[R] - factanal scores correlated?

[Prof Brian Ripley]

This is a Heywood case, and you don't have a valid fit:

> myfac

Call:
factanal(x = m1, factors = 3, scores = "regression")

Uniquenesses:
   v1    v2    v3    v4    v5    v6 
0.005 0.101 0.005 0.224 0.084 0.005 

notice no less than 3 very small uniquenesses.


On Fri, 11 Aug 2006, Christian Montel wrote:

> Hi,
> 
> I wonder why factor scores produced by factanal are correlated, and I'd 
> appreciate any hints from people that may help me to get a deeper 
> understanding why that's the case. By the way: I'm a psychologist used 
> to SPSS, so that question my sound a little silly to your ears.
> 
> Here's my minimal example:
> 
> ***********************************************
>       v1 <- c(1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,4,5,6)
>       v2 <- c(1,2,1,1,1,1,2,1,2,1,3,4,3,3,3,4,6,5)
>       v3 <- c(3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,5,4,6)
>       v4 <- c(3,3,4,3,3,1,1,2,1,1,1,1,2,1,1,5,6,4)
>       v5 <- c(1,1,1,1,1,3,3,3,3,3,1,1,1,1,1,6,4,5)
>       v6 <- c(1,1,1,2,1,3,3,3,4,3,1,1,1,2,1,6,5,4)
>       m1 <- cbind(v1,v2,v3,v4,v5,v6)
>       myfac <- factanal(m1, factors=3, scores="regression")#
>       cor(myfac$scores)
> ***********************************************
> 
> Tells me
>              Factor1     Factor2     Factor3
> Factor1 1.000000000 0.001624383 0.002862785
> Factor2 0.001624383 1.000000000 0.001956953
> Factor3 0.002862785 0.001956953 1.000000000
> 
> which means that factor correlations are indeed quite low with regard to 
> interpretation issues, but an analysis of a larger dataset yielded 
> factor intercorrelations up to .10.
> 
> I guess this is an optimization issue because a lower setting of "lower" 
> tends to lower factor intercorrelations, but I'm still confused because 
> I (misleadingly?) thought that factor scores are (completely) 
> independent by definition?
> 
> Any hints would be greatly appreciated,
> 
> best regards,
> 
> Christian
> 
> 
> 

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595