[R] normal score transform

[Liaw, Andy]

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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> -- 
> __________________________________________________
> 
> 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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