# Whether to use correlation matrix between latent variables or raw data as input to SEM?

I have a fairly large model - a total of 8 latent variables and each one has 10 items (observed variables). Drawing this model is a mess (there is a mediation effect as well).

Is it better to just compute correlations among my latent variables and import the correlation table instead of using all the raw data?

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Can you say more about what you're trying to do? Is this SEM? Are you talking about visualizing the model (ie, making plots of the data & relationships), or about a way to input the structure you want to know about into the software for analysis? – gung Sep 18 '12 at 13:28
Yes, SEM, I am using AMOS. I was wondering is it better to use the correlation matrix or raw data as input data files? – Sara Sep 18 '12 at 20:04
You say "compute correlations among my latent variables". Thus, it sounds like you are asking about two things: (1) whether it makes a difference whether you import raw data or a correlation matrix based on raw data? (2) whether it makes sense to compute composite scores (e.g., from your 10 items per scale) and use these composite scores as input to SEM? – Jeromy Anglim Sep 19 '12 at 6:16
You ask "is it better....". Better for what? – Peter Flom Sep 29 '12 at 17:53

For many of the most common applications in SEM, analyzing the raw data is equivalent to analyzing a covariance / correlation matrix. In these applications, one of the first things your computer program will do is calculate a covariance / correlation matrix.

I should note, though, that analyzing a covariance matrix is not equivalent to analyzing a correlation matrix, and in general analyzing the same data via a covariance matrix and a correlation matrix will yield different standard errors, different confidence intervals around your path coefficients, and different fit statistics. Which analysis you choose (covariances vs correlations) mostly depends on whether you're interested in the units of your measures.

Patrick

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Hi Patrick, you don't need to sign your name at the end of your posts. You can change your user name by clicking it at the top of the page, then pressing 'edit'. – naught101 Sep 19 '12 at 4:19
Unfortunately, my username got changed when I merged my CV account with my Stackoverflow account, so I can't change the name back for another 7 days. – Patrick S. Forscher Sep 19 '12 at 4:22
I disagree with your statement about equivalence of SEM on covariances and raw data. If you need to perform more advanced estimation and testing, including any of: Satorra-Benter scaled/adjusted tests, ADF/WLS estimation, Bollen-Stine bootstrap, you need the raw data. In other words, the raw data will likely allow a wider range of estimation techniques. With the covariance/correlation matrix, you are stuck with the normal theory based methods and GLS, and that will hardly work well with 80 variables, which are probably on Likert scale, too. – StasK Sep 19 '12 at 4:48
StasK, thanks for the comment. I have edited my statement to be more limited in scope. – Patrick S. Forscher Sep 19 '12 at 4:54

This doesn't directly answer your question, since you are using AMOS, but I wanted to point out that there are two approaches to SEM. One uses an approach based on covariances and maximum likelihood, the other uses an approach based on the original data and partial least squares (PLS).

I believe AMOS (LISREL, Mplus, etc) use the first approach, which is generally called SEM. The other approach, often called PLS Path Modeling (or sometimes PLS SEM) is also available in various software, including several R packages. Different horses for different courses, but as I'm learning about the PLS approach, it seems like it has advantages in many applications.

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