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st: Re: Oblique Rotation returns no correlation between factors?
From
"Joseph Coveney" <[email protected]>
To
<[email protected]>
Subject
st: Re: Oblique Rotation returns no correlation between factors?
Date
Wed, 13 Mar 2013 22:52:08 +0900
Ivan Kuznetsov wrote:
I doing some research using factor analysis (principle axis factoring)
using categorical data. I have used polychoric correlations to correct for
the categorical variables problem. But now when I try to rotate obliquely
using "oblimin" and use "estat common" to find the correlation between
factors, Stata returns that there is 0 correlation, which is very strange.
I have tried different extraction methods and different rotation methods
and yet I still find no correlation. Any suggestions?
--------------------------------------------------------------------------------
It seems to work for me, at least in the toy example below. Even if you set the
correlation matrix such that the factors are uncorrelated (change the 0.3's
below to zeroes) there is still a small positive value reported by -estat
common-. That is, there doesn't appear to be any set-to-zero behavior if the
correlation estimate falls below some threshold. Negative correlations (change
the sign of the 0.3's below) are also faithfully reported.
Is there something unusual about your dataset, for example, heavy skewness?
(-polychoric- is from SSC.)
Joseph Coveney
. clear *
. set more off
. set seed `=date("2013-03-12", "YMD")'
. tempname Correlation
. matrix define `Correlation' = (1, 0.3 \ 0.3, 1) # (1, 0.5, 0.5 \ ///
> 0.5, 1, 0.5 \ 0.5, 0.5, 1)
. drawnorm M1 M2 M3 M4 M5 M6, double corr(`Correlation') n(200)
(obs 200)
.
. *
. * Original continuous values
. *
. factor M?, pf factors(2)
(obs=200)
Factor analysis/correlation Number of obs = 200
Method: principal factors Retained factors = 2
Rotation: (unrotated) Number of params = 11
--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 1.97500 1.31624 0.8824 0.8824
Factor2 | 0.65876 0.54130 0.2943 1.1767
Factor3 | 0.11746 0.10758 0.0525 1.2292
Factor4 | 0.00988 0.25203 0.0044 1.2336
Factor5 | -0.24215 0.03858 -0.1082 1.1254
Factor6 | -0.28074 . -0.1254 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(15) = 308.16 Prob>chi2 = 0.0000
Factor loadings (pattern matrix) and unique variances
-------------------------------------------------
Variable | Factor1 Factor2 | Uniqueness
-------------+--------------------+--------------
M1 | 0.6467 -0.2908 | 0.4972
M2 | 0.5735 -0.2938 | 0.5848
M3 | 0.5516 -0.3699 | 0.5589
M4 | 0.6091 0.3126 | 0.5312
M5 | 0.4666 0.3695 | 0.6457
M6 | 0.5786 0.3417 | 0.5484
-------------------------------------------------
. rotate , oblique oblimin
Factor analysis/correlation Number of obs = 200
Method: principal factors Retained factors = 2
Rotation: oblique oblimin (Kaiser off) Number of params = 11
--------------------------------------------------------------------------
Factor | Variance Proportion Rotated factors are correlated
-------------+------------------------------------------------------------
Factor1 | 1.66759 0.7451
Factor2 | 1.60701 0.7180
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(15) = 308.16 Prob>chi2 = 0.0000
Rotated factor loadings (pattern matrix) and unique variances
-------------------------------------------------
Variable | Factor1 Factor2 | Uniqueness
-------------+--------------------+--------------
M1 | 0.6743 0.0664 | 0.4972
M2 | 0.6330 0.0228 | 0.5848
M3 | 0.6936 -0.0655 | 0.5589
M4 | 0.0650 0.6506 | 0.5312
M5 | -0.0767 0.6288 | 0.6457
M6 | 0.0183 0.6629 | 0.5484
-------------------------------------------------
Factor rotation matrix
--------------------------------
| Factor1 Factor2
-------------+------------------
Factor1 | 0.8755 0.8488
Factor2 | -0.4833 0.5288
--------------------------------
. estat common
Correlation matrix of the oblimin(0) rotated common factors
----------------------------------
Factors | Factor1 Factor2
-------------+--------------------
Factor1 | 1
Factor2 | .4875 1
----------------------------------
.
. *
. * Discretized values
. *
. foreach var of varlist M? {
2. generate byte C`var' = 0
3. forvalues cut = 0.25(0.25)0.75 {
4. quietly replace C`var' = C`var' + 1 if normal(`var') > `cut'
5. }
6. }
.
. polychoric C*
Polychoric correlation matrix
CM1 CM2 CM3 CM4 CM5 CM6
CM1 1
CM2 .48408458 1
CM3 .47677285 .46502406 1
CM4 .40142969 .23287674 .14154395 1
CM5 .12098617 .22584329 .08295264 .41714915 1
CM6 .25471765 .07127948 .20458655 .49077708 .43353546 1
. factormat r(R), n(`r(N)') pf factors(2)
(obs=200)
Factor analysis/correlation Number of obs = 200
Method: principal factors Retained factors = 2
Rotation: (unrotated) Number of params = 11
--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 1.87721 1.16953 0.8843 0.8843
Factor2 | 0.70768 0.65029 0.3334 1.2177
Factor3 | 0.05739 0.06274 0.0270 1.2447
Factor4 | -0.00535 0.23165 -0.0025 1.2422
Factor5 | -0.23700 0.04016 -0.1116 1.1306
Factor6 | -0.27716 . -0.1306 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(15) = 289.74 Prob>chi2 = 0.0000
Factor loadings (pattern matrix) and unique variances
-------------------------------------------------
Variable | Factor1 Factor2 | Uniqueness
-------------+--------------------+--------------
CM1 | 0.6511 -0.2714 | 0.5024
CM2 | 0.5550 -0.3507 | 0.5690
CM3 | 0.5182 -0.3685 | 0.5956
CM4 | 0.6151 0.3051 | 0.5286
CM5 | 0.4628 0.3641 | 0.6533
CM6 | 0.5332 0.3867 | 0.5662
-------------------------------------------------
. rotate , oblique oblimin
Factor analysis/correlation Number of obs = 200
Method: principal factors Retained factors = 2
Rotation: oblique oblimin (Kaiser off) Number of params = 11
--------------------------------------------------------------------------
Factor | Variance Proportion Rotated factors are correlated
-------------+------------------------------------------------------------
Factor1 | 1.57736 0.7431
Factor2 | 1.51799 0.7151
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(15) = 289.74 Prob>chi2 = 0.0000
Rotated factor loadings (pattern matrix) and unique variances
-------------------------------------------------
Variable | Factor1 Factor2 | Uniqueness
-------------+--------------------+--------------
CM1 | 0.6524 0.1063 | 0.5024
CM2 | 0.6666 -0.0239 | 0.5690
CM3 | 0.6604 -0.0615 | 0.5956
CM4 | 0.0967 0.6388 | 0.5286
CM5 | -0.0518 0.6096 | 0.6533
CM6 | -0.0294 0.6710 | 0.5662
-------------------------------------------------
Factor rotation matrix
--------------------------------
| Factor1 Factor2
-------------+------------------
Factor1 | 0.8623 0.8324
Factor2 | -0.5063 0.5542
--------------------------------
. estat common
Correlation matrix of the oblimin(0) rotated common factors
----------------------------------
Factors | Factor1 Factor2
-------------+--------------------
Factor1 | 1
Factor2 | .4372 1
----------------------------------
.
. exit
end of do-file
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