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st: RE: Negative eigen values in factor, pf command?


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Negative eigen values in factor, pf command?
Date   Tue, 28 Apr 2009 15:40:48 +0100

This is normal. The key point is not that some of the eigenvalues are
negative, but that some of them are near zero. It may well be that if
the data were as you would like them to be that all the eigenvalues
could come out positive, but Stata is not going to lie to you. 

With just this number of variables, you would be well advised to set
aside factor and principal component analysis and look first at the
results of -graph matrix- and -correlate-, and screen out variables not
really related to any of the others, as they won't add worthwhile
flavour to the multivariate analysis. 

Nick 
n.j.cox@durham.ac.uk 

Jean-Gael Collomb

I am having trouble interpreting the results of a principle factor  
analysis I am conducting. The command and results are shown below.  
Several things puzzle me about the results table. Why are some  
eigenvalues < 0? Why are some of the proportions <0? Why are most of  
the cumulative values >1. I suspect the answer to one of these  
questions applies to all three. My understanding of factor analysis is  
that I would interpret the results table as retaining all factor with  
an eigen value >1 because they explain more of the variance than the  
original variable and that the set of retained factors explains the  
"cumulative" percent of the variance in the dataset. I thought that  
all the variance (100%) would be explained by all the factors, but  
that a subset of those factors would therefor only explain less than  
100%. In my case, I would retain factor 1 and by itself it would  
explain 133% of the variance, which does not make much sense to me.  
When I run a principle component analysis on the same data, I get a  
two component solution explaining 52% of the variance. That result  
table is more similar to what I have seen elsewhere, but I am puzzled  
as to why there seems to be such a difference between procedures on  
the same data (and the single factor solution of the pfa also makes  
more theoretical sense as this point)

I am not a statistician but would like to understand in general terms  
what is happening with the factor command and how to interpret its  
results. I have spoken with two statisticians I work with and they are  
surprised to see eigen values<0 and cumulative values >1, but they are  
not STATA users. Maybe we are misinterpreting the results or maybe I  
am doing something wrong with the software. If the results were not  
valid, I would have expected STATA to give me some sort of error  
message rather than an aberrant result.

Thank you very much for your help.

FACTOR ANALYSIS WITH PRINCIPLE FACTOR EXTRACTION

factor att2r att3r att9r att20r att22 att23, mineigen(1)

   
------------------------------------------------------------------------
--
          Factor  |   Eigenvalue   Difference        Proportion    
Cumulative
     ------------- 
+------------------------------------------------------------
         Factor1  |      1.34388      1.21292            1.3335        
1.3335
         Factor2  |      0.13096      0.14728            0.1300        
1.4635
         Factor3  |     -0.01632      0.04961           -0.0162        
1.4473
         Factor4  |     -0.06593      0.09743           -0.0654        
1.3819
         Factor5  |     -0.16336      0.05812           -0.1621        
1.2198
         Factor6  |     -0.22148            .           -0.2198        
1.0000
      
------------------------------------------------------------------------
--
     LR test: independent vs. saturated:  chi2(15) =  304.22 Prob>chi2  
= 0.0000

PRINCIPLE COMPONENT ANALYSIS

quietly pca att2r att3r att9r att20r att22 att23, mineigen(1)
rotate
   
------------------------------------------------------------------------
--
        Component |     Variance   Difference         Proportion    
Cumulative
     ------------- 
+------------------------------------------------------------
            Comp1 |      2.05242       .95265             0.3421        
0.3421
            Comp2 |      1.09977            .             0.1833        
0.5254
      
------------------------------------------------------------------------
--


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