HervÈ Stolowy <email@example.com> asks:
When I run a factor analysis with Stata
factor var1 var2 ... varN, pcf mineigen(1)
and with SPSS (Analyze>Data reduction>Extraction: Principal
in the Rotated Factor Loadings, I find that some factors have the
same figures in Stata and SPSS, but with opposite signs. This
does not happen for all factors but only some of them. The others
are similar in both results.
Being a beginner, I would expect to find the same matrix with
There is probably a logical explanation but I miss it.
I would have guessed (given the words I am seeing for your SPSS
command selection) that you were running in SPSS the equivalent
of Stata's -pca- followed by -rotate-. But, I could easily be
wrong about that. Maybe someone who knows more about SPSS can
comment on that?
I just want to make sure that you are clear on the fact that
-factor, pcf- is not the same as -pca-. Rencher (2002) pages
415-416 says concerning the "principal component method" of
"factor analysis" that
"... This name is perhaps unfortunate in that it adds to
the confusion between factor analysis and principal
component analysis. ..."
And he goes on to explain more about it.
Assuming you are asking for the same thing in both SPSS and
Stata, I would still not be surprised by a change of sign for
some columns of the reported factor loadings. Starting on page
414, Rencher (2002) discusses the nonuniqueness of factor
loadings. The loadings can be multiplied by an orthogonal matrix
and still reproduce the same covariance matrix. Sign flips are a
common event. The interpretation of the underlying factors
remains fundamentally the same.
For example, if one column of the factor loading matrix was
researchers would say that this factor is comparing var1 and var3
against var4 and var5 (with var2 close to zero and not important
for this factor). If the signs were flipped for this column, you
would still end up with the same interpretation of it comparing 1
and 3 against 4 and 5.
By the way, the arbitrariness of the sign happens in many other
multivariate techniques. Heuristically think of it like this --
if one of these multivariate techniques were trying to draw a
picture of your house, they might draw your house or the mirror
image of your house (a sign flip). Either way, it still is a
visual description of your house.
Rencher, A.C. (2002) Methods of Multivariate Analysis,
2nd Ed., Wiley: New York.
Ken Higbee firstname.lastname@example.org
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