It is dificult if not irrealistic to set Y to be 0/1 (ou interger counts
or similar) in such model since this would impose severe contraints in the
a's and x's as well as in the model structure.
This is why the hierarquical model structure is one possible
working around. The ideia is the same as in generalised linear models
relating the covariates (x's) and spatial effect to as function of the
expected value of Y instead of directly with Y.
In a "loose" notation:
Y_i ~ "some distribution" with E[Y_i] = \mu_i
g(\mu_i) = a1*x1+a2*x2+spatial effect
where g() is a "convenient" function mapping (-Inf, +Inf)
to the parameter space of \mu_i
Some examples:
1. For binay (0/1) observations a possible model would be
Y_i ~ B(p_i)
log(p_i/(1-p_i) = a1*x1+a2*x2+spatial effect
2. For count data:
Y_i ~ B(\lambda_i)
log(\lambda_i) = a1*x1+a2*x2+spatial effect
3. For Gaussian data
Y_i ~ N(\mu_i, \tau^2)
\mu_i = a1*x1+a2*x2+spatial effect
which in this particular case can be written as
Y_i = a1*x1+a2*x2+spatial effect
Paulo Justiniano Ribeiro Jr
LEG (Laboratorio de Estatistica e Geoinformacao)
Universidade Federal do Parana
Caixa Postal 19.081
CEP 81.531-990
Curitiba, PR - Brasil
Tel: (+55) 41 3361 3573
Fax: (+55) 41 3361 3141
e-mail: paulojus AT ufpr br
http://www.leg.ufpr.br/~paulojus
On Tue, 2 Feb 2010, rusers.sh wrote:
It works. The problem is that it only generates the simulated data based
on our observed dataset,e.g. "meuse" here.
I wonder if we can generate the simulated dataset from the user-specified
model with covariates included, such as y~a1*x1+a2*x2+spatial effect. Y can
be continuous or 0/1 variables. Something like this.
The idea is we first specify a theoretical model, and then generate the
simulated data based on this model. The coefficients and spatial effects are
fixed by users, so we may study some new methods.
Thanks.
2010/2/2 Edzer Pebesma <edzer.pebe...@uni-muenster.de>
rusers.sh wrote:
Hi Tomislav,
Thanks for your info on unconditional simulation. For conditional
simulations, i still cannot find any useful information.
I searched the R site and didnot find the possible method to do
conditional simulations.
1. CondSimu(RandomField): trend: Not programmed yet. (used by universal
kriging)
2. grf(geoR): generates unconditional simulations of Gaussian random
fields
3. sim.Krig(fields) #Conditonal simulation of a spatial process
It seems to be based on the actual dataset,not a theoretical model.
4. krige(gstat ):Simple, Ordinary or Universal, global or local, Point or
Block Kriging,or simulation
x <- krige(log(zinc)~x+y, meuse, meuse.grid, model = m, block =
c(40,40),nsim=1)
rusers.sh, please use
x <- krige(log(zinc)~x+y, meuse, meuse.grid, model = m, nmax=40, nsim=1)
both adding the block=c(40,40) as well as omitting the nmax=40 tremendously
increased the computing time you needed, the second even more (in an O(n^2)
manner) than the first.
--
Edzer
I used the above modified codes from krige(gstat ) example to see the
effect of "nsim", but unfortunately, it took a longer time and cannot get
the results. I guess it used the simulation method to test the model, not
what i want. (My system is XP, R2.10.0, gstat09.-64.)
Anybody can give me further information on generating the conditional
simulations from a theoretical model just like the unconditional examples
that Tomislav provided?
Thanks a lot.
2010/1/31 Tomislav Hengl <he...@spatial-analyst.net>
Dear rusers.sh,
Here are few simple examples of how to simulate (not-normal)
distributions and point processes using geoR and spatstat:
http://spatial-analyst.net/book/node/388
See also:
http://leg.ufpr.br/geoR/geoRdoc/vignette/geoRintro/geoRintrose8.html#x9-120008
I guess that covariates can be also included (I guess that you then need
to switch to conditional simulations - not sure).
This should also work for lattice (polygon) data so that you will have
jumps in values (but I guess you would still work in gridded systems?).
T. Hengl
http://home.medewerker.uva.nl/t.hengl/
rusers.sh wrote:
Hi all,
In classical statistics, we always need to generate a theoretical model
such as y=a+b1*x1+b2*x2+e to study some new estimation content. I am
wondering how to generate the similar spatial dataset for a theoretical
model.
Say y is response variable, x1 and x2 are explanatory variables.
1. If y is a continous variable, how should we generate the dataset for
a
theoretical spatial point process model in R?
2. If y is a continous variable, how should we generate the dataset for
a
theoretical spatial lattice data model in R?
3. If y is 0/1 binary variable, how should we generate the dataset for a
theoretical spatial point process model in R?
4. If y is 0/1 binary variable, how should we generate the dataset for a
ttheoretical spatial lattice data in R?
spatstat and other packages allow us to generate a dataset of a
specified
point process and other models, but it seems that they donot allow us to
include possible explanatory variables into a theoretical model. Maybe i
missed some ideas in them.
Anybody can express some ideas or point out some useful resources on
the
above four different situations? Small examples in R are preferred.
Thanks a lot.
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--
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of M?nster Weseler Stra?e
253, 48151 M?nster, Germany. Phone: +49 251 8333081, Fax: +49 251 8339763
http://ifgi.uni-muenster.de http://www.52north.org/geostatistics
e.pebe...@wwu.de
--
-----------------
Jane Chang
Queen's
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