On 8/19/2009 10:14 AM, Petr PIKAL wrote:
Duncan Murdoch <murd...@stats.uwo.ca> napsal dne 19.08.2009 15:25:00:
On 19/08/2009 9:02 AM, Petr PIKAL wrote:
> Thank you
>
> Duncan Murdoch <murd...@stats.uwo.ca> napsal dne 19.08.2009 14:49:52:
>
>> On 19/08/2009 8:31 AM, Petr PIKAL wrote:
>>> Dear all
>>>
>
> <snip>
>
>> I would say the answer depends on the meaning of the variables. In
the
>> unusual case that they are measured in dimensionless units, it might
>> make sense not to scale. But if you are using arbitrary units of
>> measurement, do you want your answer to depend on them? For example,
if
>
>> you change from Kg to mg, the numbers will become much larger, the
>> variable will contribute much more variance, and it will become a
more
>> important part of the largest principal component. Is that sensible?
>
> Basically variables are in percentages (all between 0 and 6%) except
dus
> which is present or not present (for the purpose of prcomp transformed
to
> 0/1 by as.numeric:). The only variable which is not such is iep which
is
> basically in range 5-8. So ranges of all variables are quite similar.
>
> What surprises me is that biplot without scaling I can interpret by
used
> variables while biplot with scaling is totally different and those two
> pictures does not match at all. This is what surprised me as I would
> expected just a small difference between results from those two
settings
> as all numbers are quite comparable and does not differ much.
If you look at the standard deviations in the two cases, I think you can
see why this happens:
Scaled:
Standard deviations:
[1] 1.3335175 1.2311551 1.0583667 0.7258295 0.2429397
Not Scaled:
Standard deviations:
[1] 1.0030048 0.8400923 0.5679976 0.3845088 0.1531582
The first two sds are close, so small changes to the data will affect
I see. But I would expect that changes to data made by scaling would not
change it in such a way that unscaled and scaled results are completely
different.
their direction a lot. Your biplots look at the 2nd and 3rd components.
Yes because grouping in 2nd and 3rd component biplot can be easily
explained by values of some variables (without scaling).
I must admit that I do not use prcomp much often and usually scaling can
give me "explainable" result, especially if I use it to "variable
reduction". Therefore I am reluctant to use it in this case.
when I try "more standard" way
fit<-lm(iep~sio2+al2o3+p2o5+as.numeric(dus), data=rglp)
summary(fit)
Call:
lm(formula = iep ~ sio2 + al2o3 + p2o5 + as.numeric(dus), data = rglp)
Residuals:
Min 1Q Median 3Q Max
-0.41751 -0.15568 -0.03613 0.20124 0.43046
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.12085 0.62257 11.438 8.24e-08 ***
sio2 -0.67250 0.20953 -3.210 0.007498 **
al2o3 0.40534 0.08641 4.691 0.000522 ***
p2o5 -0.76909 0.11103 -6.927 1.59e-05 ***
as.numeric(dus) -0.64020 0.18101 -3.537 0.004094 **
I get quite plausible result which can be interpreted without problems.
My data is a result of designed experiment (more or less :) and therefore
all variables are significant. Is that the reason why scaling may bye
inappropriate in this case?
No, I think it's just that the cloud of points is approximately
spherical in the first 2 or 3 principal components, so the principal
component directions are somewhat arbitrary. You just got lucky that
the 2nd and 3rd components are interpretable: I wouldn't put too much
faith in being able to repeat that if you went out and collected a new
set of data using the same design.
Duncan Murdoch
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