Folks --
	 A recent exchange between daiane and Benjamin Warr used the word
"golp" apparently to indicate a [standardized?] blow for the purpose of
driving in a measuring rod.  I do not find this word in any dictionary.
Does anyone know its origin?  Does it have anything to do with the Spanish
word "golpear", to strike a blow?
Thanks, Roger

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Hi

not sure if anyone included this reference as a response, but here is a
paper by Pierre Goovaerts and Hirotaka Saito, 2000, Geostatistical
interpolation of positively skewd and censored data in a Dioxin contaminated
site, Environ, Sci, Technol. 34, 4228-4235,

Benjamin Warr

Research Associate
Geostatistics - Environmental Science - Industrial Ecology
Centre for the Management of Environmental Resource(CMER)
INSEAD
Boulevard de Constance,
77305 Fontainebleau Cedex,
France

Tel: 33 (0)1 60 72 4456
Fax: 33 (0)1 60 74 55 64
e-mail: benjamin.warr@...


> -----Original Message-----
> From: Gregoire Dubois [mailto:gregoire.dubois@...]
> Sent: Sunday, January 07, 2001 2:36 PM
> To: Berterretche Mercedes
> Cc: ai-geostats@...
> Subject: Re: [AI-GEOSTATS: MSE to compare different methods]
>
>
> Dear Mercedes,
>
> doing k fold cross validation (taking out X % of the samples)
> will not give
> you any reliable results unless you repeat the operation
> several times. Taking
> out 15% of the samples one time only will give you an MSE
> that will depend
> strongly on the data you have removed. Has the selection of
> the 15% been made
> randomly? You may get a strong bias if the 15% of the samples
> have been taken
> in one region in particular or if you have taken out extreme
> values only. At
> this stage, I would trust more the results obtained by standard cross
> validation (leave one out method).
>
> I didn't check your previous mail but if you have few samples only,
> k-fold cross validation won't help you much.
>
> If you have many samples, then you should repeat the
> procedure at least 10
> times to be sure that the way you  have extracted the data
> has not influenced
> too much the results.
> Also, if you have a phenomenon that fluctuates at different
> scales, you may
> have removed the short scale effect by taking out only few
> samples (15% is not
> much).
>
> My suggestion is the following: it is time consuming but
> might be worth the
> effort. The idea is to take out an increasing number of
> samples (10, 20, 30,
> 40, 50, 60, ...,X%) of samples, this 10 times, and see how
> the average MSE
> evolves. You may find out that methods A & B work better than
> C & D when only
> few samples are removed and that C & D give better results
> than A & B when
> more than 40% of the samples have been removed. This would
> mean that C & D
> describe better the general trend of the  phenomenon while A
> & B are more
> sensitive to the local structures (since you have more dense data).
>
> If you don't have the time to proceed in such a way, you
> should use standard
> cross validation only and investigate the regions/samples
> where you have the
> highest errors.
>
> Just few thoughts.
>
> Gregoire
>
> "Berterretche, Mercedes" <Mercedes.Berterretche@...> wrote:
> >
> > I would like to thank Benjamin Warr for his siggestion about doing
> > difference images instead of global measures as MSE.
> >
> > I'm confused because crossvalidation MSE (taking one sample out and
> > recalculating) and validation MSE (taking 15 percent of the
> samples out and
> > recalculating) are giving me opposite results. The
> validation method would
> > allows me to compare kriging vs cokriging vs Kriging with
> an external drift
> > vs regression , but I don't know if I can trust the results
> at this point.
> >
> > Does anybody have any input about this?
> > Thanks in advance,
> > Mercedes Berterretche
> >
> > --
> > * To post a message to the list, send it to ai-geostats@...
> > * As a general service to the users, please remember to
> post a summary of
> any useful responses to your questions.
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> body. DO NOT SEND Subscribe/Unsubscribe requests to the list
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>
>
> Gregoire Dubois (Ph.D.)
> Institute of Mineralogy and Petrography
> Dept. of Earth Sciences
> University of Lausanne
> Switzerland
>
> http://www.ai-geostats.org
>
> ____________________________________________________________________
> Get free email and a permanent address at
http://www.netaddress.com/?N=1

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[Non-text portions of this message have been removed]

Hello Ai-geostats list

I am developing a sampling plan for a retrospective analysis of deciduous
forests.  We intend to use airphotos from the 1930s to develop an inventory
to compare with the current inventory.  The area within our study area that
is covered by airphotos is approximately 350,000 ha and we can't afford to
map it all, so we are looking a ways of capturing the variation in deciduous
distribution and composition using a sample or subset of the photos.  One
approach we are considering is based on the National Forest Inventory of
Canada, which recommends sampling about 1% of the study area using a 20km x
20km grid and 2km x 2km typed areas at the the grid intersections.  Other
ideas include transects, simple random, or stratified random designs.  Any
other suggestions or references would be appreciated.


Ian Parfitt
Nelson, BC


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Hi Roger,

to be honest I have never heard of a golp either adn was rather foolishly
trying to hide my technical ignorance by assuming the somewhat mediaeval
sounding "tech. speak" of Daiane. Onomatapaeically I imagined that a "golp"
was a blow as that is how these data are collected. I like golp, I suggest
that it be ISO'd and accepted as standard.

Anyway, seriously - do people agree with me that a golp is actually additive
to all intents and purposes ?

Ben


> -----Original Message-----
> From: Friedman, Roger [mailto:rdf4@...]
> Sent: Friday, June 29, 2001 2:58 PM
> To: 'ai-geostats@...'
> Subject: AI-GEOSTATS: Golp
>
>
> Folks --
>  A recent exchange between daiane and Benjamin Warr used the word
> "golp" apparently to indicate a [standardized?] blow for the
> purpose of
> driving in a measuring rod.  I do not find this word in any
> dictionary.
> Does anyone know its origin?  Does it have anything to do
> with the Spanish
> word "golpear", to strike a blow?
> Thanks, Roger
>
> --
> * To post a message to the list, send it to ai-geostats@...
> * As a general service to the users, please remember to post
> a summary of any useful responses to your questions.
> * To unsubscribe, send an email to majordomo@... with no
> subject and "unsubscribe ai-geostats" followed by "end" on
> the next line in the message body. DO NOT SEND
> Subscribe/Unsubscribe requests to the list
> * Support to the list is provided at http://www.ai-geostats.org
>


[Non-text portions of this message have been removed]

This is a summary of my questions and of the answers I collected. The issue is
the development of a geostatistical model to predict density of wildlife
population interpolating density estimates collected by mark-resight and
radiotelemetry:

My question to Ai-Geostat 28/06/01:

1) I'haven't primary variables measures, I have estimates. It was suggested me
to use a variogram model to study spatial dependence that could be different by
zero for lag=0, as of course in such a situation an exact interpolator could not
be the best solution. But how could I use such a model in a linear model of
coregionalization? My covariates are measured, not estimated.
Is it better to use my estimates as measures (so using a classic variogram = 0
for lag=0) or to discard the linear model of coregionalization, estimating my
error variance by cross-validating results?

Brian Gray  28/06/01

My only question (I'm not a cokriging expert) is regarding the potential
for measurement error:  if deer are continually on the move, then I
wonder if you might, by force, end up with a substantial positioning
error contribution to the nugget?  cheers, Brian Gray

Isobel Clark 28/06/01

You say that you primary variables are estimates. Is
there any way in which you can assess the reliability
of the estimates. For example, do you have repeated
estimates at the same locations? Or do you have
estimates very close together. In practice, the nugget
effect is a composite of all random-type errors
including inherent variation in the variable being
measured. One component of this nugget effect should
be the variance between repeated estimates at the same
location. If you can put a number to this, you can do
your geostatistics as follows:

a) model the semi-variogram as usual.
b) Subtract the 'repeatability' variance from this
nugget effect
c) Carry out the kriging using the 'reduced'
semi-variogram
d) To your estimation variances, add twice the
'repeatability variance'

In this way you will admit the original estimation
error into the final assessment of your confidence for
predictions without having to compromise your other
variables.

My question    29/06/01:

My next question: these estimates don't share the same accuracy, there are
confidence intervals narrower or larger then others. So, what the variance to
account for in the semi-variogram? An average of my estimates variance? The
largest?

Isobel Clark  30/06/01

For the 'estimates variance', the classical way to
approach this is as follows (from traditional
statistics, not geostatistics):

For each sample location, calculate your average
estimated density;
For each repeat measurement within that sample
location, calculate the difference between this
measurement and square it;
Repeat for all sample sites;
Add up all sums of squares and divide by the original
number of samples (all repeats) minus the number of
sample locations.

This is the best estimate for the 'within sample
location'  variance. This should be subtracted from
the bugget effect and twice this value added back on
to all kriging variances.

If you want to are worried about whether the 'within
sample location' variance is actually stationary over
all sample locations, you should also calculate the
variance of all the repeat measurements around the
global average for all sample locations. That is, the
ordinary statistical variance but including all of the
original estimated densities before you averaged them
by site.

A standard F ratio test between the two variances will
tell you if they are really different. See any basic
statistics book or our Practical Geostatistics 2000,
Chapter 5.



My question 28/06/01

My density estimate is obtained by 'averaging' the position of deer by
radiotelemetry, i.e., given a population in a place, I put some boundaries
on a map, and I count the fraction of positions of the radiotagged sample of
the population that are inside these boundaries. My aim is to obtain in this
way the 'average density' in that place.
Do you think this procedure could avoid the problems that deer mobility can
give to the reliability of the confidence interval?


Brian Gray 28/06/01

Your approach should work fine provided that you are interested in
averages rather than in individuals.  And, since you are working with
averages, your confidence interval should be narrower.  If you get
simultaneous locations on all deer, then you may have a different
situation than if your locations arrive over time.  In the latter
case and if you work with individuals, any increase in your relative
nugget may arise from location/positioning error

My question 28/06/01

As I never listened about positioning error contribution to the nugget, where
could I
find some references?

Brian Gray 28/06/01

The nugget may derive from measurement error, positioning error or
from small scale variation--or a combination of the three.  For
example, I work with oyster infection rates--which are a function of
oyster age.  If I measure oysters that are infinitely close to one
another, I am still not guaranteed that they will have the same
infection level.  Reason:  different ages, different life histories,
etc.  This latter issue is a small scale issue.  If I say oyster 1 is
at location y and it's really at location y + 1, then I have a
positional error.  If I measure the infection as i but its really j
then I have a measurement error.  Chiles and Delfiner 1999, as I
recall discuss these issues more.

Donald E. Myers 28/06/01

Reference on nugget effect and positioning error, see

"Geostatistics: modeling spatial uncertainty",  J.-P. Chiles and P. Delfiner, 
J. Wiley and sons


My question 28/06/01

2) the sill of my variograms are equal or larger than primary variable variance
(so, more or less twice the semivariance). It is probably because of a trend in
the density, that decreased with time. The primary variable (deer density) is
probably a second order stationary one, at least for a much larger area than my
study area, being the last surrounded by  many kilometers of deer suitable
habitat. But it behaves like non stationary in the few square kilometers of
interest and in the few years of sampling. May I ignore this problem or do I
have to incorporate the trend?

Isobel Clark 28/06/01

If you are seeing a sill, the problem is not
non-stationarity in the sense of a trend. If it is
important at all, it is more likely to be caused by a
discontinuity in the study area or a change in some
characteristic of the habitat in the area. Trend shows
as a rising  parabola, not a sill. If the cross
validation stage works, the height of the sill is not
an important factor. Remember when carrying out the
cross validation, you should be using the increased
kriging variance as described above.

My question 28/06/01

3) when I cross-validate my predictions (obtained with linear model of
coregionalization and ordinary cokriging) I obtain enough good results. But I
argue that perhaps they are even better than it could seem. Not only because of
problems of all cross-validations, but because I have to compare my predictions
not with actual measures, but with estimates. Probably the average error is
influenced by both uncertainties. Given that I know the confidence intervals of
my primary variable estimates, how could I account for them to estimate
correctly the average error of my prediction model?
my doubt: imagine I collect some estimates of a variable, and I have un
uncertainty about them, say a 95% confidence interval of 20, and I know this
uncertainty. Now I develop a kriging model to predict my variable, and I
cross-validate it. Well, even if I had a perfect model, completely precise and
accurate, I should have a MAE of 10, more or less. Do someone think this is
correct? And, given that I know the uncertainty about my estimates, is there a
way to 'correct' the MAE of my cross-validation accounting for it?

Isobel Clark 30/06/01

You need to keep your mind clear between your original
uncertainty in the estimates and the kriging error.
There really is no reason why the kriging error should
be less than your 'estimates' error. If fact, I would
be surprised if this were so. You are trying to
estimate the value at a location from other samples.
This prediction error will be in addition to yoru
sample value uncertainty and could be orders of
magnitude higher.



Thank you very much and hoping to listen you soon. All new ideas, or remarks or
criticism about what listed above will be welcome.

Daniele







[Non-text portions of this message have been removed]

Hi, Isobel,
thank you very much for your exahustive and deeply useful explanations!

Yes! I have something like a sill, that, if I understood correctly, should put
me on the safe side choosing to use ordinary cokriging.

About my first question: yes! I have repeated measures of density in each
sampling area, and this allows me to have confidence intervals. My next
question: these estimates don't share the same accuracy, there are confidence
intervals narrower or larger then others. So, what the variance to account for
in the semi-variogram? An average of my estimates variance? The largest?

About my third question: I had no answers for it. Maybe I was not enough fair in
explaining the problem, or maybe there are not solutions. To be sure I'll try to
explain better:

my doubt: imagine I collect some estimates of a variable, and I have un
uncertainty about them, say a 95% confidence interval of 20, and I know this
uncertainty. Now I develop a kriging model to predict my variable, and I
cross-validate it. Well, even if I had a perfect model, completely precise and
accurate, I should have a MAE of 10, more or less. Do someone think this is
correct? And, given that I know the uncertainty about my estimates, is there a
way to 'correct' the MAE of my cross-validation accounting for it?

Greetings to all list members.

X Isobel - I ignored the presence of the King in Frascati (and the same everyone
around me). Usually people from Roma goes to Frascati just to spend the evening
drinking. I'll spread the information and I will look like an history expert, so
thank you again!

Cheers!

Daniele


[Non-text portions of this message have been removed]

hello list,

how to simultanously use two "variables of influence" - say x and y (not
coordinates!) -
and use them as one external drift variable - say z - within wingslib
(kriging with
external drift)? what is an appropiate way of combination?:
1. summation (z=x+y)?
2. multiplication (z=x*y)?
3. doing a multiple linear regression analysis first (primary variable as
dependent variable!) and use the resulting trend (z=a+b1*x+b2*y)?
4. any other way??
hope somebody has some suggestions
regards
Lenz



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Hi;

My name is Tom Juenger.  I'm a postdoc at UC Berkeley in the Integrative
Biology Department.  I study plant evolutionary ecology.  Most of my
research focuses on how plants interact with other species (pollinators,
herbivores, bacteria etc).  I'm fairly new to spatial statistical
approaches in ecology, but I'm very interested in learning more.  I have a
set of observations that I'm currently starting to analyze and thought it
might be helpful to bounce a few thoughts off of the geostats group.
Please cut me some slack for the simplicity of my questions - I'm just
getting started.

I've been studying a neat plant that occurs in sand dune habitats just
north of the San Francisco Bay area.  The plant is a lupine.  Many species
in this group form a symbiotic relationship with bacteria in specialized
root organs called nodules.  The general understanding is that the bacteria
can fix atmospheric nitrogen which it then supplies to the plant, while the
plant fixes carbon through photosynthesis which it shares with the
bacteria. This is probably an important interaction in this habitat as sand
dunes have few mineral resources.  I'm very interested in how tightly
co-evolved or adapted this interaction is and whether environmental factors
influence the cost or benefits of the symbiosis.  For example, do plants
restrict their interaction with the bacteria when they already occur in
soil patches that are high in plant available nitrogen. Do certain plant
genotypes prefer certain bacterial genotypes?

I've collected two years of (x y) coordinate data in a natural population
of lupines.  The thought is to use these data as a pilot study to direct
some future experimental manipulations.  I created a nice 10 m x 20 m grid
over a plant population.  In 2000, I mapped the location of all Lupinus
bicolor (an annual lupine) individuals to the nearest cm (oh, my knees
hurt......over 2,000 plants!).  I also placed small ion-exchange membranes
in the soil to estimate plant available nitrate, ammonium, and phosphorus.
These membranes were placed so that a membrane was planted systematically
at each 1 m spacing over the entire grid and at a .5 m spacing in 4 dense
subplots (this ends up being @ 400 sampling points).  At the end of the
season, I randomly harvested at least one (and often two) plants per square
meter over the entire plot.  I've measured plant biomass and the number of
nodules on all harvested plants.  I repeated this sampling in 2001,
although the density of plants dropped dramatically, presumably due to the
dry year we are having.  I have also collected tissue from both the harvest
plants and their nodules - we are currently developing genetic markers to
"dna fingerprint" both the bacteria and the plant from each of the
harvested individuals.

I'm interested in a suite of questions.  First, I'd like to say something
about the spatial structuring of soil resources.  I've been using PROC
Variogram in SAS for some preliminary investigations of the soil resource
data.  Does anyone have a suggestion on how to bin my samples for
calculating variograms.  It seems logical to pick 0.5 (my smallest
"inter-membrane" distance) and yet then I have very different sample sizes
across the distance categories? The data is very non-normal with a skewed
distribution - many low values and a few large values.  The variograms seem
to be very dependent on the inclusion of the high outliers, and yet I do
not have a good reason to just throw them out.  Is there any particular
rule of thumb I should follow...........or am I in the realm of opinion.
Alternatively, I'm really only interested in the relative amount of soil
resources across space - should I think about a rank transformation?  or
other transformations?

It makes sense to use variograms and a geostats approach to look at spatial
pattens in the soil resources - nitrogen COULD have been measured at each
point so the notion of a random spatial field makes sense to me.  However,
I'm not sure if this applies to the plant characteristics.  For example,
there can only be nodules where a plant occurs.  In some sense this is a
point process.  Does it still make sense to fit variograms for nodule
production across space?  Would this sort of analysis be interpreted as an
"average" nodule number across space.  Is there some way I could adjust
this analysis if I was interested in "absolute" numbers of nodules in the
soil (given I know exact numbers of plants and their location)?  I
apologize if that question seems ill formed - I'm not sure I've thought
through the problem completely.

  A major question I have is whether nodule production is correlated with
soil nitrogen levels.  Many ecologist would just go in the field and pull
up plants, count nodules, measure N in the soil, ignore the locations of
sampling, and test for a correlation.  I get the idea that this could be a
problem given the the pairs of points might not be independent given
spatial correlation  - I have heard people speak about co-kriging.  I have
the impression this method is often used to predict one variable (often an
expensive variable to measure) based on measuring a different variable
(often a cheap variable to measure).  Is this an approach I should
investigate for this question?  Are there other means of calculating a
correlation between variables, controlling for their spatial correlation?

We are still working on the dna fingerprinting but hope to ask whether
particular plant genotypes are correlated with bacterial genotypes - this
is a nice test of co-adaptation.  The fingerprinting will let us categorize
the sampled plants and bacteria into "clones" (nominal identifiers A,B,C, D
for plants and bacteria).  One approach would be to test for a
nonparametric correlation between the plant and bacteria clones using a
permutation test - but this would not include the problem of spatial
correlation in the occurrences of the various genotypes.  Would there be a
corresponding non-parametric test for a correlation, controlling for
spatial locations?

SAS is a bit clunky - do you folks have any suggestions on software I
should investigate?

Once again, I apologize for my naive questions and for the rambling email.
I'd love to hear any thoughts or suggestions you may have.

Take care
Tom J.


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Hi Tom,
Cool study!

One thing that you migth want to think about is that your plants are
discrete entities, you do not have a continuous random field. A marked
point process on the otherhand is more in line with your variables. The
locations of your plants are the points, number of nodules, biomass, etc.
and local nitrogen level are the marks. A slight complication is that the
soil variables are continous, so you are associating a point process with
an estimated continuous random variable. I don't know if there is much
literature on that, i believe Steve Rathbun at U. Georgia wrote some stuff
about that, I have the tech report, I don't know if he published it.

In regards to the permutation tests you were talking about, you can
incorporate spatial information, there is quite a bit written about this,
look for papers by Peter Smouse, Robert Sokal, and Brian Manly in the
80's. Also go down the hall and talk to Monty Slatkin, he has done quite a
bit in spatial population genetics ;)

Lastly, interms of a reccomended software package, use R
(http://cran.r-project.org) there are packages for geostatistics (Rgeo),
and point processes (splancs) and best of all it is free!

Nicholas


On Wed, 4 Jul 2001, Tom Juenger wrote:

> Hi;
>
> My name is Tom Juenger.  I'm a postdoc at UC Berkeley in the Integrative
> Biology Department.  I study plant evolutionary ecology.  Most of my
> research focuses on how plants interact with other species (pollinators,
> herbivores, bacteria etc).  I'm fairly new to spatial statistical
> approaches in ecology, but I'm very interested in learning more.  I have a
> set of observations that I'm currently starting to analyze and thought it
> might be helpful to bounce a few thoughts off of the geostats group.
> Please cut me some slack for the simplicity of my questions - I'm just
> getting started.
>
> I've been studying a neat plant that occurs in sand dune habitats just
> north of the San Francisco Bay area.  The plant is a lupine.  Many species
> in this group form a symbiotic relationship with bacteria in specialized
> root organs called nodules.  The general understanding is that the bacteria
> can fix atmospheric nitrogen which it then supplies to the plant, while the
> plant fixes carbon through photosynthesis which it shares with the
> bacteria. This is probably an important interaction in this habitat as sand
> dunes have few mineral resources.  I'm very interested in how tightly
> co-evolved or adapted this interaction is and whether environmental factors
> influence the cost or benefits of the symbiosis.  For example, do plants
> restrict their interaction with the bacteria when they already occur in
> soil patches that are high in plant available nitrogen. Do certain plant
> genotypes prefer certain bacterial genotypes?
>
> I've collected two years of (x y) coordinate data in a natural population
> of lupines.  The thought is to use these data as a pilot study to direct
> some future experimental manipulations.  I created a nice 10 m x 20 m grid
> over a plant population.  In 2000, I mapped the location of all Lupinus
> bicolor (an annual lupine) individuals to the nearest cm (oh, my knees
> hurt......over 2,000 plants!).  I also placed small ion-exchange membranes
> in the soil to estimate plant available nitrate, ammonium, and phosphorus.
> These membranes were placed so that a membrane was planted systematically
> at each 1 m spacing over the entire grid and at a .5 m spacing in 4 dense
> subplots (this ends up being @ 400 sampling points).  At the end of the
> season, I randomly harvested at least one (and often two) plants per square
> meter over the entire plot.  I've measured plant biomass and the number of
> nodules on all harvested plants.  I repeated this sampling in 2001,
> although the density of plants dropped dramatically, presumably due to the
> dry year we are having.  I have also collected tissue from both the harvest
> plants and their nodules - we are currently developing genetic markers to
> "dna fingerprint" both the bacteria and the plant from each of the
> harvested individuals.
>
> I'm interested in a suite of questions.  First, I'd like to say something
> about the spatial structuring of soil resources.  I've been using PROC
> Variogram in SAS for some preliminary investigations of the soil resource
> data.  Does anyone have a suggestion on how to bin my samples for
> calculating variograms.  It seems logical to pick 0.5 (my smallest
> "inter-membrane" distance) and yet then I have very different sample sizes
> across the distance categories? The data is very non-normal with a skewed
> distribution - many low values and a few large values.  The variograms seem
> to be very dependent on the inclusion of the high outliers, and yet I do
> not have a good reason to just throw them out.  Is there any particular
> rule of thumb I should follow...........or am I in the realm of opinion.
> Alternatively, I'm really only interested in the relative amount of soil
> resources across space - should I think about a rank transformation?  or
> other transformations?
>
> It makes sense to use variograms and a geostats approach to look at spatial
> pattens in the soil resources - nitrogen COULD have been measured at each
> point so the notion of a random spatial field makes sense to me.  However,
> I'm not sure if this applies to the plant characteristics.  For example,
> there can only be nodules where a plant occurs.  In some sense this is a
> point process.  Does it still make sense to fit variograms for nodule
> production across space?  Would this sort of analysis be interpreted as an
> "average" nodule number across space.  Is there some way I could adjust
> this analysis if I was interested in "absolute" numbers of nodules in the
> soil (given I know exact numbers of plants and their location)?  I
> apologize if that question seems ill formed - I'm not sure I've thought
> through the problem completely.
>
>  A major question I have is whether nodule production is correlated with
> soil nitrogen levels.  Many ecologist would just go in the field and pull
> up plants, count nodules, measure N in the soil, ignore the locations of
> sampling, and test for a correlation.  I get the idea that this could be a
> problem given the the pairs of points might not be independent given
> spatial correlation  - I have heard people speak about co-kriging.  I have
> the impression this method is often used to predict one variable (often an
> expensive variable to measure) based on measuring a different variable
> (often a cheap variable to measure).  Is this an approach I should
> investigate for this question?  Are there other means of calculating a
> correlation between variables, controlling for their spatial correlation?
>
> We are still working on the dna fingerprinting but hope to ask whether
> particular plant genotypes are correlated with bacterial genotypes - this
> is a nice test of co-adaptation.  The fingerprinting will let us categorize
> the sampled plants and bacteria into "clones" (nominal identifiers A,B,C, D
> for plants and bacteria).  One approach would be to test for a
> nonparametric correlation between the plant and bacteria clones using a
> permutation test - but this would not include the problem of spatial
> correlation in the occurrences of the various genotypes.  Would there be a
> corresponding non-parametric test for a correlation, controlling for
> spatial locations?
>
> SAS is a bit clunky - do you folks have any suggestions on software I
> should investigate?
>
> Once again, I apologize for my naive questions and for the rambling email.
> I'd love to hear any thoughts or suggestions you may have.
>
> Take care
> Tom J.
>
>
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>

                  CH3
                   |
                   N             Nicholas Lewin-Koh
                  / \            Dept of Statistics
            N----C   C==O        Program in Ecology and Evolutionary Biology
           ||   ||   |           Iowa State University
           ||   ||   |           Ames, IA 50011
           CH    C   N--CH3      http://www.public.iastate.edu/~nlewin
             \  / \ /            nlewin@...
              N    C
              |   ||             Currently
             CH3   O             Graphics Lab
                                 School of Computing
                                 National University of Singapore
      The Real Part of Coffee    kohnicho@...


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Hi Tom,

just a few thoughts from your neighbours at UC Davis.

> Is there any particular
> rule of thumb I should follow...........or am I in the realm of opinion.
>

I think that a lot of subjects in geostatistics are in the realm of opinion,
and I'm sure you will receive many from the list' participants. Without
having looked at your data at all, I think you should probably do some sort
of transformation (lognormal or indicator) on your data, in order to
normalize your dataset. I think that other members will probably recommend
some papers or texts on that subject. If not, you can always send me an
e-mail.

I was, however, more interested in your research itself. We recently got a
paper accepted for Soil Science Society of America Journal, entitled
'short-range spatial variability of nitrogen fixation by chickpea'. Although
this is a study in an agroecosystem rather than a natural one, it might be
of interest to you. In short, we measured N-fixation using the N15 natural
abundance isotope dilution method, and tried to relate it to a range of soil
factors. We sampled at 0.3 m distance, but the range of spatial variability
was extremely short, i.e. 3-4 meters. My guess would be that nodule biomass
and type might be even more variable. If you would be interested in a copy
of the manuscript, let me know.

The prof. I currently work for, Chris van Kessel, has published a number of
papers in SSSAJ during the 80-s and 90-s on spatial variability of nitrogen
fixation and some related microbiology. I grant that there is not many (if
any) geostatistical analysis, but I think these papers might still be of
interest to you. He found strong correlations between N fixation and
hydrological characteristics. The availability of water controls various
crucial  processes of the N cycle (denitrification, nitrification,
leaching), and will therefore dictate the need for the plant to fixate N. In
addition, you need water to transport the inorganic N to the roots.

In short, I think it would be a good idea to include hydrology somehow in
your analysis, even if it is as simple as elevation. Next to that, I think
you should definitely try some multivariate geostatistical techniques (like
cokriging), because N fixation is an extremely complex process, controlled
by many biotic and abiotic variables that all can vary considerably within a
few meters.

On a different note, I was interested in the performance of your ion
exchange membrane. In another study, we linked N uptake in plants to N
availability indices from anion exchange membranes, and compared that to
results from total N, mineral N, incubations, hot KCl extractable N, etc.
The membrane performed terrible, just total N in the soil was much better
(and cheaper). I was wondering what your experiences were. Sorry to divert a
bit from the main topic of this list....

JW.

Jan Willem van Groenigen
University of California - Davis
Dept. of Agronomy and Range Science
1 Shield Avenue
Davis, CA 95616





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Dear List,

I am wondering whether somebody has any experiences in using GSLIB under
Linux. Is it working quite well. Has somebody translated it to the f90
version (with dynamic parameters)?

Regards, Ulrich

__________________________________________________

Ulrich Leopold

Dep. Phys. Geography and Soil Science
Institute for Biodiversity and Ecosystem Dynamics
Faculty of Science
University of Amsterdam
Nieuwe Achtergracht 166
NL-1018 WV Amsterdam

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

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Just a follow-up on the rathbun comment. He published a paper with an
ecologist looking at nesting sites in turtles (if my memory serves me
correctly) that uses the techniques outlined in the tech report.
Continuous environment and discrete events. He also published the tech
report but I forget where. I know this isn't very specific but if people
would like I can dig up the references...
Steve


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Hello everybody,

I am modelling forest roads in GIS and I' d like to find for a specific road
how similar is this road with the one generated with the GIS model. I am
working with ArcINFO and the datasets are in raster format (generated with
PATHDIST and COSTPATH functions). ArcINFO has a number of spatial
autocorrelation functions (Moran, Geary, Correlation). Are these functions
appropriate for my purpose? Any other ideas?

Thank you very much.


Ionut



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Are you comparing an actual vs. predicted road, is that what I understand?
If so, I don't think spatial autocorrelation measures are appropriate.

What is your question?  Is the GIS model generating a road from any sort of
stochastic process?  If it's COSTPATH, I'm assuming you're placing the
simulated road in the most "efficient" location? (e.g., least cost?)?

I would suggest creating some sort of map with predicted and acutal location
- if the COSTPATH road represents an idealized road, I would assign that
road a value of 0, then create another grid with increasing values for
terrain that is less suitable for a road.  For example, if you're just
looking at topography, reclassify the grid according to some measure of
ruggedness (in however many categories you think apply), and then create a
grid of the acutal road (with some value that you know will stand out), and
then subtract the topography grid, then overlay the simulated road grid - so
that it has a value of 0 wherever you have a correct prediction, and
increasing negative values the less suitable the terrain.

Does that make sense?  Plotting model results is something I and some
colleagues have been discussing for a while - summarizing model results
spatially to show accuracy.

Hope that was helpful - just a suggestion.
Darla

*******************************
Darla Munroe
Postdoctoral Fellow
Indiana University
Center for the Study of Institutions,
Population, and Environmental Change
dmunroe@...

-----Original Message-----
From: Ionut Aron
To: ai-geostats@...
Sent: 7/5/2001 3:06 PM
Subject: AI-GEOSTATS: spatial correlation of forest roads

Hello everybody,

I am modelling forest roads in GIS and I' d like to find for a specific
road
how similar is this road with the one generated with the GIS model. I am
working with ArcINFO and the datasets are in raster format (generated
with
PATHDIST and COSTPATH functions). ArcINFO has a number of spatial
autocorrelation functions (Moran, Geary, Correlation). Are these
functions
appropriate for my purpose? Any other ideas?

Thank you very much.


Ionut



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Hi list members,

I am new to geo/spatial statistics and I don't have any expert spatial
epidemiologist in my country. So I thought I'd run through what I have done
with you all, and check whether I am on the right track. If anyone has any
better ideas, please feel free to let me know too!

I am working on the following questions:
How can I test the hypothesis that most of the dengue cases are located
where most of the population are?
How can I test the hypothesis that significantly more dengue cases are
located in the east than in the west of my country?
How can I detect if there are any clustering or any other spatial trends of
dengue in relation to population?

In my Arcview GIS 3.2, I have a polygon layer of population according to
postal sectors (83 polygons with sizes ranging from 0.3 km(superscript: 2)
to 33 km(superscript: 2)). I also have a point layer of dengue cases.

What I've done so far:
    Correlated number of dengue cases with population in each postal sector
    polygon.
    Correlated number of dengue cases with population density (i.e.
    population/ area) in each postal sector.
    Correlated dengue morbidity rate (i.e. no. of cases/ population) with
    population in each postal sector.
    Correlated dengue morbidity rate with population density in each postal
    sector.

What more can I do?

Thanks very much in advance. Best wishes.

Basil
Vector Control & Research Dept
Singapore


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Hello list !

Dealing with satellite cloud data and derived cloud parameters I would like
to analyze and describe the inhomogeneities in clouds (stratocumulus and
broken cloud fields) produced by different processes like the entrainment/mixing
of dry air on the edges of the clouds in the small scale and by cloud free
pixels in larger scales. Which parameters or methods you would recommend to do
this ? Do you know some literature, projects or homepages worked on these
theme or relevant themes ?

Thanks for your help

Klemens

--
GMX - Die Kommunikationsplattform im Internet.
http://www.gmx.net

GMX Tipp:

Machen Sie Ihr Hobby zu Geld bei unserem Partner 1&1!
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I have recently compiled an 800 entry bibliography on the application
of Geographic Information Science & Technology (GI S&T) to problems in
public health and disease. This is not complete but I could make a copy
available to you in digital form.

--
Professor Emeritus Duane F. Marble
Center for Mapping 	 Email: marble.1@...
The Ohio State University
1216 Kinnear Road 	 Telephone: 614-292-4419
Columbus, Ohio 43212 	 Fax:    614-292-8062
U.S.A.

	 "From now on, space by itself and time by itself
	  are doomed to fade away into mere shadows, and
	  only a kind of union of the two will preserve
	  an independent reality."
				 - Minkowski, 1908


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Hi everyone,

Thank you so much for those who replied so quickly to my earlier e-mail
with great advise on how I could solve my problem.

Here's another one-- unrelated to the first:

We are trying to re-locate our present 6 environmental health offices to
better places to serve the public. The main functions of each office are
cleaning up roads and drains, checking on the hygiene of food
establishments, performing mosquito surveillance, issuing licenses to the
public, public education, ...etc.

How can I determine the best number of health offices to have to serve the
population? And where are the best locations for these offices?
As you already know, I have a data on the spatial distribution of
population as a GIS polygon layer.

Thanks very much for your help, everyone. Have a great weekend!

Basil
Ministry of the Environment
Singapore


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Hi everyone,
Thank you so much for your great responses.

Below is a sum of a SUM on what I got. But first, here's my original
question.

ORIGINAL QUESTION:
Hi list members,

I am new to geo/spatial statistics and I don't have any expert spatial
epidemiologist in my country. So I thought I'd run through what I have done
with you all, and check whether I am on the right track. If anyone has any
better ideas, please feel free to let me know too!

I am working on the following questions:
How can I test the hypothesis that most of the dengue cases are located
where most of the population are?
How can I test the hypothesis that significantly more dengue cases are
located in the east than in the west of my country?
How can I detect if there are any clustering or any other spatial trends of
dengue in relation to population?

In my Arcview GIS 3.2, I have a polygon layer of population according to
postal sectors (83 polygons with sizes ranging from 0.3 km(superscript: 2)
to 33 km(superscript: 2)). I also have a point layer of dengue cases.

What I've done so far:
    Correlated number of dengue cases with population in each postal sector
    polygon.
    Correlated number of dengue cases with population density (i.e.
    population/ area) in each postal sector.
    Correlated dengue morbidity rate (i.e. no. of cases/ population) with
    population in each postal sector.
    Correlated dengue morbidity rate with population density in each postal
    sector.

What more can I do?

Thanks very much in advance. Best wishes.

Basil
Vector Control & Research Dept
Singapore


----- Forwarded by Basil LOH/ENV/SINGOV on 16-07-2001 09:15 -----

                     Nicholas
                     Lewin-Koh               To:     Basil LOH/ENV/SINGOV@SINGOV
                     <kohnicho@...        cc:
                     us.edu.sg>              Subject:     Re: AI-GEOSTATS: Dengue
& population

                     13-07-2001 22:31






On Fri, 13 Jul 2001 Basil_LOH@... wrote:
Hi,
Actually there are a few of us here at NUS.

>
> Hi list members,
>
> I am new to geo/spatial statistics and I don't have any expert spatial
> epidemiologist in my country.

Actually there are a few of us here at NUS.

> I am working on the following questions:
> How can I test the hypothesis that most of the dengue cases are located
> where most of the population are?
> How can I test the hypothesis that significantly more dengue cases are
> located in the east than in the west of my country?
> How can I detect if there are any clustering or any other spatial trends
of
> dengue in relation to population?

What you are looking for is tests of case clustering and small area
estimation.
There is a very nice package for R (or Splus if available) called Splancs
that has a lot of the procedures you might be looking for.

You might want to
a) test for significant clusters of Dengue cases.
b) Fit a Spatial poisson model on the counts of dengue per postal area
(probably over dispersed due to lots of 0's)

c) test environmental covariates against incidence

d) fit a model to determine risk of contracting the disease (hazard rate)

You have the luxury of using either point pattern type approaches or
lattice models on the postal areas.

You can call me if you want more advice at
874-6559

Nicholas

  >
> In my Arcview GIS 3.2, I have a polygon layer of population according to
> postal sectors (83 polygons with sizes ranging from 0.3 km(superscript:
2)
> to 33 km(superscript: 2)). I also have a point layer of dengue cases.
>
> What I've done so far:
>    Correlated number of dengue cases with population in each postal
sector
>    polygon.
>    Correlated number of dengue cases with population density


                  CH3
                   |
                   N             Nicholas Lewin-Koh
                  / \            Dept of Statistics
            N----C   C==O        Program in Ecology and Evolutionary Biology
           ||   ||   |           Iowa State University
           ||   ||   |           Ames, IA 50011
           CH    C   N--CH3      http://www.public.iastate.edu/~nlewin
             \  / \ /            nlewin@...
              N    C
              |   ||             Currently
             CH3   O             Graphics Lab
                                 School of Computing
                                 National University of Singapore
      The Real Part of Coffee    kohnicho@...

----- Forwarded by Basil LOH/ENV/SINGOV on 16-07-2001 09:15 -----

                     "Richard M
                     Webb"                To:     Basil LOH/ENV/SINGOV@SINGOV
                     <rmwebb@usgs.        cc:
                     gov>                 Subject:     Re: AI-GEOSTATS: Dengue &
population

                     14-07-2001
                     00:07





Basil,

I hope the following reference can offer you some guidance and/or ideas.

Morrison, A.C., Santiago, Marilyn, Rigau-Pérez, J.G., and Reiter, Paul,,
1998, The
      Transmission of Dengue fever in Puerto Rico: an epidemiologic approach
using a
      geographic information system: U.S. Geological Survey Water-Resources
      Investigations Report 98-4119, 86 p.

Regards,

Rick Webb

************************************************************
Richard MT Webb
USGS, WRD                          Telephone: 303-236-5025
Box 25046, MS 413, DFC             Fax:       303-236-5034
Denver, CO 80225-0046              Email: rmwebb@...
************************************************************


* To post a message to the list, send it to ai-geostats@...

----- Forwarded by Basil LOH/ENV/SINGOV on 16-07-2001 09:15 -----

                     "Richard Hoskins"
                     <healthmaps@...        To:    
<waphgis@...>
                     >                           cc:
                     Sent by:                    Subject:     RE: Dengue &
population
                     WAPHGIS-owner@...
                     ington.edu


                     14-07-2001 03:49
                     Please respond to
                     waphgis






Basil: I think one very effective way to  get the information you need is
to
use a spatial scan statistic approach. Your data is made for it. You do not
need to test the hypothesis of E vs W, and of course

likely, there are more cases where there are more people - I suspect the
mossies like areas where
there is lots of food(people).
I think you need to know where the rates are higher than anywhere else, if
the idea is to deal with those areas first.
Also it can tell you where areas are lower than expected and give an easy
to
understand way to determine if the rates are really elevated or not.

The spatial scan statistic can be easily calculated. The background is
http://www.sph.umich.edu/~lestberg/GeoMed/Scan/ScMain.htm

http://sun2539.sph.umich.edu:2000/geomed/stats/kullscan/scan.html

http://sun2539.sph.umich.edu:2000/geomed/stathelp/advisor.html

http://dcp.nci.nih.gov/bb/SaTScan.html  has free software

and there is a commercial product now which does cluster calculations

http://www.terraseer.com/clusterseer.html  which has a whole lot of cluster
tests bundled in one place.

A link directly to ArcView  http://www.phrl.org/REGS/Order.htm

Dick Hoskins
WA State Dept of Health



-----Original Message-----
From: WAPHGIS-owner@...
[mailto:WAPHGIS-owner@...]On Behalf Of Basil_LOH@...
Sent: Friday, July 13, 2001 1:36 AM
To: waphgis@...; ai-geostats@...;
fnpbb@...; getis@...;
owner-health-gis@...
Subject: Dengue & population



Hi list members,

I am new to geo/spatial statistics and I don't have any expert spatial
epidemiologist in my country. So I thought I'd run through what I have done
with you all, and check whether I am on the right track. If anyone has any
better ideas, please feel free to let me know too!


--
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* As a general service to the users, please remember to post a summary of any
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"unsubscribe ai-geostats" followed by "end" on the next line in the message
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Hello,

I am presently using geostatistical tools to analyze my data and would like to
clarify a few things about the interpretation of (co)kriging estimates or
predictions in the linear model of (co)regionalization. I would greatly
appreciate any feedback, comment or suggestion on the following issues. I am
planning to send to the LIST a summary of the answers received.

Thank you in advance for your help

Yours truly,

Bernard Pelletier

Natural Resource Sciences

Macdonald Campus, McGill University


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


Question 1

Using a linear model of regionalization, consider a random function Z that is a
linear combination of three independent random functions (Y1, Y2, Y3)
corresponding to three semivariogram models: a nugget (Y1)and two spherical
models (Y2,Y3). We can then compute, by kriging, the estimates Y1*, Y2*, Y3* at
each point on the original sampling grid. In theory, the random functions or
spatial components Y1, Y2, and Y3 are uncorrelated. In practice, however, I get
significant correlations (sometimes as high as 0.4) among Y1*, Y2*, and Y3*.

Are Y1*, Y2*, and Y3* supposed to be orthogonal (by some mathematical
construction) or is it acceptable to observe a certain degree of correlation
between them? I assume that this is due to some bias in the correlation
estimation as a consequence of the presence of autocorrelation in Y2* and Y3*.
What would be the consequences of an orthogonalization of the estimates after
kriging? Note that I use all the original sampling points in the kriging
equations and the sum of the three estimates does give me the initial Z back
(exact interpolation). Since I have modified a MATLAB kriging module to
calculate these estimates, I want to verify whether the presence of correlation
between them is due to a mistake in the modified module.

Question 2

Consider three regionalized variables: Z1, Z2 and Z3. Using a linear model of
coregionalization and ordinary co-kriging, the predictions of Z1at unsampled
locations (Z1*) are based on the information contained in both the fitted
auto-variogram model for Z1 and the two fitted cross-variograms models (Z2-Z1
and Z3-Z1). Therefore, a part of Z1* is predicted from the autocorrelation
structure of Z1, while another part (not exclusive) is predicted from the
spatial dependency of Z1 on Z2 and Z3.

Is there any way to calculate the component of Z1* that is specifically related
to the spatial dependency of Z1 on Z2 and Z3 ? Would it be possible to modify
the system of co-kriging equations in order to include only the information
contained in the fitted cross-variograms? What constraints should be put on the
co-kriging weights? I am not sure about the theoretical ramifications of trying
to calculate a new Z1* based only on cross-variograms. I am aware, however, that
this could not really be called "kriging" since we would not find Z1 back when
interpolating at sampling grid points.

Thank you again...

Bernard Pelletier



[Non-text portions of this message have been removed]

hello list,
are there any courses in geostatistics (for beginners with some experience
;-)) beginning in october 2001 or later ???

kind regards
Lenz



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Hi Bernard,

  Here is a stab at an answer to your questions. I think that my reasoning is
more or less correct - I hope it's not too obscure!

   1)  There is no reason for the estimates Y1* and Y2*  to be uncorrelated. In
fact they would only be under unusual circumstances. The easiest way to see this
is to think of kriging as a projection (this is kind of hard to draw on this
sort of screen - but see, for example, Journel + Huijbrets (ch 8).
         Simple Kriging of Z  can be interpreted as the projection of the unknown
Z unto the linear space, S, generated by the data Zi (+ the constant vector 1)
using the covariance as a metric. The characteristic of the kriged result is
that the error Z-Z* is orthogonal to each vector in the space S.
      Now you have Z = Y1 + Y2 + Y3. likewise the kriging of each component Yi
can be done by projecting onto the same linear space and is characterised by the
fact that the error Yi - Yi* is orthogonal to each vector in S.  Therefore the
error vector is 'perpendicular' to the S space.
      As you noted, the overall space of random variables can be decomposed into
3 orthogonal subspaces (the Y1 Y2 and Y3 are orthogonal by virtue of the fact
that they 'live' in these orthogonal subspaces).   For the projections Yi*,
which live in the space S to remain orthogonal, the projections onto S would
have to take place parallel to these orthogonal subspaces. However, we have
already noted that the error is 'perpendicular' to the S space. Thus, the only
way this can happen is that S is congruent to the decomposition of the space
into the 3 components. However this is most unlikely - it would mean that all of
the observed data was missing some of the Yi components - in general the S space
will be 'at an angle' to all three subspaces and the Yi* will not be orthogonal.

  2) If I understand correctly here you wish to estimate Z1 from just Z2 and Z3.
There is nothing impossible about doing this. The most important thing to note
is that there is no way just using information about Z2 and Z3 to estimate the
mean of Z1 - so all you can hope to estimate is the residual Z1 - m1. This will
mean that the sum of weights must be zero.

    You can krige by  z1* = sum_i  ( lambda_i * z2(x_i))  +  sum_i ( mu_i *
z3(x_i))

     (the kriging equations can be found in the usual way) and your weights must
satisy

        sum_i  lambda_i = 0
        sum_i mu_i = 0




Best Regards

Colin Daly



----- Original Message -----
   From: Bernard Pelletier
   To: ai-geostats@...
   Sent: Monday, July 16, 2001 11:15 PM
   Subject: AI-GEOSTATS: (co)kriging predictions in the linear model of
(co)regionalization


   Hello,

   I am presently using geostatistical tools to analyze my data and would like to
clarify a few things about the interpretation of (co)kriging estimates or
predictions in the linear model of (co)regionalization. I would greatly
appreciate any feedback, comment or suggestion on the following issues. I am
planning to send to the LIST a summary of the answers received.

   Thank you in advance for your help

   Yours truly,

   Bernard Pelletier

   Natural Resource Sciences

   Macdonald Campus, McGill University



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


   Question 1

   Using a linear model of regionalization, consider a random function Z that is
a linear combination of three independent random functions (Y1, Y2, Y3)
corresponding to three semivariogram models: a nugget (Y1)and two spherical
models (Y2,Y3). We can then compute, by kriging, the estimates Y1*, Y2*, Y3* at
each point on the original sampling grid. In theory, the random functions or
spatial components Y1, Y2, and Y3 are uncorrelated. In practice, however, I get
significant correlations (sometimes as high as 0.4) among Y1*, Y2*, and Y3*.

   Are Y1*, Y2*, and Y3* supposed to be orthogonal (by some mathematical
construction) or is it acceptable to observe a certain degree of correlation
between them? I assume that this is due to some bias in the correlation
estimation as a consequence of the presence of autocorrelation in Y2* and Y3*.
What would be the consequences of an orthogonalization of the estimates after
kriging? Note that I use all the original sampling points in the kriging
equations and the sum of the three estimates does give me the initial Z back
(exact interpolation). Since I have modified a MATLAB kriging module to
calculate these estimates, I want to verify whether the presence of correlation
between them is due to a mistake in the modified module.

   Question 2

   Consider three regionalized variables: Z1, Z2 and Z3. Using a linear model of
coregionalization and ordinary co-kriging, the predictions of Z1at unsampled
locations (Z1*) are based on the information contained in both the fitted
auto-variogram model for Z1 and the two fitted cross-variograms models (Z2-Z1
and Z3-Z1). Therefore, a part of Z1* is predicted from the autocorrelation
structure of Z1, while another part (not exclusive) is predicted from the
spatial dependency of Z1 on Z2 and Z3.

   Is there any way to calculate the component of Z1* that is specifically
related to the spatial dependency of Z1 on Z2 and Z3 ? Would it be possible to
modify the system of co-kriging equations in order to include only the
information contained in the fitted cross-variograms? What constraints should be
put on the co-kriging weights? I am not sure about the theoretical ramifications
of trying to calculate a new Z1* based only on cross-variograms. I am aware,
however, that this could not really be called "kriging" since we would not find
Z1 back when interpolating at sampling grid points.

   Thank you again...

   Bernard Pelletier


   ----------

This message may contain privileged and confidential information.  If you
are not the intended recipient, then please notify the sender of this error.
Any disclosure, copying, distribution or misuse of this information is
prohibited.  Copyright Roxar limited.


[Non-text portions of this message have been removed]

Dear all,

Please forgive the newbie style question...I've looked on the website
at software listings and can't quite work out what I'm after.

I'm running poisson regressions for a large number of small areas
(several thousand contiguous polygons) - predicting counts of events
with several predictor variables for each small area. I'd like to be
able to adjust these models to account for spatial autocorrelation.
Does anyone know of software (ideally free/cheap) that will do this in
a reasonably straightforward way? Either stand-alone or as an add-on to
Arc/info or arcview. I can also use Stata, SAS, SPSS etc.

Any ideas much appreciated,

Thanks a lot

Cheers
Ben


-------------------------
Ben Wheeler
MRC Research Student
Department of Social Medicine
University of Bristol
UK

e-mail ben.wheeler@...
-------------------------


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You might want to contact Dan Griffith, Dept of Geography at Syracuse
University - he is working on an estimator for this exact case.

As far as I know, there is no built-in model for spatial autocorrelation in
a poisson regression (though there may be some code out there - probably for
GAUSS or something - you'd have to code the autocorrelation into the maximum
likelihood estimator - pretty sticky stuff).

Good luck,
Darla Munroe

--
***************************************
Darla Munroe, Ph.D.
Postdoctoral Fellow
Center for the Study of Institutions,
Population, and Environmental Change
Indiana University
408 N. Indiana
Bloomington, IN 47408
dmunroe@...
php.indiana.edu/~dmunroe




-----Original Message-----
From: Ben Wheeler [mailto:Ben.Wheeler@...]
Sent: Thursday, July 19, 2001 7:49 AM
To: ai-geostats@...
Subject: AI-GEOSTATS: Spatial poisson regression software?


Dear all,

Please forgive the newbie style question...I've looked on the website
at software listings and can't quite work out what I'm after.

I'm running poisson regressions for a large number of small areas
(several thousand contiguous polygons) - predicting counts of events
with several predictor variables for each small area. I'd like to be
able to adjust these models to account for spatial autocorrelation.
Does anyone know of software (ideally free/cheap) that will do this in
a reasonably straightforward way? Either stand-alone or as an add-on to
Arc/info or arcview. I can also use Stata, SAS, SPSS etc.

Any ideas much appreciated,

Thanks a lot

Cheers
Ben


-------------------------
Ben Wheeler
MRC Research Student
Department of Social Medicine
University of Bristol
UK

e-mail ben.wheeler@...
-------------------------


--
* To post a message to the list, send it to ai-geostats@...
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Just to be a little more clear: spatial effects in qualitative data
regression models are UGLY UGLY things...and no one has many good solutions
yet (though a few people are working furiously on it).

Basically, in any sort of qualitative data model, such as a possion model -
where your observed dependent variable is a count of a
occurrence/nonoccurence of some event - the observed process is not where
the spatial effect would/should be modeled.  These regressions are called
latent, because there is some underlying process (that we do not observe)
that is generating the qualitative outcome.

For this reason, any spatial autocorrelation would be part of this latent,
unobserved process, not necessarily corresponding one-to-one to the observed
outcome.

Kurt Beron and Wim Vijverberg of U Texas, Dallas, have a chapter coming out
in the new Anselin spatial econometrics book (should come out this year),
New Advances in Spatial Econometrics, that has a really good and careful
review of spatial effects in probit models, and how difficult it is to
specify a full covariance structure taking these into account.

As I mentioned, Dan Griffith of Syracuse is working on poisson models.  I
think Harry Kelejian (Dept of Economics, Maryland) has developed a TEST for
autocorrelation in possion models (but no correction).

You say you have thousands of polygons?  YIKES.  Beron and Vijverberg
developed a spatial probit estimator for 48 observations (or something like
that), and it takes several hours to run.  The nXn weighting
structure/incidental parameter problem makes it very hard to identify
anything that big.

Anyway - suffice to say - there is no COTS solution to your problem.  If you
find something out there that I haven't already mentioned, please let me
know!

Best,
Darla Munroe



--
***************************************
Darla Munroe, Ph.D.
Postdoctoral Fellow
Center for the Study of Institutions,
Population, and Environmental Change
Indiana University
408 N. Indiana
Bloomington, IN 47408
dmunroe@...
php.indiana.edu/~dmunroe




-----Original Message-----
From: Ben Wheeler [mailto:Ben.Wheeler@...]
Sent: Thursday, July 19, 2001 7:49 AM
To: ai-geostats@...
Subject: AI-GEOSTATS: Spatial poisson regression software?


Dear all,

Please forgive the newbie style question...I've looked on the website
at software listings and can't quite work out what I'm after.

I'm running poisson regressions for a large number of small areas
(several thousand contiguous polygons) - predicting counts of events
with several predictor variables for each small area. I'd like to be
able to adjust these models to account for spatial autocorrelation.
Does anyone know of software (ideally free/cheap) that will do this in
a reasonably straightforward way? Either stand-alone or as an add-on to
Arc/info or arcview. I can also use Stata, SAS, SPSS etc.

Any ideas much appreciated,

Thanks a lot

Cheers
Ben


-------------------------
Ben Wheeler
MRC Research Student
Department of Social Medicine
University of Bristol
UK

e-mail ben.wheeler@...
-------------------------


--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of
any useful responses to your questions.
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Numerically, how does the external drift variable affect the estimated
value when doing ordinary kriging.

Thanks  - Annemarie Dahm



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Hi AI-Geostats Member
Do you know how I can simulate a 2-D spatial Data set (of type geostatistics),
which sill and nugget effect are constant but the range vary with direction
(anisotropy in range).
Note that I need the range vary irregular, not in a regularar shape such as
ellipse.
(I have an extention of elliptic anisotropy (of range) and want to show, by
simulation, it works better than elliptic anisotropy.)
Thank you:
Yadollah Waghei
Dep.of Biostatistics
Tarbiat Modarres Univ.(Tehran)Po.Box: 14115-111
Tel:8011001-3872  Fax:8007989
___________________________________________________________________________
Visit http://www.visto.com.
Find out  how companies are linking mobile users to the
enterprise with Visto.


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Dr. List members,

The following publication is not available in our university library. Therefore,
If anybody has, I would like to ask him/her to send me a copy of it.
"Cressie A.C. Noel. and Grondona O. Martin (1992); A comparison of Variogram
Estimation with Covariogram Estimation, In The art of statistical Science
Edited by K.V. Mardia Jhon pp:191-208, Wiley & Sons Ltd. "

Thank you for your help in advance.
Mahmut
--------------------------------------------------------------------------------\
-----------------
Associate Prof. Dr. Mahmut CETIN
Department of Agricultural Structures and Irrigation
Faculty of Agriculture
University of Cukurova
01330 Balcali-Adana/TURKEY
Tel: +90-322-338 68 77 (Direct)
        +90-322-338 63 18 (Switchboard, ext. : 25)
Fax: +90-322-338 63 86

E-Mail:  mcet64@...



[Non-text portions of this message have been removed]

Dear all,

Many thanks to Brian Gray, Darla Munroe, Carlos Carroll, Wayne
Thogmartin, who replied to the question below...I've pasted in
responses FYI.
Basically, it seems as if there is no off-the-peg solution to this
problem. I'm going to look into the Gotway & Stroup paper, and also
look at transforming the data to utilise linear regression instead. The
response variable is counts of deaths, so I reckon I might get away
with age-sex specific/standardised mortality rates to use as a linear
outcome.

Cheers
Ben

Original question:

> I'm running poisson regressions for a large number of small areas
> (several thousand contiguous polygons) - predicting counts of events
> with several predictor variables for each small area. I'd like to be
> able to adjust these models to account for spatial autocorrelation.
> Does anyone know of software (ideally free/cheap) that will do this in
> a reasonably straightforward way? Either stand-alone or as an add-on to
> Arc/info or arcview. I can also use Stata, SAS, SPSS etc.

1.
How are you adjusting your p-values to account for the multiple
regressions--each with a potential for a Type I error/s?  And, how do
you determine which points are in which polygon: if they are
spatially-correlated, could information associated with points be
shared across polygons?  sorry for the questions, but my interest is in
modeling spatially-correlated nonnormal data.  frankly, I haven't seen
extensions to multiple, practically-simultaneous regressions.
depending on the answers to the above questions, you might enjoy
reading Gotway, C.A. and W.W. Stroup. 1997.  A generalized linear model
approach to spatial data analysis and prediction. Journal of
Agricultural, Biological, and Environmental Statistics 2: 157-178..
they examine issues pertaining to the analysis of nonnormal data under a
generalized linear model context.
_________________________________________
2.
You might want to contact Dan Griffith, Dept of Geography at Syracuse
University - he is working on an estimator for this exact case.

As far as I know, there is no built-in model for spatial
autocorrelation in a poisson regression (though there may be some code
out there - probably for GAUSS or something - you'd have to code the
autocorrelation into the maximum likelihood estimator - pretty sticky
stuff
__________________________________________
3.
Cressie indicates in his book on spatial statistics that an
"auto-Poisson" procedure (a Poisson regression incorporating spatial
autocorrelation) is infeasible.  There are linear methods available in
Splus with the Spatial Statistics add-on that allow you to include
spatial autocorrelation in your models, but obviously a transformation
of the data would first be required.
___________________________________________
4.
You may be able to implement this in BUGS. You could ask the BUGS
listserv:
BUGS@...

or check the bugs WWW site

      http://www.mrc-bsu.cam.ac.uk/bugs

__________________________________________
5.
Just to be a little more clear: spatial effects in qualitative data
regression models are UGLY UGLY things...and no one has many good
solutions yet (though a few people are working furiously on it).

Basically, in any sort of qualitative data model, such as a possion
model - where your observed dependent variable is a count of a
occurrence/nonoccurence of some event - the observed process is not
where the spatial effect would/should be modeled.  These regressions
are called latent, because there is some underlying process (that we do
not observe) that is generating the qualitative outcome.

For this reason, any spatial autocorrelation would be part of this
latent, unobserved process, not necessarily corresponding one-to-one to
the observed outcome.

Kurt Beron and Wim Vijverberg of U Texas, Dallas, have a chapter coming
out in the new Anselin spatial econometrics book (should come out this
year), New Advances in Spatial Econometrics, that has a really good and
careful review of spatial effects in probit models, and how difficult it
is to specify a full covariance structure taking these into account.

As I mentioned, Dan Griffith of Syracuse is working on poisson models.
I think Harry Kelejian (Dept of Economics, Maryland) has developed a
TEST for autocorrelation in possion models (but no correction).

You say you have thousands of polygons?  YIKES.  Beron and Vijverberg
developed a spatial probit estimator for 48 observations (or something
like that), and it takes several hours to run.  The nXn weighting
structure/incidental parameter problem makes it very hard to identify
anything that big.

___________________________
In response to 5:

I wonder if probit and Poisson are here confused?  Continuous outcomes
are typically categorized using categories rather than counts.  This
approach doesn't appear to describe Ben's case.  Further, I am not sure
why a latent process must be assumed.

Counts are theoretically Poisson only if they meet a certain number of
assumptions/postulates.  Autocorrelation is a violation, as I recall,
of these postulates.  However, over- or underdispersion arising from
spatial autocorrelation may, in an estimation context, be handled from
a number of perspectives, including generalized estimating equations
and generalized linear mixed models.  The negative binomial distribution
may also be used to model count data.  I recommend Gotway, C.A. and
W.W. Stroup. 1997.  A generalized linear model approach to spatial data
analysis and prediction. Journal of Agricultural, Biological, and
Environmental Statistics 2: 157-178..  they examine issues pertaining
to the analysis of nonnormal data under a generalized linear model
context.




-------------------------
Ben Wheeler
MRC Research Student
Department of Social Medicine
University of Bristol

Tel. (0117) 928 7288
e-mail ben.wheeler@...
-------------------------


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Hi Ben,
Just one more place to look is R (or Gnu Splus). There is a module on cran
for generalized linear mixed models, which is actually a port of the
software (beam) that was used by Clayton and Kaldor 1987 JASA. They use a
hierarchical modeling approach and get the randome effects distributions
using mcmc. You can also use bugs to do this as was mentioned in your
summary.

In your question I was not sure if you wanted to model the functional
relationship between your response and predictors or to predict unobserved
locations. If the former then the glm approach might be the best, if the
latter than the Gottaway and stroup approach might be better. I recall
that articale dealt more with prediction. Another article to look at is
diggle, tawn and moyeed (or some permutation of the names) I think the
article is called Model Based Geostatistics and is in JRSS A or C,
whichever is applied statistics. I don't know if they ever distributed
software for the application, I think the MCMC procedure they used was not
very stable.

So the question is what are the goals of this analysis and the methods
will follow.

Nicholas

                  CH3
                   |
                   N             Nicholas Lewin-Koh
                  / \            Dept of Statistics
            N----C   C==O        Program in Ecology and Evolutionary Biology
           ||   ||   |           Iowa State University
           ||   ||   |           Ames, IA 50011
           CH    C   N--CH3      http://www.public.iastate.edu/~nlewin
             \  / \ /            nlewin@...
              N    C
              |   ||             Currently
             CH3   O             Graphics Lab
                                 School of Computing
                                 National University of Singapore
      The Real Part of Coffee    kohnicho@...


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