I'm using "factor." When I ask for a rotated solution (using the default - varimax orthogonal) it gives me (aside from the loadings etc) a value called "proportion" for each factor (with the first factor having the highest value). Stata's documentation never explicitly says what this value actually is but I assume that "proportion" represents the proportion of the total variance in the observed variable explained by each latent factor. However, when I view a rotated solution the total "proportion" values often add up to more than 1, implying that the factors in total explain more than 100% of the variance in the observed variables, which seems nonsensical. This can be seen in Stata's example dataset for the "factor" commaand:

. webuse bg2
(Physician-cost data)

. factor bg2cost1 bg2cost2 bg2cost3 bg2cost4 bg2cost5 bg2cost6
(obs=568)

Factor analysis/correlation Number of obs = 568
Method: principal factors Retained factors = 3
Rotation: (unrotated) Number of params = 15

--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 0.85389 0.31282 1.0310 1.0310
Factor2 | 0.54107 0.51786 0.6533 1.6844
Factor3 | 0.02321 0.17288 0.0280 1.7124
Factor4 | -0.14967 0.03951 -0.1807 1.5317
Factor5 | -0.18918 0.06197 -0.2284 1.3033
Factor6 | -0.25115 . -0.3033 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(15) = 269.07 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

-----------------------------------------------------------
Variable | Factor1 Factor2 Factor3 | Uniqueness
-------------+------------------------------+--------------
bg2cost1 | 0.2470 0.3670 -0.0446 | 0.8023
bg2cost2 | -0.3374 0.3321 -0.0772 | 0.7699
bg2cost3 | -0.3764 0.3756 0.0204 | 0.7169
bg2cost4 | -0.3221 0.1942 0.1034 | 0.8479
bg2cost5 | 0.4550 0.2479 0.0641 | 0.7274
bg2cost6 | 0.4760 0.2364 -0.0068 | 0.7175
-----------------------------------------------------------

.
.
.
. rotate

Factor analysis/correlation Number of obs = 568
Method: principal factors Retained factors = 3
Rotation: orthogonal varimax (Kaiser off) Number of params = 15

--------------------------------------------------------------------------
Factor | Variance Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 0.72646 0.05991 0.8772 0.8772
Factor2 | 0.66655 0.64139 0.8048 1.6820
Factor3 | 0.02516 . 0.0304 1.7124
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(15) = 269.07 Prob>chi2 = 0.0000


you can see that the "proportion" values for the 3 retained factors add up to 1.7124.:


So what's going on here? Obviously I'm confused about what "proportion" means, but Stata's documentation doesn't seem to provide any guidance on how I should interpret this value. Also, how can I correctly characterize the explanatory power of rotated factors? I would like to be able to say that my first factor explains X% of the variance while the second factor explains Y%, but is that even possible with rotated solutions?

Someone else already asked this exact same question but never got a response:
https://www.statalist.org/forums/for...eater-than-100