normal score transform

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
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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.

==============================================================================

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 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
--

--------------------------------------------------------------
----------------

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.

==============================================================
================

--

http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To:

r-help-request at stat.math.ethz.ch

_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._.
_._._._._._._.

_._

--------------------------------------------------------------
----------------

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
on 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.

==============================================================
================

--

http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
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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.

==============================================================================

--