In article <[EMAIL PROTECTED]>,
Gottfried Helms <[EMAIL PROTECTED]> wrote:
>toby989 schrieb:
>> Hi All
>Hi toby -
> I couldn't read the SAS-statements in detail. Just one aspect,
> which may be not considered, but may be understood better,
> when expressed in terms of rotation.
> The initial factor solution is often simply a principal
> components/principal factors approach, which will iteratively
> enhanced with respect to the new communalities.
> In the view of rotations-to-pc/pf-position it gives different
> solutions, if you
There is nothing in a good factor analysis approach which
requires correlations; there is much to suggest avoiding
them. The FA model is
x_i = Lambda*f_i + s_i,
where x_i is the observed result of the i-th individual,
f_i is the unobserved "common" factor, and s_i is the
specific factor. The IMPORTANT part of the usual assumptions
is that all of the coordinates of s_i are independent and
that f_i are independent of s_i. These can be relaxed to
some extent.
Although the estimates are derived under the assumption
of normality, the estimated structure is quite robustly
estimated provided that one does not do such things as
normalizing the variances of anything involved. In fact,
if all of the normalizing assumptions are on Lambda, the
asymptotic distribution of the errors in the estimation
of Lambda, in the difference of the covariance matrices
of the common factors and the variances of the specific
factors from their SAMPLE values, is a multivariate
normal distribution, insensitive to the actual distributions,
but only to the covariance structure.
Doing anything else, like making normalizing assumptions
on the factor variances, or using correlations, just adds
uncertainty to the process, and loses robustness. This
is generally the case; just use the covariances.
--
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, Department of Statistics, Purdue University
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
.
.
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