## Factor analysis question

### Factor analysis question

Hello

We have a data set which includes, for each of 96 cities, 4 estimates
of the number of drug injectors in that city.  Each of these estimates
contains error.

We ran a factor analysis to determine their commonality.

We now wish to use the results of this analysis to come up with a
better estimate of the number of drug injectors in each city.

It seems intuitively reasonable to multiply the standardized scoring
coefficients by the estimates, add these together, and then divide by
the sum of the standardized scoring coefficients.  I've even seen this
done.  But I haven't seen a good proof that this is correct (it may not
be correct!)

Any advice on how to proceed will be appreciated.

Peter L. Flom, PhD
Assistant Director, Statistics and Data Analysis Core
Center for Drug Use and HIV Research
National Development and Research Institutes
71 W. 23rd St
New York, NY 10010
(212) 845-4485 (voice)
(917) 438-0894 (fax)

This may be a stupid question, but I can't seem to find the answer anywhere.
When reporting the results of a factor analysis, specifically the percentage
of varience the factor solution accounts for, do you report the extraction
sums of squares % of varience or the rotated % of varience?  Intuitively, I
think it should be the rotated % of varience, but I would be most grateful
for some input here.

Also, with factor analysis when looking at the loadings on each factor, some
of the items load on more than one item.  What questions should I be asking
if this happens?

Thanks very much