This has to do with factor extraction. Methods like PCA extract factors so they explain the maximum variation each time a factor is taken out. That is the way it is usually written. But I think they actually mean that they extract factors based on the amount of common variation between the factors (the covariance) not the variance itself. This is different because part of the variation in the variables is not I believe shared with other variables, is not part of covariance.
Anyone know the answer to this?
"Facts are stubborn things, but statistics are more pliable." Mark Twain
I believe (but others should correct me if I am mistaken) that what you have described is the difference between factor analysis and principal component analysis. That is, principal component analysis operates on all of the observed variance, while factor analysis operates on the shared variance.
In God we trust. All others must bring data.
~W. Edwards Deming
noetsi (08-24-2012)
thanks although to follow my comments up the notes I am working from use PCA to extract data for EFA. So are you saying if you use PCA for EFA (not the method PCA by itself but as an extraction method), that it would be the shared variance not the total variance?
Comps going to kill me....
"Facts are stubborn things, but statistics are more pliable." Mark Twain
The terminology is a little confusing. When people say they are using PCA as "an extraction method for factor analysis", they are considering PCA to be a "type" of factor analysis. So what this really means is just that they are doing PCA. I found this document which might shed some light on things:
http://graduate.tuiu.edu/res620sum08...orAnalysis.pdf
In God we trust. All others must bring data.
~W. Edwards Deming
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