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st: Negative eigen values in factor, pf command?


From   Jean-Gael Collomb <jg@ufl.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Negative eigen values in factor, pf command?
Date   Tue, 28 Apr 2009 10:24:17 -0400

Dear Statlistserv members,

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 --------------------------------------------------------------------------

Jean-Gael "JG" Collomb
PhD candidate
School of Natural Resources and Environment / School of Forest Resources and Conservation
University of Florida
jgcollomb@gmail.com
jg@ufl.edu




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