In article <9gg7ht$qa3$[EMAIL PROTECTED]>,
haytham siala <[EMAIL PROTECTED]> wrote:
>Hi,
>I have a question regarding factor analysis: Is normality an important
>precondition for using factor analysis?
>If no, are there any books that justify this.
Factor analysis is quite robust against non-normality.
The essential factor structure is little affected by it
at all, although the representation may get somewhat
sensitive if data-dependent normalizations are used, such
as using correlations rather than covariances, or forcing
normalization on the covariance matrix of the factors.
Some of this is in my paper with Anderson in the
Proceedings of the Third Berkeley Symposium. The result
on the asymptotic distribution, not at all difficult to
derive, is in one of my abstracts in _Annals of
Mathematical Statistics_, 1955. It is basically this:
Suppose the factor model is
x = \Lambda f + s,
f the common factors and s the specific factors. Further
suppose that f and s, and also the elements of s, are
uncorrelated, and there is adequate normalization and
smooth identification of the model by the elements of
\Lambda alone. Now estimate \Lambda, M, the covariance
matrix of f, and S, the diagonal covariance matrix of s.
Assuming the usual assumptions for asymptotic normality of
the sample covariances of the elements of f with s, and of
the pairs of different elements of s, the asymptotic
distribution of the estimates of \Lambda and the SAMPLE
values of M and S from their actual values will have the
expected asymptotic joint normal distribution. This makes
no assumption about the distribution of M and S about
their expected values, which is the main place were there
is an effect of normality.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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