Indirect path coefficient PreviousNext
Mplus Discussion > Structural Equation Modeling >
 George Young posted on Tuesday, December 12, 2006 - 5:57 pm
I have a model like this:


f1 by a1@1 a2 a3 a4;
f2 by b1@1 b2 b3 ;
f3 by c1@1 c2 c3 c4 c5;

y on f1 f2 f3;

I want to establish the indirect path coefficient from a, b and c to y. Model complains no indirect path exists.

Could you please give me an instruction for how to get the path coefficients from a's, b's and c's to y? For example the indirect coefficient from a1 to y, b2 to y etc.

To me this model liiks like: a <-->y,
so the indirect coeffs can not be simply multiplied from each path. Any formula you can suggest?

Thanks a lot!!
 Linda K. Muthen posted on Wednesday, December 13, 2006 - 7:53 am
This model does not contain indirect effects from a, b, c to y. The variables a, b, and c are regressed on f and y is regressed on f.
 George Young posted on Wednesday, December 13, 2006 - 12:12 pm
Thanks, Linda.

I have this model because I can not do Y on a, b and c's due to the colinearity among a, b and c's.

My final goals are to answer "How well f1, f2 and f3 predict Y?" and "how variables A1-A4, B1-B3 and C1-C5 affect Y?"

Do you have any suggestions?

Thank you very much for the answers.
 Bengt O. Muthen posted on Thursday, December 14, 2006 - 5:40 am
You can say how well the f's influence y. You can also say how well the a's, b's, and c's measure the f's (factor loadings). That's about all.
 George Young posted on Friday, December 15, 2006 - 6:09 am
Are the "factor loadings" you referred here = estimates in the model output?

Then I have another related question. In general, if
A = alpha F + Int1 ... (1); and
F = beta A + int2 ... (2).
Then: beta = R-square from (1) /alpha.

By saying "how well the a's, b's, and c's measure the F's" using the loadings, kind of equally using 1/loadings to say how well the a, b and c's "predict" F, am I right? Since the scale is inversed, I may get opposite conclusions. For example; if
a1 = 10 f1;
a2 = .1 f1;
with R^2 = 0.5. Looks like a2 is a poor measure for f1 in this case. However, if you rewrite the above to:

f1 = 0.05 a1; (R^2/10 = 0.5/10=0.05)
f1 = 5 a2;

a2 is then a good "predictor for f1?

Why this happens?

Thanks a lot.
 Bengt O. Muthen posted on Friday, December 15, 2006 - 8:55 am
Yes, loadings are the "f BY a" estimates given in the output.

How well an indicator measures a factor is related to the R-square in the indicator as a function of the factor, so not only the loading size - you will get this information when requesting Standardized in the Output command. The way an indicator contributes to the factor score estimation is seen in the factor score coefficient matrix which is a function of all the parameter estimates of the model - see the matrix C expression in equation (226) in appendix 11 of the technical appendices on the web site, and also general factor analysis books.
 George Young posted on Sunday, December 17, 2006 - 11:17 am
Thank you for the instructions.

Is there an option that I can request Mplus to provide these estimations, i.e. the indicator contributes to the factors or the equation (226)?

Because the formula looks very complicate, it may be hard to do it manually.

Thanks and have a good weekend.
 Linda K. Muthen posted on Sunday, December 17, 2006 - 4:16 pm
See the FSCOEFFICIENT option of the OUTPUT command.
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