Factor rotation matrix - Interpretation

[Sabrina Nasir]

Hi everyone,

I am running a factor analysis with principal-component factors in STATA and am trying to interpret the results.

I understand how to read the variance and factor loadings to see if it is a 2, 3, 4 factor solution and which variables are best explained by what factor.

However, I am having trouble interpreting the Factor rotation matrix. I have been reading all morning about this but it seems glossed over on most of the sites I read that interpret factor results (i.e. UCLA Idre site).

Do any folks out there know more about how to interpret the factor rotation matrix? I've pasted my output just in case it is helpful to have something specific to refer to. Thank you very much!




Factor analysis/correlation Number of obs = 1030
Method: principal-component factors Retained factors = 4
Rotation: orthogonal varimax (Kaiser off) Number of params = 30

--------------------------------------------------------------------------
Factor | Variance Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 1.49873 0.14717 0.1665 0.1665
Factor2 | 1.35155 0.12471 0.1502 0.3167
Factor3 | 1.22684 0.12318 0.1363 0.4530
Factor4 | 1.10366 . 0.1226 0.5756
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(36) = 448.14 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

---------------------------------------------------------------------
Variable | Factor1 Factor2 Factor3 Factor4 | Uniqueness
-------------+----------------------------------------+--------------
neihomo | -0.0099 0.7483 0.0478 0.2321 | 0.3838
neirace | 0.5688 0.0836 0.0512 0.4469 | 0.4671
neidrink | -0.0518 0.1385 0.7631 0.0847 | 0.3886
neiimmig | 0.5848 -0.1546 0.0102 0.0994 | 0.6242
neiaids | 0.0915 0.7338 0.0776 -0.0926 | 0.4386
neidrug | 0.0744 -0.0465 0.7776 -0.1476 | 0.3658
neirelig | 0.5108 0.4377 -0.1511 -0.2914 | 0.4398
neiunmar | 0.7448 0.0841 0.0468 0.0022 | 0.4361
neilang | 0.0306 0.0482 -0.0614 0.8472 | 0.2752
---------------------------------------------------------------------

Factor rotation matrix

--------------------------------------------------
| Factor1 Factor2 Factor3 Factor4
-------------+------------------------------------
Factor1 | 0.7653 0.5882 0.1158 0.2343
Factor2 | -0.3084 0.3637 0.8217 -0.3120
Factor3 | 0.3313 -0.6786 0.5563 0.3467
Factor4 | -0.4576 0.2473 0.0427 0.8530
--------------------------------------------------

[Phil Bromiley]

Since you didn't get a quick answer, let me try to help out. I'm not an expert in exploratory factor analysis.

Exploratory factor analysis is inherently unidentified meaning there is an infinite set of factor specifications (rotated factor loadings) that equally well fit the data. The factor rotation rules are rules or criteria to select which of those specifications you want to discuss. In my experience, folks usually interpret the rotated factor loadings mostly. Check in you discipline whether folks say much about the rotation matrix.

[Mona Faris]

I am also trying to work this out and cannot find anything online about the meaning of the output table 'Factor rotation matrix'. Is it showing the correlation between the two factors?