[R-sig-Geo] generate simulation data for a theoretical spatial model

Wed Feb 3 12:55:30 CET 2010

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.pebesma at 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 <hengl at 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.
>>>>>
>>>>>
>>>>>
>>>>>
>>>> _______________________________________________
>>>> R-sig-Geo mailing list
>>>> R-sig-Geo at stat.math.ethz.ch
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>>>>
>>>>
>>>>
>>>
>>>
>>>
>>>
>>>
>>
>> --
>> 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.pebesma at wwu.de
>>
>>
>
>
> -- 
> -----------------
> Jane Chang
> Queen's
>
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