René Mayer mayer at psychologie.tu-dresden.de
Fri Sep 9 12:50:07 CEST 2011

```thanks for explaining Duncan and Ted,
Indeed, I did compare my results from a textbook
and noticed that I consitenly get flipped signs and biplots.
regards
René

Zitat von ted.harding at wlandres.net:

> The point is that a principal component vector is a solution,
> say V, of a matrix equation A%*%V = L*V where A is the matrix
> and L is a scalar..
>
> Since this equation can be written A%*%(-V) = L*(-V), the
> result is indeterminate with respect to its sign. If V is a
> solution, so is (-V), and vice versa. It is not a case of
> "direction reversal", since neither L nor (-L) has a primary
> role -- they are equivalent, and you can adopt either one.
> Just make it clear which one you adopt -- or someone else
> might think that they disagree!
>
> You originally wrote "I get the right principal components,
> but with the wrong sign in front." You did not get "the wrong
> sign" -- both are correct! It may be that you are comparing
> your result from R with the result from some other software
> (or from a textbook, or whatever) which produced the equivalent
> result but with the opposite sign. Again, both are correct.
>
> If, for some reason, you do not like the sign of the result
> you get, then change its sign.
>
> Hoping this helps,
> Ted.
>
> On 09-Sep-11 09:42:49, René Mayer wrote:
>> thanks for pointing out Paul,
>> but the thing which is annoying me in the first place IS this
>> direction reversal.
>> this makes no sense for me
>> why could this be?
>>
>> Zitat von "Paul Hiemstra" <paul.hiemstra at knmi.nl>:
>>
>>>  Hi,
>>>
>>> If all the signs are switched the PC's are still the same. The
>>> principal
>>> vectors are along the same axis, only in a different direction. So
>>> there
>>> is no problem :).
>>>
>>> hope this helps,
>>> Paul
>>>
>>> On 09/09/2011 09:01 AM, René Mayer wrote:
>>>> Dear All,
>>>>
>>>> when I'm running a PCA with
>>>>
>>>> prcomp(USArrests, scale = TRUE)
>>>>
>>>> I get the right principal components, but with the wrong sign infront
>>>>
>>>> Rotation:
>>>> PC1 PC2 PC3 PC4
>>>> Murder 0.5358995 -0.4181809 0.3412327 0.64922780
>>>> Assault 0.5831836 -0.1879856 0.2681484 -0.74340748
>>>> UrbanPop 0.2781909 0.8728062 0.3780158 0.13387773
>>>> Rape 0.5434321 0.1673186 -0.8177779 0.08902432
>>>>
>>>>
>>>> PC1 PC2 PC3 PC4
>>>> Murder -0.5358995 0.4181809 -0.3412327 0.64922780
>>>> Assault -0.5831836 0.1879856 -0.2681484 -0.74340748
>>>> UrbanPop -0.2781909 -0.8728062 -0.3780158 0.13387773
>>>> Rape -0.5434321 -0.1673186 0.8177779 0.08902432
>>>>
>>>> what is happening here?
>>>> any ideas?
>>>>
>>>> thanks,
>>>> René
>>>>
>>> --
>>> Paul Hiemstra, Ph.D.
>>> Global Climate Division
>>> Royal Netherlands Meteorological Institute (KNMI)
>>> Wilhelminalaan 10 | 3732 GK | De Bilt | Kamer B 3.39
>>> P.O. Box 201 | 3730 AE | De Bilt
>>> tel: +31 30 2206 494
>>>
>>> http://intamap.geo.uu.nl/~paul