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st: RE: constructing a scale from factor analysis


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: constructing a scale from factor analysis
Date   Thu, 31 Jul 2008 13:59:27 -0400

Benjamin Highton wrote:

>>I assume that there is a simple way to do this, but I haven't been
able to
find out how.  I would like to construct a scale based on n items where
each item is weighted in proportion to its factor loading.  My clunky
way
of doing it is to construct the scale myself by (a) accessing the matrix
of loadings e(L), (b) multipling each item by its loading, and (c)
adding
them up.  Any advice about a simpler way to do this will be greatly
appreciated.<<

You want factor scoring, available in postestimation. Weighting by the
loadings is not equivalent. One thing I should note is that you are
often better off not differentially weighting. Simple sum scores often
do better on replication, are much easier to give to other people to
use. A mathematically equivalent and often better method is to use
average scoring which has the benefit of being in the metric of the
original responses, assuming that the original responses are on the same
scale. If the loadings and uniquenesses are roughly the same, the
reliability of the factor score is going to be only slightly higher than
that of the simple sum scores. Average scoring is just (sum score)/K,
where K is the number of indicators, and it has the same reliability,
being a linear transformation of the sum score. 

May I suggest getting a copy of the best "user's guide" factor analysis
book: R. P. McDonald (1985), Factor Analysis and Related Methods,
Erlebaum? (aka "Old MacDonald's FARM"---he'd hit me with his cane if he
heard that) 



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