Pattern and structure coefficients in... PreviousNext
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 Matthew Cole posted on Sunday, February 19, 2006 - 3:25 pm
I am curious if someone could help me calculate structure coefficients from the CFA results reported in Mplus.

I understand that the pattern coefficients reflect factor loadings as reported by the StdYX values in the Mplus output, but I don't know how to generate the values for structure coefficients. In reading the literature I am not quite clear on the difference between the two coefficients, although I do notice that researchers are starting to report Pattern/Structure Coefficients in their tables.

Thanks, Matt
 Matthew Cole posted on Sunday, February 19, 2006 - 8:24 pm
I just figured this out folks.
Structure coefficients represent the correlation between an item and the factors. To calculate the structure coefficient, multiply the correlation between the latent factors by the factor loading (i.e., pattern coefficient) for the specific observed variable.
 bmuthen posted on Sunday, February 19, 2006 - 8:43 pm
The general formula for structure coefficients (in covariance metric) is Lambda*Psi, where Lambda is the factor loading matrix and Psi is the factor covariance matrix. Mplus does not print this. One way to get it is to put a factor behind each item and request Tech4.
 Matthew Cole posted on Sunday, February 19, 2006 - 9:44 pm
I am sorry Bengt, but I do not understand what the following statement means: "put a factor behind each item".
 bmuthen posted on Sunday, February 19, 2006 - 10:09 pm
For example, for item y1:

f1 by y1;

means that f1 = y1 (the loading is 1, and the residual variance is zero in the regression of y1 on f1). Thereby, the factor correlations in Tech4 will have correlations between this f1 factor (= y1)and your original factors. Just make sure to make f1 (and other item factors) uncorrelated with other factors.
 Matthew Cole posted on Monday, February 20, 2006 - 3:30 pm
Thank you for the explanation. I am actually trying to replicate results that are presented in Schumacker & Lomax (2004) A Beginner's Guide to Sructural Equation Modeling. Unfortunately, I am not getting the same values as when I take pattern coefficent*r of latent factors. In other words, when I take the factor loading for the observed variables from the StdYX column and multiply that by the correlation value between the latent factors, I am able to replicate the structure coefficient values reported in the text. Perhaps I am not able to use the approach you mentioned to replicate the structure coefficients because I am working with summary data (correlation matrix, means and SD)? What do you think?
 bmuthen posted on Tuesday, February 21, 2006 - 12:42 am
If you work with a correlation matrix (so unit item variance) and factors standardized to unit variance, the matrix formula

L * P

where L is the pattern matrix and P is the factor correlation matrix should give you the structure values in correlation form.
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