Matrices
Message/Author
 Rick Sawatzky posted on Thursday, November 16, 2006 - 5:20 pm
I am trying to figure out which terms are included in the alpha matrix (Tech1). It seems to me that in some models this matrix includes the means of observed variables whereas in other models it includes the intercepts of latent factors. Am I understanding this correctly? And is there a summary description of of the various matrices used in MPlus (as reported in Tech1)?

Thanks so much ...
 Bengt O. Muthen posted on Thursday, November 16, 2006 - 10:30 pm
See the Technical Appendices through Version 2 on the Mplus web site. alpha contains the means - or intercepts depending on the model - of the latent variables.
 Rick Sawatzky posted on Friday, November 17, 2006 - 7:51 am
Thanks so much! I found it. I'd just like to clarify the following. The Technical appendix states that the alpha vector contains the means or intercepts of latent factors, but am I correct in saying that it could also contain the means or intercepts of exogenous observed variables?
 Linda K. Muthen posted on Friday, November 17, 2006 - 8:39 am
Means and intercepts of observed variables can appear in alpha if their use in the model causes a latent variable to be created for them.
 Rick Sawatzky posted on Friday, November 24, 2006 - 8:37 am
Dear Linda and Bengt,

I would like to determine how Mplus has parameterized the following model:
MODEL: F1 by y2 y5 y6 y7;
F2 BY y8 y11 y15 y16 y38;
F3 BY y18 y21 y23 y24;
F4 BY y35 y36 y37 y38;
y18 on y35;
y21 on y35;
y23 on y35;
y24 on y35;
F by F1* F2 F3 F4;
F@1;

The factor loadings for Y18, Y21, Y23, Y24 for this model are located in the BETA matrix (TECH1) so, it seems to me, that Mplus must be using latent variables with variances of zero to represent each of the above four variables. Is that correct? (see my follow up posting on this topic)
 Rick Sawatzky posted on Friday, November 24, 2006 - 8:39 am
In following of my previous posting (one minute ago), I would expect the following two models to be equivalent:

MODEL: F1 by y2 y5 y6 y7;
F2 BY y8 y11 y15 y16 y38;
F3 BY y18 y21 y23 y24;
F4 BY y35 y36 y37 y38;
y18 on y35;
y21 on y35;
y23 on y35;
y24 on y35;
F by F1* F2 F3 F4;
F@1;

MODEL: F1 by y2 y5 y6 y7;
F2 BY y8 y11 y15 y16 y38;
F3 BY y18 y21 y23 y24;
F4 BY y36 y37 y38;
F6 by y35;
F7 by y18@1;
F8 by y21@1;
F9 by y23@1;
F10 by y24@1;
F6@1;
F7@1;
F8@1;
F9@1;
F10@1;
F6 with F7-F10@0;
F7 with F8-F10@0;
F8 with F9-F10@0;
F9 with F10@0;
F6 on F4;
F7 on F6;
F8 on F6;
F9 on F6;
F10 on F6;
F by F1* F2 F3 F4;
F@1;

Am I correct in saying that these are essentially equivalent models with respect to their parameterization in Mplus?
 Linda K. Muthen posted on Friday, November 24, 2006 - 9:27 am
The two models you present are not equivalent.

In the first input, Mplus puts factors behind the observed indicators so that the regression of the the observed variables on each other can appear in beta. This is done using the following specification:

f1 BY y1@1;
y1@0;

for each observed variable. The fixed factor loadings of one appear in lambda. The regression coefficients appear in beta.