HELP: Factor analysis used in personality scale

#1
I am struggling through this article on a personality measure scale (NEO-PI-R) : http://jenni.uchicago.edu/econ-psych-traits/CostaMcCrae1995.pdf

On the article p. 27~8, they seem to be looking for specific variance for each variable, and they apparently do this by deriving specificity. ("Specificity is estimated by subtracting communality from reliability, and the loading of each variable on its specific factor is the square root of its specificity."). According to some factor analysis textbooks, communality + specificity = 1, but this (http://bit.ly/haTW2K) seems to imply otherwise...

Anyway, on Table 2 (p.28), they display s (square root of specificity) on the last column. I tried to get specificity by subtracting squared values of each of the common factors from 1 (e.g., s for N1:anxiety = 1- {.772 +(-.04)2 +(-.01)2 +.002 +(-.10)2}. However, the values I got for specificity (sqrt of .39 = 0.63 for aforementioned N1) won't give the s values listed (.41).

Further complicating my understanding is the fact that it says on p. 27 "seven of the variables show their highest loading on the specific factor, notably Openness to Values." Yet I see just SIX variables loading the highest on Openness to EXPERIENCE. So I'm not sure if this is right, they made one typo, or even two... this is problematic since it's supposed to explain the underpinnings of the most widely-used personality scale by its own authors. If anyone can shed light on these, it would be GREATLY appreciated. Thank you!
 

pmcc

New Member
#2
I wasn't able to solve your problem, but maybe you could spot something useful in my attempts.

Starting with your first concern, I think that communalities only add up to 1 in principal components factoring PCF, but not so in principal axis factoring. The choice of table header in the paper suggests a principal axis factoring, but I'm not 100% sure.

So what you mean is:

1 - (0.77² + 0.04² + 0.01² + 0.10²) = 0.3954

If you're trying to calculate the specific variance I think you would have to calculate:

Specific Variance = 0.77 + 0.04 + 0.01 + 0.10 - (communalities/n)​

where n is the number of factor loadings, i.e. 5.

and then take the square root of that to achieve s:

SQRT(0.92 - (communalities/5))​

The communalities in PCF are calculated by the familiar equation you already figured out in part:tup::

0.77² + 0.04² + 0.01² + 0.10² = 0.6046​

Thus:

SQRT(0.92 - (0.6046/5)) = SQRT(0.79908)

SQRT(0.79908) = 0.89...


I know that's not the result, which suggests that I did something wrong. Maybe the above would only apply to PCF?