Correlated residual variance in path ... PreviousNext
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Message/Author
 Cameron McPhee posted on Thursday, September 21, 2006 - 11:38 am
Hi, I am running a VERY simple path model with repeated measures over time (math scores at T1, T2, T3). I want earlier math scores to predict later math scores but I also want to account for the autoregressive nature of it. I was under the impression that I cannot have the same variables in an ON statement and a WITH statement. Therefore, how do I account for the correlation of the errors between Y1, Y2, and Y3 in the following model?

Model: Y3 ON Y2 Y1;
Y2 ON Y1;
Y1 ON X1-X5;

Thanks so much!
 Bengt O. Muthen posted on Sunday, October 01, 2006 - 11:40 am
You can add

y3 with y2;

etc

because that refers to the residuals of y3 and y2 given that they are dependent variables. But, your model will not be identified if you both regress y3 on y2 and let their residuals correlate.
 Cameron McPhee posted on Wednesday, October 04, 2006 - 12:30 pm
Right, that is what I was afraid of. So what is the right way to specify this model that had these lagged effects without getting biased coeficients?

Or am I totally not understanding?

Thanks!
 Bengt O. Muthen posted on Thursday, October 05, 2006 - 6:57 am
You have to limit yourself to the model

y2 on y1;
y3 on y2;

and hope any residual correlation is small.

To also identify correlated residuals you have to have multiple indicators at each timepoint - see the Wheaton et al (1977) article in the Soc Meth book.
 Annie Desrosiers posted on Wednesday, November 09, 2011 - 1:01 pm
Hi Dr Muthen,

I'm doing a path model with 2 forms of aggression (Y1 and Y2) on 8 independent variables (X1-X8). I need to control for the high correlation between Y1 and Y2. Will the command "Y1 with Y2;" control for shared variance or will it only report error correlation ?

I also tried Y1 on Y2; Y2 on Y1; But I have a just-identified model.

My question : How can I control for the shared variance between Y1 and Y2 ?

Y1 on X1-X8;
Y2 on X1-X8;
Y1 with Y2;

Thank you
 Linda K. Muthen posted on Wednesday, November 09, 2011 - 5:46 pm
The statement y1 WITH y2 estimates a residual covariance. I'm not sure what you mean about the shared variance.
 Xiaoshuang Lin posted on Monday, October 06, 2014 - 4:26 pm
Dear Prof. Bengt and Linda,
I have a similar question with above post. I do SEM and my IV is OT, DVs are V and S. My model structure is as follows:
MODEL: OT BY ot7 ot3 ot2;
RC BY rc3 rc6 rc8;
TC BY tc2 tc3 tc4;
PCBR BY pcb5 pcb4 pcb1;
VO BY v5 v2 v1;
SI BY s4 s2 s1;
RC ON OT;
TC ON OT;
PCBR ON RC TC;
SI ON TC PCBR OT;
VO ON RC PCBR OT;
SI ON sex age otenure ft;
VO ON sex age otenure ft;
I want control correlations between RC and TC, and between VO and SI. Should I write like as follows?
RC TC;
[RC TC];
RC WITH TC;
VO SI;
[VO SI];
VO WITH SI;
Or write directly as
RC WITH TC;
VO WITH SI;
Thank you very much and I look forward to your reply.
 Bengt O. Muthen posted on Monday, October 06, 2014 - 4:39 pm
Write directly as

RC WITH TC;
VO WITH SI;
 Xiaoshuang Lin posted on Tuesday, October 07, 2014 - 3:54 pm
Thank you very much, Prof. Bengt.
 Paula Vagos posted on Monday, August 24, 2015 - 3:00 pm
Dear Professor Bengt,
I am testing for multi-group invariance using the MLR estimator and get modification indices suggesting WITH mofications. I take they represent correlation between residuals, and I was wondering if the way to put them into a mplus syntax is simply u1 with u2 for example, or if this only applies to ML. I have tried doing this and get what I think is a correlation value between the two observed variables in the ouput, though the model fit improves.

Thank you for your reply.
My kindest regards,
Paula Vagos
 Linda K. Muthen posted on Tuesday, August 25, 2015 - 6:05 am
WITH statements are covariances among residuals for endogenous variables and covariances for exogenous variables.
 Daniel Gladwell posted on Tuesday, January 12, 2016 - 2:35 am
Dear Muthens

I would appreciate your advice on the degree to which I should incorporate WITH commands in a moderately complex SEM.

A simplification of my current Model is
(wave 1 variables generally are latent, wave 7 variables are generally binary indicator variables):

W7GH on W1GH W1Ability W4MH W1Fr (and controls)
W7NEET on W1Ability W1GH W1MH W1Fr (and controls)
W4MH on W1MH W1Ability W1GH W1Fr (and controls)
W7Fr on W1Fr W1MH W1Ability W1GH (and controls)

W7Lifesat on W7GH W7NEET W4MH W7Fr (and controls)

For an additional command I have two options:
1) W7GH W7NEET W4MH W7Fr WITH
W7GH W7NEET W4MH W7Fr
2) W7GH W7NEET W4MH W7Fr W7Lifesat WITH
W7GH W7NEET W4MH W7Fr W7Lifesat

I have generally seen equivalents of option "1" used more often in the literature.

If I type in option "2"
a) will MPlus allow the residuals from all the structural regressions to be correlated?
b) what is your view on the legitimacy of this approach if I think there may be unexplained characteristics relating to the individuals which impact all the W7 variables?

When I do option "2" I get some quite odd results whereas the results when I do option 1 are quite intuitive.

Many thanks in advance

Dan
 Daniel Gladwell posted on Tuesday, January 12, 2016 - 2:39 am
Apologies,

One correction to the above point is that the W7GH regression should read:

W7GH on W1GH W1Ability W1MH W1Fr (and controls)

I.e. it is regressed on W1MH not W4MH

Many thanks

Dan
 Bengt O. Muthen posted on Tuesday, January 12, 2016 - 6:58 pm
You may get a more varied response to this analysis strategy question on SEMNET.
 Daniel Gladwell posted on Wednesday, January 13, 2016 - 1:15 am
Thank you Prof. Muthen - I will ask it on SEMNET.

Do you have any thoughts to offer? I would be very interested in your view.

Thanks,

Dan
 Bengt O. Muthen posted on Wednesday, January 13, 2016 - 12:20 pm
In general, option 2 does not give an identified model because you have both a regression of W7Lifesat on W7GH and a correlation between their residuals. So you should probably go with option 1.
 Daniel Gladwell posted on Thursday, January 14, 2016 - 6:24 am
Thank you
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