[ncl-talk] How to keep PC orthogonal in REOF？

Dennis Shea shea at ucar.edu
Tue Sep 22 14:24:35 MDT 2020

NCL offers only 'Kaiser-Varimax' rotation. To my knowledge, once any
rotation method is applied to the subset there is a loss of orthogonality
in either the spatial mode or the PCs

From: *https://en.wikipedia.org/wiki/Factor_analysis#Rotation_methods*
<https://en.wikipedia.org/wiki/Factor_analysis#Rotation_methods>

"Varimax rotation <https://en.wikipedia.org/wiki/Varimax_rotation> is an
orthogonal rotation of the factor axes to maximize the variance of the
squared loadings of a factor (column) on all the variables (rows) in a
factor matrix, which has the effect of differentiating the original
variables by extracted factor. Each factor will tend to have either large
results which make it as easy as possible to identify each variable with a
single factor. This is the most common rotation option. *However, the
orthogonality (i.e., independence) of factors is often an unrealistic
assumption. *Oblique rotations are inclusive of orthogonal rotation, and
for that reason, oblique rotations are a preferred method. Allowing for
factors that are correlated with one another is especially applicable in
psychometric research, since attitudes, opinions, and intellectual
abilities tend to be correlated, and since it would be unrealistic in many
situations to assume otherwise"

I am sure that the *R* <https://www.r-project.org/> package offers multiple
methods for performing rotation.

Good Luck

On Sat, Sep 19, 2020 at 6:35 AM 杨显轲 via ncl-talk <ncl-talk at mailman.ucar.edu>
wrote:

> Hello ncl-users,
>
>    I would like to ask whether it is possible to keep PC orthogonal in
> REOF. As we known, both the spatial mode and the PC remain orthogonal in
> EOF. When using *eofunc_varimax_Wrap* in NCL for monthly Equatorial
> central and eastern pacific SST, the spatial mode and PC are not
> orthogonal, and the correlation coefficient of PC1 and PC2 can reach 0.9.
>
>    I want to keep PC orthogonal in Reof, and the spatial modes can be
> non-orthogonal, can this be achieved in NCL?
>
>
> Thanks! All the best!
>
> Xianke Yang
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