[R] Help with factanal and missing values

John Fox jfox at mcmaster.ca
Wed Jul 14 01:06:59 CEST 2004

Dear Antonio, 

> -----Original Message-----
> From: Antonio Prioglio [mailto:a.prioglio at city.ac.uk] 
> Sent: Tuesday, July 13, 2004 5:54 PM
> To: John Fox
> Cc: r-help at 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

> 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
This appendix doesn't include a CFA example, but it does explain how to
prepare input to the sem() function.


> Saluti,
> Antonio Prioglio
> --
> We are what we repeatedly do. Excellence, then, is not an 
> act, but a habit.
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