From: John Fox <jfox_at_mcmaster.ca>

Date: Wed 14 Jul 2004 - 09:06:59 EST

R-help@stat.math.ethz.ch mailing list

https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Jul 14 09:14:09 2004

Date: Wed 14 Jul 2004 - 09:06:59 EST

Dear Antonio,

> -----Original Message-----

*> From: Antonio Prioglio [mailto:a.prioglio@city.ac.uk]
**> Sent: Tuesday, July 13, 2004 5:54 PM
**> To: John Fox
**> Cc: r-help@stat.math.ethz.ch
**> Subject: RE: [R] Help with factanal and missing values
**>
**> On Tue, 13 Jul 2004, John Fox wrote:
**>
**> > Dear Antonio,
**> >
**> > This example is (as stated) a second-order CFI, where each of the
**> > primary factors, F1, F2, and F3 depends upon the
**> second-order factor
**> > F4. To have no second-order structure, simply define variances and
**> > (assuming that you're specifying correlated factors)
**> covariances among
**> > the factors. For the Thurstone example, these would be, in
**> addition to
**> > the variances already set to 1, F1 <-> F2, F1 <-> F3, and F2 <-> F3.
**>
**> Ok I understand the second order part in relation to F4.
**>
**> I'm afraid I'm a bit slow on the last part.
**>
**> "Fn <-> Fn NA 1" is the variance for the factor n.
*

Yes. This is set to 1, standardizing the factors, which is conventional.

> "Fn -> Item.a lam.z NA" is the grouping of the items to each factor

These (i.e., the lambdas) are conventionally called factor loadings.

> "Fn <-> Fm gam.w NA" I take is the covariance among factors.

*>
*

Yes, though it is unconventional to use gamma to represent a covariance (a correlation, since the factors are presumably standardized) in factor analysis.

> Is this correct? Do I need to set variances for each item

*> (Item.a <-> Item.a)?
**>
*

Yes. These *error* variances, which should be free parameters, are conventionally called uniquenesses in factor analysis.

As a general matter, it would help, I think, to look more carefully at the example, since it includes factor loadings and uniquenesses. If you haven't already done so, you might also look at the appendix on structural-equation models to my R and S-PLUS Companion, which is at <http://socserv.socsci.mcmaster.ca/jfox/Books/Companion/appendix-sems.pdf>. This appendix doesn't include a CFA example, but it does explain how to prepare input to the sem() function.

Regards,

John

*> Saluti,
**> Antonio Prioglio
**>
**> --
*

> We are what we repeatedly do. Excellence, then, is not an

*> act, but a habit.
**> Aristoteles
**>
**>
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>

R-help@stat.math.ethz.ch mailing list

https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Jul 14 09:14:09 2004

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