[R] normal score transform

Ulrich Leopold uleopold at science.uva.nl
Fri Sep 13 14:24:29 CEST 2002 

But is it also possible to transform the prediction VARIANCE back to non 
normalized variances? I do not have these variances before hand. Or would be 
a solution to use the standard deviation as this will be within the range of 
the predictions? I'm not quite sure...

Ulrich

Liaw, Andy wrote:
> I suppose you can use approx() to linearly interpolate.  For example:
> 
> 
>>x <- rnorm(10, mean=100, sd=10)
>>x
> 
>  [1]  92.46931  96.71141 103.82640 110.57520  88.30825 106.35602  90.60754
>  [8] 102.29406  94.19188 107.28770
> 
>>z <- qnorm(ppoints(x))
>>z
> 
>  [1] -1.5466353 -1.0004905 -0.6554235 -0.3754618 -0.1225808  0.1225808
>  [7]  0.3754618  0.6554235  1.0004905  1.5466353
> 
>>z.test <- rnorm(10)  ## pretend these are the "predicted values"
>>z.test
> 
>  [1]  1.1733989  1.3471282 -0.2409461  0.6951916 -0.6365362 -1.0181946
>  [7] -0.5347734  2.2335172  0.4747204  0.4917223
> 
>>x.test <- approx(z, x, ztest)$y
>>x.test
> 
>  [1] 100.35171  98.74701  94.90596 107.39995  98.42442  94.84765  91.54209
>  [8] 106.87274        NA 103.25218
> 
> Note that approx() by default does not extrapolate (thus the NA), and the
> alternative (rule=2) probably isn't appropriate for this application.
> 
> HTH,
> Andy
> 
> 
>>-----Original Message-----
>>From: Ulrich Leopold [mailto:uleopold at science.uva.nl]
>>Sent: Friday, September 13, 2002 4:10 AM
>>To: r-help at stat.math.ethz.ch
>>Subject: Re: [R] normal score transform
>>
>>
>>How would I do a backtransform of predicted values (derived 
>>from the given
>>data) AND the variance?
>>
>>Ulrich
>>
>>Liaw, Andy wrote:
>> > The "normal scores" are just ranks of the data mapped onto 
>>the normal CDF,
>> > so something like:
>> >
>> > qnorm((rank(x) - 0.375)/(sum(!is.na(x)) + .25))
>> >
>> > should do what you want.  Another alternative (as 
>>calculated in qqnorm) is
>> >
>> > qnorm(ppoints(x))
>> >
>> > Andy
>> >
>> >
>> >>-----Original Message-----
>> >>From: Ulrich Leopold [mailto:uleopold at science.uva.nl]
>> >>Sent: Thursday, September 12, 2002 12:59 PM
>> >>To: r-help at stat.math.ethz.ch
>> >>Subject: [R] normal score transform
>> >>
>> >>
>> >>Dear list,
>> >>
>> >>could someone point me to the normal score transform and it's
>> >>use in R?
>> >>
>> >>I would like to transform my data with normal score
>> >>transform, do some
>> >>geostatsitical predictions and would like to transform the
>> >>estimated values
>> >>back including the estimation variance.
>> >>
>> >>Any suggestions?
>> >>
>> >>Ulrich
>> >>--
>> >>__________________________________________________
>> >>
>> >>Ulrich Leopold MSc.
>> >>
>> >>Department of Physical Geography
>> >>Institute for Biodiversity and Ecosystem Dynamics
>> >>Faculty of Science
>> >>University of Amsterdam
>> >>Nieuwe Achtergracht 166
>> >>NL-1018WV Amsterdam
>> >>
>> >>Phone: +31-(0)20-525-7456 (7451 Secretary)
>> >>Fax:   +31-(0)20-525-7431
>> >>Email: uleopold at science.uva.nl
>> >>http://www.frw.uva.nl/soil/Welcome.html
>> >>
>> >>Check us also out at:
>> >>Netherlands Centre for Geo-ecological Research
>> >>http://www.frw.uva.nl/icg
>> >>
>> >>
>> >>
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>> >
>> >
>> > 
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>>-- 
>>__________________________________________________
>>
>>Ulrich Leopold MSc.
>>
>>Department of Physical Geography
>>Institute for Biodiversity and Ecosystem Dynamics
>>Faculty of Science
>>University of Amsterdam
>>Nieuwe Achtergracht 166
>>NL-1018WV Amsterdam
>>
>>Phone: +31-(0)20-525-7456 (7451 Secretary)
>>Fax:   +31-(0)20-525-7431
>>Email: uleopold at science.uva.nl
>>http://www.frw.uva.nl/soil/Welcome.html
>>
>>Check us also out at:
>>Netherlands Centre for Geo-ecological Research
>>http://www.frw.uva.nl/icg
>>
>>
>>
>>
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-- 
__________________________________________________

Ulrich Leopold MSc.

Department of Physical Geography
Institute for Biodiversity and Ecosystem Dynamics
Faculty of Science
University of Amsterdam
Nieuwe Achtergracht 166
NL-1018WV Amsterdam

Phone: +31-(0)20-525-7456 (7451 Secretary)
Fax:   +31-(0)20-525-7431
Email: uleopold at science.uva.nl
http://www.frw.uva.nl/soil/Welcome.html

Check us also out at:
Netherlands Centre for Geo-ecological Research
http://www.frw.uva.nl/icg



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