday, January 09, 2019 - 6:27 pm
It is a single construct (narcissism) with two correlated factors (admiration and rivalry); see Back, Kufner, Dufner et al. 2014, Journal of Personality and Social Psychology.
 Bengt O. Muthen posted on Thursday, January 10, 2019 - 8:29 am
So do you have 2 moderator variables (admiration and rivalry)? Or, is narcissism a second-order factor with admiration and rivalry as first-order indicators and you want to use the single variable narcissism to be the moderator?
 Ghufran Ahmad posted on Thursday, January 10, 2019 - 9:12 am
I have one moderator variable (narcissism). The relevant literature quoted earlier does not define narcissism as a second-order factor, but as consisting of two correlated factors (of admiration and rivalry). Being new to SEM, I am not sure if I can create a second-order variable, if it is not conceptually proposed.

It appears I may have three options:
a) artifically create a second-order factor,
b) collapse the two correlated factors into a single factor, or
c) treat the single moderator variable as two variables.

Please advise and, if possible, suggest relevant examples.
 Bengt O. Muthen posted on Thursday, January 10, 2019 - 3:53 pm
I would recommend using both the admiration factor and the rivalry factor as moderators at the same time.

For instance, if what you moderate is the influence of X on Y, you can write

Model:

y on x;
admin by ...;
rival by ...;
xadmin | x xwith admin;
xrival | x xwith rival;
y on admin rival xadmin xrival;
 Ahmad posted on Friday, February 01, 2019 - 9:58 am
Hi, in implementing the LMS technique (TYPE = RANDOM; ALGORITHM = INTEGRATION) I am receiving warning: "THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE....CHECK THE TECH4 OUTPUT FOR MORE INFORMATION."

However, specifying TECH4 as OUTPUT generates fatal error message that TECH4 is not available with LMS. Please advise.
 Bengt O. Muthen posted on Friday, February 01, 2019 - 3:50 pm
It is available only for models that can be written as on the bottom of page 10 in

http://statmodel2.com/download/LVinteractions.pdf

In most cases just checking the correlations between the latent variables would be enough - but it will have to be done by hand or by presetting the scale so the factor variance is 1.
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