Hello,
I ran factor analysis(factor, pf) in Stata to develop factor scores for my latent variables. However, after orthogonal varimax rotation, the proportion of variance accounted for by the factors is greater than 1.00 (100%).
Is this problematic? I think this is happening because I do not specify the option "normalize." Normalize places an equal weight on all rows of the matrix to be rotated--maybe I should have done this? However, I have some indicator variables that have high uniqueness and the normalize option would weight these items equally with other items that had lower uniqueness, which seems like the wrong move. Output is included below:
factormat r, n(140) mineigen(1) sds(stdev) means(mean) factors(1)
(obs=140)
Factor analysis/correlation Number of obs = 140
Method: principal factors Retained factors = 1
Rotation: (unrotated) Number of params = 3
--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 1.67735 1.74060 1.1655 1.1655
Factor2 | -0.06324 0.11172 -0.0439 1.1216
Factor3 | -0.17497 . -0.1216 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(3) = 157.62 Prob>chi2 = 0.0000
Factor loadings (pattern matrix) and unique variances
---------------------------------------
Variable | Factor1 | Uniqueness
-------------+----------+--------------
Q3 | 0.5942 | 0.6469
Q5 | 0.8293 | 0.3123
Q7 | 0.7979 | 0.3634
---------------------------------------
.
. do "/var/folders/kx/2rhtmrz11ml9xqnpxzcw50h80000gn/T//SD01864.000000"
. rotate
Factor analysis/correlation Number of obs = 140
Method: principal factors Retained factors = 1
Rotation: orthogonal varimax (Kaiser off) Number of params = 3
--------------------------------------------------------------------------
Factor | Variance Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 1.67735 . 1.1655 1.1655
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(3) = 157.62 Prob>chi2 = 0.0000
Rotated factor loadings (pattern matrix) and unique variances
---------------------------------------
Variable | Factor1 | Uniqueness
-------------+----------+--------------
Q3 | 0.5942 | 0.6469
Q5 | 0.8293 | 0.3123
Q7 | 0.7979 | 0.3634
---------------------------------------
Factor rotation matrix
-----------------------
| Factor1
-------------+---------
Factor1 | 1.0000
-----------------------
. predict QUICKTREATX
(regression scoring assumed)
Scoring coefficients (method = regression; based on varimax rotated factors)
------------------------
Variable | Factor1
-------------+----------
Q3 | 0.17032
Q5 | 0.46105
Q7 | 0.37630
------------------------
. label variable QUICKTREATX "standardized Factor score of Q3, Q5, Q7 - getting treatment quickly"
. summarize QUICKTREATX
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
QUICKTREATX | 140 .0230575 .8292956 -1.990456 1.034425
. alpha Q3 Q5 Q7, std item detail
Test scale = mean(standardized items)
average
item-test item-rest interitem
Item | Obs Sign correlation correlation correlation alpha
-------------+-----------------------------------------------------------------
Q3 | 232 + 0.7790 0.3485 0.6558 0.7921
Q5 | 371 + 0.8965 0.6316 0.3096 0.4728
Q7 | 637 + 0.9236 0.5573 0.4190 0.5905
-------------+-----------------------------------------------------------------
Test scale | 0.4964 0.7473
-------------------------------------------------------------------------------
Interitem correlations (obs=pairwise, see below)
Q3 Q5 Q7
Q3 1.0000
Q5 0.4190 1.0000
Q7 0.3096 0.6558 1.0000
Pairwise number of observations
Q3 Q5 Q7
Q3 232
Q5 160 371
Q7 193 304 637
.
end of do-file
This also happens in the Stata example provided on see p. 15 (use link below).
https://www.stata.com/manuals/mvfact...estimation.pdf
I ran factor analysis(factor, pf) in Stata to develop factor scores for my latent variables. However, after orthogonal varimax rotation, the proportion of variance accounted for by the factors is greater than 1.00 (100%).
Is this problematic? I think this is happening because I do not specify the option "normalize." Normalize places an equal weight on all rows of the matrix to be rotated--maybe I should have done this? However, I have some indicator variables that have high uniqueness and the normalize option would weight these items equally with other items that had lower uniqueness, which seems like the wrong move. Output is included below:
factormat r, n(140) mineigen(1) sds(stdev) means(mean) factors(1)
(obs=140)
Factor analysis/correlation Number of obs = 140
Method: principal factors Retained factors = 1
Rotation: (unrotated) Number of params = 3
--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 1.67735 1.74060 1.1655 1.1655
Factor2 | -0.06324 0.11172 -0.0439 1.1216
Factor3 | -0.17497 . -0.1216 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(3) = 157.62 Prob>chi2 = 0.0000
Factor loadings (pattern matrix) and unique variances
---------------------------------------
Variable | Factor1 | Uniqueness
-------------+----------+--------------
Q3 | 0.5942 | 0.6469
Q5 | 0.8293 | 0.3123
Q7 | 0.7979 | 0.3634
---------------------------------------
.
. do "/var/folders/kx/2rhtmrz11ml9xqnpxzcw50h80000gn/T//SD01864.000000"
. rotate
Factor analysis/correlation Number of obs = 140
Method: principal factors Retained factors = 1
Rotation: orthogonal varimax (Kaiser off) Number of params = 3
--------------------------------------------------------------------------
Factor | Variance Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 1.67735 . 1.1655 1.1655
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(3) = 157.62 Prob>chi2 = 0.0000
Rotated factor loadings (pattern matrix) and unique variances
---------------------------------------
Variable | Factor1 | Uniqueness
-------------+----------+--------------
Q3 | 0.5942 | 0.6469
Q5 | 0.8293 | 0.3123
Q7 | 0.7979 | 0.3634
---------------------------------------
Factor rotation matrix
-----------------------
| Factor1
-------------+---------
Factor1 | 1.0000
-----------------------
. predict QUICKTREATX
(regression scoring assumed)
Scoring coefficients (method = regression; based on varimax rotated factors)
------------------------
Variable | Factor1
-------------+----------
Q3 | 0.17032
Q5 | 0.46105
Q7 | 0.37630
------------------------
. label variable QUICKTREATX "standardized Factor score of Q3, Q5, Q7 - getting treatment quickly"
. summarize QUICKTREATX
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
QUICKTREATX | 140 .0230575 .8292956 -1.990456 1.034425
. alpha Q3 Q5 Q7, std item detail
Test scale = mean(standardized items)
average
item-test item-rest interitem
Item | Obs Sign correlation correlation correlation alpha
-------------+-----------------------------------------------------------------
Q3 | 232 + 0.7790 0.3485 0.6558 0.7921
Q5 | 371 + 0.8965 0.6316 0.3096 0.4728
Q7 | 637 + 0.9236 0.5573 0.4190 0.5905
-------------+-----------------------------------------------------------------
Test scale | 0.4964 0.7473
-------------------------------------------------------------------------------
Interitem correlations (obs=pairwise, see below)
Q3 Q5 Q7
Q3 1.0000
Q5 0.4190 1.0000
Q7 0.3096 0.6558 1.0000
Pairwise number of observations
Q3 Q5 Q7
Q3 232
Q5 160 371
Q7 193 304 637
.
end of do-file
This also happens in the Stata example provided on see p. 15 (use link below).
https://www.stata.com/manuals/mvfact...estimation.pdf
