# RE: [R] Help with factanal and missing values

From: John Fox <jfox_at_mcmaster.ca>
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
> > 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.

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
>
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