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)?
The intercept/mean of a latent variable in a cross-sectional study is zero. To refer to the intercept, say:
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.
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?
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.
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?