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Re: A comparison of implementations of PAF and promax rotation in R and SPSS
It would be interesting to see whether the scoring keys differ. In order to maximize divergent validity (clarity of concept), items are assigned to only one scale. Items the load on more than say .30 on more than one factor are not used in the scoring key. The operational definition of a construct is based on the meaning of the items used in getting a score.
Foe example, in the late 60s or early 70s Lorr found 3 factors considered to be related to Conservative-Liberal: General C-L, egalitarian, and sexual freedom. When I did my dissertation about the 1976 election, I added a few more contemporary potential items to the instrument. As an example, "equal rights for gay people" loaded with both egalitarian and with sexual freedom" so it would would not be used in the scoring key.
One of the most frequent uses of any factor analysis is to find out whether there are meaningful and useful distinctions in a more general construct. In this context retaining splitting items is analogous to allowing a case to be used in both sides of a comparison as in a part to a whole like SPSS users vs all stat package users, when the comparison should be SPSS users vs users of other packages.
At one time, correlation of an item vs total of all items in a score was used in internal consistency analysis. Then it was figured out that internal consistency was more meaningfully looked at as corrected item-total correlation. Corrected item-total correlation is correlation of an item with sum/mean of the other items in the scale.
The distinction is between the measurement process and the construct. People's height and weight are correlated across cases, but are measured separately.