Your CIOS file request: Q-METHOD/06059115.432 hotline item

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Received:  by CIOS Mailer; Friday 5 Jun 2009 11:54:32
Date:         Fri, 5 Jun 2009 10:53:36 -0500
From:         Bob Braswell 
Organization: AGWM
Subject: Re: Analysis?
To:           Q-METHOD@LISTSERV.KENT.EDU
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Peter Schmolck wrote:
> That's not possible, or should not be possible, in fact. If the
> cumulative percentages of the unrotated factors above and the %'s
> explained variance below originate from the same analysis the figures
> must be the same, i.e. 41 +   26 +  4 +  5 (=76) should add up to 72.55,
> within rounding error. Even if you rotated more than 4 factors but kept
> only 4, the sum of expl. variances could be smaller only but not larger
> than the cumulative variance explained by the first 4 unrotated factors. 
>   
Sam's original post left out the number of factors rotated and the total
of variance explained by that number, but it is clear, as Peter points
out, that the total variance at the beginning of the rotation has to be
the same as the total variance at the end. If the data reported are
correct and from the same analysis, then we must assume that Sam rotated
more than four factors.

From that assumption, what Peter has written is almost correct, but
overlooks one possibility. It is true that each of the first four
factors extracted would have pulled out the most possible variance at
each iteration, but it does not necessarily follow that there is no
combination of four rotated factors that could add up to more total
variance explained than the originally extracted four.  Consider the
case of PCA extraction followed by rotation of all 34 extracted
components. During extraction, components 2-34 had to compete for 39%
that remained after the first was extracted.  But during rotation, with
the first factor only pulling out 41% of the variance, 59% is available
for 2-34.  From this adjusted starting point, we can be certain that
factor 2 of the rotated solution has the opportunity to explain more
variance than factor 2 of the unrotated solution, and so on for the
other factors.  Thus what Sam reports is conceivable.

Bob Braswell