[R] normal score transform

kjetil halvorsen kjetilh at umsanet.edu.bo
Mon Sep 16 17:14:14 CEST 2002 


Ulrich Leopold wrote:
> 
> When I interpolate my data values by kriging (geostatsitical interpolation
> method) I get for each estimated value a corresponding estimation variance.
> The interpolation is carried out in 2d space. I would like to map not only
> the estimated expected value but also the uncertainty and confidence
> intervals (e.g. 95%) for this method. 

So backtransform only the confidence limits and forget about the
variance.

Kjetil Halvorsen


Therefore I need to backtransform the
> so called estimation variance. See my prob?
> 
> But thanks very much so far.
> 
> Ulrich
> 
> Liaw, Andy wrote:
> > I don't know of a good way to do this.  If the transformation has a nice
> > form, then one can use the good old delta method (Taylor expansion).  MASS
> > has coverage and code, in the context of parameter estimation.  However I
> > don't think that can be applied to the normal scores transformation (at
> > least I don't see how).
> >
> > Excuse me for being nosy, but why would you need to do this?
> >
> > Andy
> >
> >
> >>-----Original Message-----
> >>From: Ulrich Leopold [mailto:uleopold at science.uva.nl]
> >>Sent: Friday, September 13, 2002 8:24 AM
> >>To: r-help at stat.math.ethz.ch
> >>Subject: Re: [R] normal score transform
> >>
> >>
> >>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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> >>>>==============================================================
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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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> >>>
> >>>
> >>
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> >>
> >>>Notice: This e-mail message, together with any attachments,
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> >>Station, New Jersey, USA) that may be confidential,
> >>proprietary copyrighted and/or legally privileged, and is
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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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> >
> > ------------------------------------------------------------------------------
> > Notice:  This e-mail message, together with any attachments, contains information of Merck & Co., Inc. (Whitehouse Station, New Jersey, USA) that may be confidential, proprietary copyrighted and/or legally privileged, and is intended solely for the use of the individual or entity named in this message.  If you are not the intended recipient, and have received this message in error, please immediately return this by e-mail and then delete it.
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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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