LCS Model with single-indicator laten... PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
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 Andrew Johnson posted on Wednesday, March 18, 2020 - 12:33 am
From what I understand, a latent change score analysis with two timepoints is equivalent to a latent growth model with the residual variances fixed to zero:

I S | x1@0 x2@1;
x1@0 x2@0;

If I wanted to instead use single-indicator latent variables, would it be equivalent to just fix the residual variances at the appropriate value (rather than declaring the additional latent variables):

I S | x1@0 x2@1;
x1@a1 x2@a2;

Where a1 = Var(x1)*(1-rho(x)), and the same for a2.

Thanks!
 Tihomir Asparouhov posted on Wednesday, March 18, 2020 - 12:45 pm
I don't see the full model so I am not 100% sure but it is very easy to check. First you can take a look at the log-likelihood of the two models (it should be the same of the two models are equivalent)

You can also use the NET procedure to verify that two models are equivalent

http://www.statmodel.com/download/NET.pdf
http://www.statmodel.com/download/NET.zip
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