

Names of SEM arrays in Version 7 

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Peter Halpin posted on Wednesday, February 05, 2014  2:48 pm



Hi, 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). LAMBDA F1 F2 PARENTAL LOW_SES ________ ________ ________ ________ READING 1.000 0.000 0.000 0.000 MATH 1.000 0.000 0.000 0.000 SPELLING 1.000 0.000 0.000 0.000 MOTIVATI 0.000 1.000 0.000 0.000 HARMONY 0.000 1.000 0.000 0.000 STABILIT 0.000 1.000 0.000 0.000 PARENTAL 0.000 0.000 1.000 0.000 LOW_SES 0.000 0.000 0.000 1.000 Similar comments apply to the other model matrices. Can you please advise me on how to interpret this? Has the SEM notation changed in Mplus 7? Has it yet to be updated in the user's guide ? Thanks, Peter 


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. 


Thanks for your reply. 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? Thanks, Peter 


These technical issues are discussed in papers at http://www.statmodel.com/techappen.shtml See in particular: "Technical Appendices 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 1112 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. 


Great, thank you for you time. This is very helpful! Peter 

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