In article <[EMAIL PROTECTED]>,
Heureka <[EMAIL PROTECTED]> wrote:
>Hi
>I'm working on my thesis in which I've used factor analysis in comparison
>with ICA (independent component analysis) on some data. In this context I'm
>have difficulties understanding the conceptual difference.
>Somewhere I heard that factor analysis estimates the same subspace as ICA
>but cannot find the proper rotation. Apart from that factor analysis has a
>gaussian prior which makes it hard -if not impossible- to estimate the true
>sources of some multiresponse system.
There are many misconceptions here.
The factor analysis MODEL is
y_it = \sum \lambda_ij f_jt + s_it,
that is, the i-th score on the t-th subject is the
appropriate linear combination of the factors on that
subject plus a specific factor. Only the y's are
observed. It is assumed that the individuals are
independent, and for each individual, each s is
independent of each other and of the f's for that
individual.
In this model, it is not necessary to normalize anything,
and this is as it should be. Normalization messes up
just about anything; with normalization on the \lambda's
ONLY, not on variances or covariances or anything else
involving them, the asymptotic distribution theory for
the estimates based on normality is particularly simple,
and if variances exist, normality has little effect, for
the inference on the errors in the estimates of \lambda,
the SAMPLE variances of the s's, and the SAMPLE covariance
matrix of f. One can then compare different populations,
etc., without too much difficulty.
On the other hand, if one uses correlations or other means
of normalization using the data, the distribution becomes
important; the above robustness disappears. Comparing
different populations becomes very difficult. But the
general unidentified factor model is still the same, not
depending on scaling.
Now principle components is very definitely affected by
any type of scaling. The answers can be quite different,
and what is important for one scaling can be trivial for
another, and vice versa.
--
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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