Peter Halpin posted on Wednesday, February 05, 2014 - 2:48 pm
I am wondering about the notation for SEM arrays. For example, the Version 7 user's guide states (p. 742):
"The lambda matrix contains information regarding factor loadings. The rows of lambda represent the observed dependent variables in the model. The columns of lambda represent the continuous latent variables in the model."
However, in my TECH 1 output I have manifest independent variables in the rows and columns of the LAMBA matrix (below: Parental_MI and Low_SES).
The Beta matrix is for regression coefficients when a latent variable is regressed on a latent variables using maximum likelihood estimation. The Gamma matrix is used only for weighted least squares estimation. For maximum likelihood, if a latent variable is regressed on an observed variable or an observed variable is regressed on an observed variable, the observed variables become latent variables that are equaivalent to the observed variables. This is what you see. It has no impact of model estimation.
For future reference I think may be worth noting the the model notation described in the user's guide (i.e., p. 742, Version 7) does not make any indication that the matrix notation depends on which estimator is used. The user's guide describes a standard SEM notation, but that is not what shows up in the output.
Also, if I could try to make my question clearer: I was asking about notation because I am teaching a class on SEM and using Mplus as one of the software packages. I wanted to be able to direct my students to the part of the Mplus user's guide that explains the model notation used in the Tech1 output. Do you have any advice on what I should tell them?
Click here for the technical appendices covering theory behind Mplus through Version 2."
The Version 2 technical appendix 2 starting on page 7 discusses various parameter matrices used in Mplus. Given the generality of Mplus, this is a bit more involved than in typical SEM programs. Pages 11-12 describes the case of not all y's continuous and discusses the model parts Part 1, Part 2, and Part 3. Part 2 uses the Gamma matrix. On page 13 the standard SEM case of all y's continuous is discussed, showing how the classic LISREL "all y" notation is used.