Why do some softwares give
negative eigenvalues
when doing
an Exploratory Factor Analysis
Depending on which factor extraction method is used, the eigenvalues that SAS (and STATA) and maybe some other softwares (I
don’t know about SPSS) produces are different than simply the eigenvalues of the correlation matrix.
NOTE: Mplus only
produces the eigenvalues of the correlation matrix.
Here I detail the different eigenvalues produced (and why) by SAS Proc FACTOR…
By default if no
method = option
is given, SAS Proc Factor will perform principal component analysis.
In this case, the
eigenvalues it presents are the eigenvalues for the observed correlation matrix.
This is because the eventual q factors it will
present (rotated or unrotated) are simply the first q eigenvectors.
Hence the concept of “variability explained by the q factors” is
represents the proportion of total variability in the standardized observed variables (which is equal to the sum of the diagonal of
the correlation matrix,i.e. p) that can be accounted for by the first q factors (which is the sum of the first q eigenvalues).
When we ask for a different extraction method, for example
method = prinit
which performs “Iterated Principal Factor
Analysis” or
method = ml
which performs “Maximum Likelihood”, then SAS will present two sets of eigenvalues the first
being “Preliminary eigenvalues” and the second being the “Eigenvalues of the Reduced Correlation Matrix”.
Given these
extraction methods, the software is now performing a true Common Factor Model and not Principal Component Analysis.
Recall
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 Fall '08
 MelanieWall
 Eigenvalues, correlation matrix

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