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Mplus Discussion > Latent Variable Mixture Modeling >
 Magda Chmiel posted on Monday, April 23, 2012 - 7:03 am
Dear Dr. Muthèn:
I have to compute a latent variable (ABS – affective balance score) that represents the latent difference of two latent variables (PA – positive affect and NA negative affect). Then I need to regress the obtained latent score (ABS) on another latent variable (IQ). I have heard of computing latent difference score which should be NA = PA@1 and then computing NA on IQ – where NA represents now the ABS. Is that syntax correct? OR do you have other suggestions how to best compute the difference of two latent variables?
Thank you



NA by Q_NA_1_2

PA by Q_PA_1_2

NA on PA@1;

NA on IQ;
 Linda K. Muthen posted on Monday, April 23, 2012 - 1:42 pm

NA on PA@1;

NA on IQ;


diff BY;
diff ON pa@1 na@-1;
 Jiawen Chen posted on Tuesday, August 26, 2014 - 4:04 pm
Dear Dr. Muthèn:

I wonder if I can model the latent difference score of two different variables because so far all I have come across is about modeling latent difference score of the same variable across different waves. I have a variable called intrinsic work values, measured by three items: "if you are to look for a full-time job, how important are the following job characteristics (5 point scale): a)job is interesting; b)I make most of the decisions; c)I feel accomplished." I have another variable called intrinsic work rewards, measured by exactly the same items, only the question was asked differently, "describe how strongly you agree with the following characteristics about your current job (5 point scale)." So if I want to study how the discrepancy between work values and rewards predicts a host of outcome variables, is it appropriate to model the latent difference score between them at the same wave? Can I also do a third-order latent growth model of the latent difference score across multiple waves? Or some other method may be more suitable for what I want to study? Thank you very much!
 Bengt O. Muthen posted on Tuesday, August 26, 2014 - 5:05 pm
It seems to me that one can do some version of latent difference modeling also with different variables, but I haven't tried.
 Lixin Jiang posted on Wednesday, September 03, 2014 - 9:07 pm
I have two time points measures (NSsad, SSsad), which have been counter-balanced in my study. Now I want to use gender and personality trait to predict this latent change. See below that I have used it as latent growth model. However, it seems to be misleading as it is not growth itself. How do I model this "latent difference/change score model"? Thanks.

i s|NSsad@0 SSsad@1;
s on sex CA;
 Linda K. Muthen posted on Thursday, September 04, 2014 - 9:06 am
A linear growth model cannot be identified with only two time points. I would instead create a change score as follows:

f BY nssad@1 sssad@-1;
f ON sex ca;
 Roger Brown posted on Thursday, September 04, 2014 - 9:39 am
I worked up this simple difference test with a covariate the other day and checked it against a group test on a difference vector. Is this what you are thinking of?

title: LCS used to estimate paried t-test with covariate
data: file is ttest.txt;
variable: names are x y1 y2;
lcs on y1@0;
lcs by y2@1;
y2 on lcs@1;
y2 on y1@1;
lcs on x;
 Bengt O. Muthen posted on Thursday, September 04, 2014 - 2:39 pm
Shouldn't there be a negative sign somewhere?
 Lixin Jiang posted on Thursday, September 04, 2014 - 4:21 pm
Thank you, Roger. The results based on your codes were more consistent with the regression results from SPSS.
 Meike Slagt posted on Thursday, November 13, 2014 - 9:43 am
Dear Dr. Muthen,

I'm trying to estimate latent change scores, using ordinal data.

I can get one part of that model to work (the measurement part), I can get the other part of that model to work (the difference scores, using factor scores saved from the measurement part as input for the difference scores), but I can't get the complete model to converge. That is, I get parameter estimates, but no standard errors. I'm providing the Mplus code I used in the next post, because it doesn't fit in this post anymore.

I would really appreciate advice on this: Why is my model not converging; Is my sample size just to small for this (N=190); Am I forgetting certain parameter constraints leading my model to be unidentified?

Thank you so much in advance!
 Meike Slagt posted on Thursday, November 13, 2014 - 9:47 am
!Measurement Part, factorial invariance across time

neg1 BY PreN_Boos PreN_Ver PreN_Bang (1-3);
neg2 BY PostN_Boos PostN_Ver PostN_Bang (1-3);

[PreN_Boos$1 PostN_Boos$1] (4);
[PreN_Boos$2 PostN_Boos$2] (5);
[PreN_Ver$1 PostN_Ver$1] (6);
[PreN_Ver$2 PostN_Ver$2] (7);
[PreN_Bang$1 PostN_Bang$1] (8);
[PreN_Bang$2 PostN_Bang$2] (9);

{PreN_Boos@1 PreN_Ver@1 PreN_Bang@1};

!Difference scores
!Works when I save factor scores of neg1 and neg2 and use those as input. Doesn’t work when I try to estimate measurement part and difference scores in one model.

Dif_Neg BY neg2@1; !define latent change by T2
neg2 ON neg1@1; !autoregression T2 T1
neg2@0 neg1; !var at T2=0, estimate var T1 & change
[neg2@0 Dif_Neg neg1]; !mean at T2=0, estimate mean T1 & change
Dif_Neg ON neg1; !intercept change association

 Bengt O. Muthen posted on Friday, November 14, 2014 - 1:25 pm
We discourage postings in several windows. For a longer question like this, please send your problematic outputs, data, and license number to
 Dmitriy Poznyak posted on Monday, March 16, 2015 - 12:28 pm
Hi, Mplus team,

I need to model a difference/change in the factor scores between the baseline model T and the model at T2. Both models are based on the same set of respondents. The goal is to estimate the change and save the corresponding score to further use in the regression analysis.

I wonder whether you could comment on the following approach or, perhaps, point me at the better alternatives. My intuition was to test for the invariance in two measurement models to ensure the scales have identical metric at T and T2, save the factor scores and compute the difference. This being said, I am not sure whether this approach would be perfectly appropriate. I think I stumbled upon Linda's answer somewhere on the forum that invariance should not be tested on the same sample of respondents. I'd appreciate any suggestions.

For what it's worth, the model to be estimated is hierarchical CFA, in which several constructs load on a general construct.
 Bengt O. Muthen posted on Monday, March 16, 2015 - 4:03 pm
Analyze a model for the 2 time points jointly. Check scalar measurement invariance. Fix the factor mean(s) at zero for the first time point and let them be free to be estimated for the second time point. No need for factor scores. The factor mean(s) at the second time point represent(s) the difference from the first time point.
 Dmitriy Poznyak posted on Monday, March 16, 2015 - 6:58 pm
Excellent! Thank you so much for the prompt reply.
 Andre Marchand posted on Thursday, May 21, 2015 - 8:37 am
Hi Mplus team,

I am new to Mplus, so please excuse my basic question. I would like to calculate latent difference scores for two latent constructs in the following model: y = (a-b) + (c-d) with a = construct with the indicators a1,a2,a3, b with b1,b2,b3, c with c1,c2,c3, and d with d1,d2,d3.

How can I translate this to a mplus model?

Thank you!
 IW posted on Monday, June 15, 2015 - 12:20 pm
Hello Dr. Muthen,

Can you explain your previous answer a bit more or perhaps point me to a resource that goes into depth(re: Monday, March 16, 2015 - 4:03 pm)?

McArdle (2009) seem to be suggesting a different approach.

McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual review of psychology, 60, 577-605.
 Bengt O. Muthen posted on Monday, June 15, 2015 - 2:10 pm
Time points are analogous to groups in that scalar measurement invariance makes it possible to identify a factor mean difference. That was my reply. I don't know about specific references. With 2 time points there is not much else one can do.
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