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

 From Jean-Gael Collomb 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

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```