SEM regression coefficient
Message/Author
 Walter Müller posted on Tuesday, July 10, 2012 - 7:12 am

I´ve run an EFA followed by a CFA for three questionnaires. The observed variables were treated as ordered categorical and I used the WLSMV-estimator. It turned out, each of the 3 questionnaire consits of 3 factors.

I´ve run a SEM with all three questionnaires using the following model command:
A1 on B1 B2 B3;
A1 on C1 C2 C3;
A2 on B1 B2 B3;
A2 on C1 C2 C3;
A3 on B1 B2 B3;
A3 on C1 C2 C3;
output: standardized (stdyx);

For example, for the Factors A1, B1 and C1 the results were (STDYX Estimates):
B1 WITH C1 0.9
A1 ON B1 0.65
A1 ON C1 0.75

B1 and C1 are highly correlated. I would like to know how much they overlap in their prediction on A1.

My question is: What do the regression coefficients ( 0.65 and 0.75) exactly mean?

Is the regression coeffizient of B1 on A1 only based on B1? Are the effects of the other B2,C1,.. partialed out?

I hope you can understand my question, despite of my bad english.

Thank you very much for your help!
 Walter Müller posted on Tuesday, July 10, 2012 - 8:50 am
Hi,

i´m sorry, but I have to correct myself.
My question is: Is the Regression
coefficient of A1 on B1 ( A1 as the idepentend factor, and not the othder way around) based on a partial regression?
 Linda K. Muthen posted on Tuesday, July 10, 2012 - 10:18 am
When you say

a1 ON b1;

a1 is the dependent variable and b1 is the independent variable.

If you have

a1 ON b1 c1;

the regression coefficients for b1 and c1 are partial regression coefficients.
 Walter Müller posted on Tuesday, July 10, 2012 - 10:58 am
Hi,
thank you very much for the quick answer!
This ist my model command:
A1 on B1 B2 B3;
A1 on C1 C2 C3;
A2 on B1 B2 B3;
A2 on C1 C2 C3;
A3 on B1 B2 B3;
A3 on C1 C2 C3;
output: standardized (stdyx);

A1-A3 are the dependend variables, B1-B3 and C1-C3 are the independet variables, I mixed that up in my last post.

If i got you right, all coefficients are partial regression coefficients and it doesn´t matter that I´ve six On-Statemants, right?

Is it possible, given all the partial regression coefficients and the correlations between B (1-3) and C(1-3), to answer the question how much B1-B3 overlaps with C1-C3 in their prediction on A, or will I have to run further analyses in order to answer that question?

Thank you very much for your help!
 Linda K. Muthen posted on Wednesday, July 11, 2012 - 11:11 am
I don't think what you want is possible because the covariates are correlated. You might want to get the opinions of others on SEMNET.