Variance explained exceeds zero in -factor-?

[David Speed]

Hello,

My colleague and I am working on a paper that investigates patriotism in immigrants. We are looking to combine several items together that have been combined previously, but we wanted to ensure that they loaded similarly in factor analysis.

. factor revans_10-revans_80
(obs=25,943)

Factor analysis/correlation                      Number of obs    =     25,943
    Method: principal factors                    Retained factors =          2
    Rotation: (unrotated)                        Number of params =          9

    --------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference        Proportion   Cumulative
    -------------+------------------------------------------------------------
        Factor1  |      1.93894      1.93527            1.1937       1.1937
        Factor2  |      0.00367      0.03434            0.0023       1.1960
        Factor3  |     -0.03067      0.07261           -0.0189       1.1771
        Factor4  |     -0.10328      0.08107           -0.0636       1.1135
        Factor5  |     -0.18435            .           -0.1135       1.0000
    --------------------------------------------------------------------------
    LR test: independent vs. saturated:  chi2(10) = 3.3e+04 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

    -------------------------------------------------
        Variable |  Factor1   Factor2 |   Uniqueness 
    -------------+--------------------+--------------
       revans_10 |   0.7571   -0.0279 |      0.4260  
       revans_30 |   0.4463    0.0020 |      0.8008  
       revans_50 |   0.7876   -0.0174 |      0.3794  
       revans_60 |   0.6168    0.0263 |      0.6189  
       revans_80 |   0.4072    0.0435 |      0.8323  
    -------------------------------------------------

As you can see, the "Proportion" value, which measures proportion of variance explained, exceeds 1.00 (which I thought was impossible).

Why did this happen, how can this value be interpreted?

[William Lisowski]

The documentation for the factor command found in the Stata Multivariate Statistics Reference Manual PDF included with your Stata installation and accessible from the Stata Help menu discusses this briefly in examples 1 and 2. Perhaps another member will explain it in more detail.

[David Speed]

Hi William,

Thanks for your prompt response, and sorry, I slightly miscommunicated my issue (I was heading for home at the time):

Why do the Eigenvalues become negative and consequently and does that make the interpretation of the proportion explained meaningless?

Cheers,

David.

[William Lisowski]

Here is a Stata FAQ discussing that issue.

https://www.stata.com/support/faqs/s...e-eigenvalues/