Re: Factor analysis: Computing factor scores

I concur. one can only estimate factor scores.

In disciplines where the analysts are emphasizing getting groups of items to combine into summative scales (achievement, aptitude, psychopathology, personality, attitudes, values, etc.) it is more common to use unit weights in getting the variables to use in further analysis.

In scale construction, using unit weights for items above some cut-off on loadings (often abs(.4) ), and zero otherwise is a way of getting scores for scales that get at the construct that is interpreted as underlying the set of items.

For the approach that perhaps was used in the article mentioned, one does the arithmetic by using syntax something like this. (in this example there would be no item reflection as there would be in areas such as attitudes, values, etc.)
compute capitalization = sum(item01, item04, item07, item18, item22).
compute punctuation = sum(item02, item06, . . . ).
compute spelling = sum(item03, . . .).



Based only on the fact that the OP said that there were not loadings for every item on every factor, I suggested checking whether this was the approach used by the article mentioned.

The factor score estimates that put some weight on every item. e.g. regression, Bartlett, or Anderson-Rubin methods are obtained by specifying /save = {reg, bart, ar} in the procedure. In disciplines where the analyst wants to reduce the data to as few variables as is reasonable under the circumstances while retaining as much as the total variability as possible, these methods are used.

I neglected to mention that if there were only 25 items in total and the first few factors had 5 to 10 items, that left very few items to be used in scales for the constructs underlying higher numbered factors. The OP should check what stopping rule was used. There is no magic number of items for a scale, but having only 4 or 5 items on a scale is often a "cross your fingers and hope" situation.


Art
Art@xxxxxxxxxxxxx
Social Research Consultants



Herman Rubin wrote:

In article <43B53068.3050103@xxxxxxxxxxx>,
Art Kendall  <Art@xxxxxxxxxxxxx> wrote:

PERHAPS the original article used a conventional way of computing scale scores based on the factor analysis. That is: reflect item responses so that the meaning of a high response on the item points toward a higher amount of the construct, then sum the items using unit weights.


Since only a few items were 'splitters' it would have helped divergent validity if those items had been left out of the scale scores. You might want to check the original article or with the authors to see if they followed the convention of an item only going on one scale. 


One cannot COMPUTE factor scores; one can only estimate
them.  The factor analysis model is

	y = Lf + u,

where y is the observed score vector, f is the unobserved
factor vector, u is the unobserved specific factor vector,
and L is the factor loading matrix.

This gives a multivariate model, and the factors are estimated by the usual regression on the observed scores,
using the estimates of the loading matrix. This gives
an estimate of the joint covariance matrix of y and f,
and allows a linear estimate of f.

.