Index sub-dimension negatively correlated

[Frank Kumah]

Hello Everybody!

I constructed a composite Index via pca containing 3 sub-dimensions.
However, checking the correlation matrix, one of the dimensions is negatively correlated with the overall index.
Does anyone know, if that is possible or what might went wrong?

             | Index_~l Availa~l Usage_~l Penetr~l
-------------+------------------------------------
Index_Normal |   1.0000
Availabili~l |   0.8488   1.0000
Usage_Normal |   0.8232   0.4503   1.0000
Penetratio~l |  -0.2810  -0.1218  -0.0372   1.0000

Thanks in advanced!

[Hemanshu Kumar]

That's perfectly possible, I see nothing wrong. The original variables may be positively or negatively correlated with each other, and consequently the index (which is a weighted average of the original variables) can be positively or negatively correlated with any of them.

[Maarten Buis]

However, the correlations are clearly lower on your negative correlation subindex. Depending on how you view your index, that could indicate that it does not belong in your overall index.