nice point. classical statisticians are slowly eating away at how to
estimate variance structures under a marginal binary assumption using
relatively simple generalized mixed models. no, I don't know how they will
handle (if ever) the problem associated with possible underestimation of
spatial variance components after--or at the same time
as/iteratively--estimating mean components. and, of course, the focus is
typically estimation rather than prediction. regardless, the variance
component estimation question *is* approached under a marginal binary
assumption--and spatial trend in the mean or equivalent is typically the
primary part of such models. of course, with trend in the mean we face
another interesting problem--namely, that the spatial variance components
under a marginal binary assumption are a function of the mean/go to zero as
the mean goes to 0 or 1. cheers, brian
****************************************************************
Brian Gray
USGS Upper Midwest Environmental Sciences Center
575 Lester Avenue, Onalaska, WI 54650
ph 608-783-7550 ext 19, FAX 608-783-8058
[EMAIL PROTECTED]
*****************************************************************
Chaosheng Zhang
<Chaosheng.Zhang@nui To: Isobel Clark
<[EMAIL PROTECTED]>
galway.ie> cc: [EMAIL PROTECTED]
Sent by: Subject: Re: AI-GEOSTATS: Normal
distributions
ai-geostats-list@uni
l.ch
05/20/2002 04:38 AM
Please respond to
Chaosheng Zhang
Isobel,
Thanks for the reply. I feel this problem deserves more discussion.
I have found the message from: Gregoire Dubois, Date: Mon Mar 5, 2001,
Subject: AI-GEOSTATS: SUMMARY: Nscore transform & kriging of log normal
data sets (The original author couldn't be found, and s/he should be in the
list): "Most of geostatistics is "distribution free", i.e., the derivation
of the simple kriging, ordinary kriging and universal kriging equations do
not depend on a distributional assumption (contrary to what is sometimes
claimed)."
An example may be the "Indicator Kriging": It is impossible for the "0"s
and
"1"s to follow the normal distribution.
The reason why I care about this issue is that there are at least two
problems related to data transformation (in order to follow the normal
distribution):
(1) The measurement scale is reduced. The orignal ratio/interval scale may
be reduced to the lower level of ordinal, even close to nominal, which
results in loss of raw information.
(2) Artificial relationship is introduced. We know that the lognormal
distribution is widely accepted. In correlation analysis, if the
log-transformed data are used, the correlation becomes the "log-log"
relationship, not the oginal linear relationship. In bivariate regression
analysis, the original function is:
y = a x + b
However, for the log-transformed data, the function becomes:
log(y) = a log(x) + b
or y = exp (a log(x) + b)
In many cases, it is not clear if the relationship should be linear or
"log-linear". However, the artificially introduced "log-linear"
relationship
need to be proved.
The most difficult situation is that if scientifically the relationship
between x and y is linear, should the data transformation still be carried
out (just to satisfy the statistical requirement)?
Cheers,
Chaosheng
----- Original Message -----
From: "Isobel Clark" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Friday, May 17, 2002 7:39 PM
Subject: AI-GEOSTATS: Normal distributions
> Short answer is yes to everything.
>
> middle length answer is that Normality is not required
> for anything except where it is a basic assumption -
> such as in simulation. It is necessary that the
> distribution be well behaved (not skewed) and conform
> to the Central Limit Theorem.
>
> Having said that, I can't tell you where the join is
> between 'well behaved' and not. It is usually fairly
> obvious from probability plots and semi-variograms
> when things start to get hairy.
>
> Isobel Clark
> http://geoecosse.bizland.com/BYOGeostats.htm
>
>
>
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