Intercept in twolevel SEM with latent... PreviousNext
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 Tino Nsenene posted on Tuesday, September 10, 2013 - 5:35 am
Apologies that this will seem like a very simple question, but I'm just finding my way around multilevel SEM using Mplus -
I estimated a twolevel SEM with latent factors (which is conceptually identical to ex.9.6 in the UG). However, I cannot find the intercept of the dependent latent variable (but for the observed indicators). Why is that so, or how could I request the intercept (maybe using model constraint)?

Thank you for your answer!

Tino
 Linda K. Muthen posted on Tuesday, September 10, 2013 - 10:59 am
The intercept/mean of a latent variable in a cross-sectional study is zero. To refer to the intercept, say:

[f];
 Tino Nsenene posted on Thursday, September 12, 2013 - 11:13 am
(referring to my question from 10th september) OK, but if I extend the syntax from ex9.6 using [fb]

MODEL:
%WITHIN%
fw BY y1-y4;
fw ON x1 x2;
%BETWEEN%
fb BY y1-y4;
y1-y4@0;
fb ON w;
[fb];
The following warning appears:
WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE
OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH.
AN ADJUSTMENT TO THE ESTIMATION OF THE INFORMATION MATRIX HAS BEEN MADE.
THE CONDITION NUMBER IS -0.285D-08.
THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE
MCONVERGENCE OR LOGCRITERION OPTIONS OR BY CHANGING THE STARTING VALUES
OR BY USING THE MLF ESTIMATOR.

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE
TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE
FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING
VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE
CONDITION NUMBER IS 0.567D-17. PROBLEM INVOLVING PARAMETER 18.



Did I use the syntax incorrectly?
 Linda K. Muthen posted on Thursday, September 12, 2013 - 11:28 am
In a cross-sectional model, the intercept cannot be identified. It is fixed at zero.
 Paraskevas Petrou posted on Monday, September 28, 2020 - 5:23 am
Dear Linda,

Thank you for answering the question above multiple times!

What is the intercept though when the model is not cross-sectional? Specifically:

- In a two-level model (measurements nested within individuals) where the within-level outcome variable is latent, what is the estimate and S.E. of the intercept?

- And in a longitudinal model where a T2 latent outcome variable is predicted by its respective T1 variable what is the estimate and S.E. of the intercept for the outcome latent variable? Should I look at the "estimated means" and the "estimated S.E." for this variable in the output?

Thank you!
Paris
 Bengt O. Muthen posted on Monday, September 28, 2020 - 5:36 pm
Q1: It is zero. Factor means are all zero in this case for identification.

Q2: Here you could identify an intercept if you have strong measurement invariance and the factor mean is fixed at zero at T1 and the intercept is free at T2 (so that the T2 factor mean is essentially free). This is not done by default in longitudinal models (only in multiple-group models) so you have to set it up that way.
 Paraskevas Petrou posted on Monday, September 28, 2020 - 11:06 pm
Thank you Bengt!

In the second case (Q2), my latent outcome variable is predicted by its respective T1 latent variable (stability), by one T1 latent predictor, one T1 latent moderator, and their interaction variable. Apart from freeing the intercept of the T2 latent variable, for which T1 latent variable do I need to fix the mean to zero? Only the one that exerts the stability path or all four T1 latent variables? Is there any other constrain I need to set?

Best,
Paris
 Bengt O. Muthen posted on Tuesday, September 29, 2020 - 5:00 pm
Because this is a single-group analysis, the factor means are fixed at zero by default and don't even show up in the output. So you need to worry only about freeing that intercept.
 Paraskevas Petrou posted on Wednesday, September 30, 2020 - 2:51 am
Thank you Bengt!

And the standard deviation of my latent predictors/moderators is simply the square root of the variance of the respective latent variable that I can find in the output, right?
 Bengt O. Muthen posted on Wednesday, September 30, 2020 - 3:03 pm
Right.
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