# [R] - factanal scores correlated?

Christian Montel christian.montel at eligo.de
Fri Aug 11 08:35:27 CEST 2006

```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

--
--------------------------
Dr. Christian Montel
eligo GmbH -- Büro Berlin
Arndtstr. 34
10965 Berlin
Tel. 030 -- 69 00 11 42
Fax  030 -- 69 00 47 61
christian.montel at eligo.de
http://www.eligo.de/

```