Factor loadings were all negative! (paf + oblimin)

[Chong-2]

I performed a principal axis factoring with oblimin rotation on a measure
with 11 items rated on a 7-point likert scale (0-6).
- Pattern matrix: two factors (as speculated)
- All factor loadings for Factor 2 were negative (pattern & structure matrix)
- Factor correlation: -0.739

I understand that a negative factor loading indicates that scores on that
item variable are inversely related to the scores of the factor.

How do I interpret the case when all factor loadings are negative??

I computed the composite score for factor 1 and 2 and examined their
bivariate correlation. r was 0.729 i.e. they were not inversely related.
This was consistent with AMOS standardised estimate of 0.82.

The above scenario did not happen if I opted for maximum likelihood with
oblimin rotation. The largest factor loadings for factor 1 was 1.079 in the
pattern matrix however. The structure matrix looked normal albeit with heavy
cross loadings. The factor correlation was 0.743 in this case.

Can someone pls educate me on what's happening?

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[David Hitchin]

Quoting chong <[hidden email]>:
> I understand that a negative factor loading indicates that scores on
> that item variable are inversely related to the scores of the factor.

The "direction" of a factor is not defined by the mathematics of the
extraction process, although some programs tidy up output by making the
largest loading or the largest number of loadings positive.

You might extract a factor with all positive loadings that corresponds
to "optimism" or the same thing could be presented as "pessimism" with
negative loadings. The signs are different but the interpretation would
be the same.

David Hitchin

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