Negative Eigenvalues

[Andrea Marchesi]

Goodevening,

I'm using primary data to test an italian version of an anglo-saxon scale. I've got more than 300 observations, and I'm trying to replicate the study. In this study, the author said that the principal axis factor analysis is better than principal components one. I've chosen to use both, because, following the previous methodological literature, the two approaches give same results in the most of cases.
The principal components analysis gave me the following results:

Component | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Comp1 | 3.60881 2.27696 0.3007 0.3007
Comp2 | 1.33184 .0765953 0.1110 0.4117
Comp3 | 1.25525 .172022 0.1046 0.5163
Comp4 | 1.08323 .237453 0.0903 0.6066
Comp5 | .845775 .0409759 0.0705 0.6771
Comp6 | .804799 .102403 0.0671 0.7441
Comp7 | .702396 .0800809 0.0585 0.8027
Comp8 | .622315 .0771328 0.0519 0.8545
Comp9 | .545183 .0766445 0.0454 0.9000
Comp10 | .468538 .0785899 0.0390 0.9390
Comp11 | .389948 .048031 0.0325 0.9715
Comp12 | .341917 . 0.0285 1.0000

The pf analysis, instead, using the command "factor varnames, pf", gave me the following results:

--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 3.02369 2.44315 0.8962 0.8962
Factor2 | 0.58054 0.17886 0.1721 1.0683
Factor3 | 0.40168 0.20612 0.1191 1.1873
Factor4 | 0.19556 0.10389 0.0580 1.2453
Factor5 | 0.09167 0.09002 0.0272 1.2725
Factor6 | 0.00165 0.04064 0.0005 1.2730
Factor7 | -0.03898 0.06565 -0.0116 1.2614
Factor8 | -0.10463 0.03007 -0.0310 1.2304
Factor9 | -0.13470 0.02525 -0.0399 1.1905
Factor10 | -0.15995 0.05104 -0.0474 1.1431
Factor11 | -0.21099 0.06070 -0.0625 1.0805
Factor12 | -0.27170 . -0.0805 1.0000

With oblique rotation ("rotate, oblique oblimin"):

--------------------------------------------------------------------------
Factor | Variance Proportion Rotated factors are correlated
-------------+------------------------------------------------------------
Factor1 | 2.82448 0.8372
Factor2 | 2.45171 0.7267
Factor3 | 1.49117 0.4420
Factor4 | 1.40048 0.4151
Factor5 | 0.44401 0.1316
Factor6 | 0.36868 0.1093
--------------------------------------------------------------------------

As you can see, the proportion of explained variance is too high, compared with principal components analysis. Also, I can't understand why I'm obtaining negative eigenvalues. STATA doesn't say to me "Heywood Case", so I can affirm that the data aren't the main problem.
Finally, I've tried to repeat these analysis using SPSS. I know that STATA is better, but this software is simple in some cases. SPSS gave to me, for the two analysis, the same output, with the same explained variance (30%) for the first factor/component, both for principal components and principal axis analysis.
I can't understand why I'm having different results using STATA, and why I'm obtaining different results from two statistic softwares. In fact, using factor analysis for other scales in my dataset, I've found the same output using both approaches and both softwares.

Thanks to everybody could help me.

[Andrea Marchesi]

Just to let you know: I've read the FAQ page (https://www.stata.com/support/faqs/s...e-eigenvalues/), but I can't understand how can I interpret the results. I can't say that the first factor is explaining the 89% of variance, because this is not true. Also, it's difficult for me to understand why the comparation between two softwares can't give to me same results.

[Andrea Marchesi]

I hope that someone could help me, because I've to finish my thesis as soon as possible.

[Nick Cox]

There is advice on bumping at https://www.statalist.org/forums/help#adviceextras #1. In particular

Any bumping that just mentions urgency, desperation, or your need for an answer is out of order. It's not that we don't sympathise; it's just that such context doesn't make your question more interesting or easier to answer or deserve extra attention.

Why did no-one answer?

1. You're trying to replicate "a study" (no reference). It's unlikely that if you gave a reference, it would be familiar to anyone, but you make it impossible to know. . Sad fact is that even with a reference it is unlikely that anyone will read an entire paper to get the context.

2. In #1 you don't understand why you're getting negative eigenvalues, but then in #2 you cite an FAQ that explains why.

3. You say first that you get the same output from SPSS but then (seem to) say that results are different. No idea what you mean there. No results from SPSS are given.

4. The dataset you have is rather big to post here, but without it it's certain that no-one else can experiment.

5. I don't think that many people active on the list use factor analysis at all. I certainly don't.

6. I don't see why you're surprised that the fraction explained goes up if you throw away some of the PCs (if that is what you're doing). I see that fraction explained is a problematic measure if some eigenvalues are negative. This can't be a new problem, but (see #5 again) it seems that no-one knows relevant literature.

I don't know your set-up and whether you are required or expected to work on your own. In my university system you'd be expected to go back to a supervisor or advisor to discuss results or identify someone else to ask.

[William Lisowski]

To Nick's comments, let me add

7. You fail to tell us the commands you used to achieve each of your outputs, specifically the first one.

I tried several times earlier to address your questions but your presentation was too confused for me to understand what you'd done, and each time I gave up.

On further review, I see now that you have apparently confused the technique of principal components analysis (implemented in Stata by the pca command) with the technique of factor analysis using principal-component factors (implemented in Stata by the factor command with the pcf option). Your first output is from pca rather than factor, pcf and that is why your two sets of results are not comparable, while the SPSS results were.

You would have gotten this advice earlier had you reviewed the Statalist FAQ linked to from the top of the page, as well as from the Advice on Posting link on the page you used to create your post, noting especially sections 9-12 on how to best pose your question. The more you help others understand your problem, the more likely others are to be able to help you solve your problem.

I commonly see "principal component analysis" used as short for "factor analysis using principal component analysis for factor extraction", but the two are not the same. This confusion is enhanced by SPSS's apparent lack of a separate command for doing principal component analysis as other than the first step of a factor analysis, and since you are an SPSS user, that may well be the source of your confusion.

Go back to the FAQ you cite. It tells you that factor, pf can produce negative eigenvalues but factor, pcf using the principal component method does not. So output from the latter command should meet your needs.