Disturbance terms in cross-lagged models PreviousNext
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 jane.ahn@ucl.ac.uk posted on Wednesday, March 13, 2019 - 7:37 am
Dear Profs Muthén

I am fitting a three wave, cross-lagged panel model. I am unsure about the syntax for estimating the covariance of disturbance terms.
X is ordered categorical and y is continuous.

The autoregressive terms:

x2 ON x1
x3 ON x2
y2 ON y1
y3 ON y2

The cross-lagged terms:

y2 ON x1
y3 ON x2
x2 ON y1
x3 ON y2

Covariance between exogenous variables:

x1 WITH y1

I am uncertain what to specify for the covariance of disturbance terms.

If dx2 was the disturbance term for x2 (and dy2 for y2, and so on), how do I specify the disturbance term and how would I model

dx2 WITH dy2
dx3 WITH dy3
dx2 WITH dx3
dy2 WITH dy3

My grasp of the syntax fails beyond the basics, and I’m not sure whether some of these things are already being modelled in the autoregressive and cross-lagged terms.

Also – I have a question about the autoregressive parameters: how do I determine what constitutes 'stable' over waves? In papers, authors will state whether the parameters are stable but I cannot find any references or information on how one interprets these parameters?

Thanks very much,
J
 Bengt O. Muthen posted on Wednesday, March 13, 2019 - 4:27 pm
Covariance of disturbance terms are also specified using WITH. Because x2, y2, x3, y3 are DVs, WITH automatically refers to the disturbances (that is, residual covariances).

Regarding your last question, you can test if this model with stable auto-regressiveness fits significantly worse

x2 ON x1 (arx);
x3 ON x2 (arx);
y2 ON y1 (ary);
y3 ON y2 (ary);

The parameter labels specify equality over time of the x and y auto-regressive coefficients.
 jane posted on Friday, March 15, 2019 - 4:46 pm
Thank you for your reply.

Re: residual covariances, would I specify these using WITH for each of the regression estimates in the model?

x2 WITH x1
x3 WITH x2
y2 WITH y1
y3 WITH y2

y2 WITH x1
y3 WITH x2
x2 WITH y1
x3 WITH y2

Thanks again.
 jane posted on Friday, March 15, 2019 - 5:01 pm
Apologies for repeat posting, but I receive the following error message:
Covariances for categorical, censored, count or nominal variables are not defined.

I've read that I need to use the BY option to specify these

f1 BY x2@1 x1;
f@1; [f@0];

But I don't understand what this means (f1, @1, f@1, [f@0])
 Bengt O. Muthen posted on Friday, March 15, 2019 - 5:46 pm
You specify the residual covariances for your contemporaneous DVs:

x2 with y2;
x3 with y3;
etc

When you have categorical outcomes, you can either use WLSMV and continue to use WITH or you can use ML and introduce a factor to capture the residual covariance. In the latter case, you say e.g. for time 2

f2 by x2 y2;
f@1; [f@0];

which means that the factor loading for y2 picks up the covariance. The last line says that the factor variance is fixed at 1 and the factor mean fixed at 0.

You may also want to study the better way to do CLPM:

http://www.statmodel.com/RI-CLPM.shtml
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