generate simulation data for a theoretical spatial model
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.
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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.pebesma at wwu.de
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