Description Details Author(s) References Examples
Code to facilitate simulation and inference of connectivity defined by random walks.
This package contains code to simulate (rGenWish) and evaluate the likelihood of (dGenWish) distance matrices from the Generalized Wishart distribution. It also contains helper functions to create and manage spatial covariance models created from landscape grids with resistance or conductance defined by landscape features.
Ephraim M. Hanks
Maintainer: Ephraim M. Hanks
McCullagh 2009. Marginal likelihood for distance matrices. Statistica Sinica 19: 631-649.
Hanks and Hooten 2013. Circuit theory and model-based inference for landscape connectivity. Journal of the American Statistical Association. 108(501), 22-33.
Hanks 2017. Modeling spatial covariance using the limiting distribution of spatio-temporal random walks. Journal of the American Statistical Association.
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## The following code conducts a simulation example by
## first simulating a heterogeneous landscape, then
## simulating pairwise distance data on the landscape
## and finally making inference on model parameters.
library(rwc)
library(MASS)
## source("GenWishFunctions_20170901.r")
##
## specify 2-d raster
##
ras=raster(nrow=30,ncol=30)
extent(ras) <- c(0,30,0,30)
values(ras) <- 1
plot(ras,asp=1)
ras
int=ras
cov.ras=ras
## simulate "resistance" raster
TL.int=get.TL(int)
Q.int=get.Q(TL.int,1)
set.seed(1248)
## values(cov.ras) <- as.numeric(rnorm.Q(Q.int
values(cov.ras) <- as.numeric(rnorm.Q(Q.int,zero.constraint=TRUE))
plot(cov.ras)
stack=stack(int,cov.ras)
plot(stack)
TL=get.TL(stack)
## Create "barrier" raster which has no effect, to test model selection
barrier=int
values(barrier) <- 0
barrier[,10:11] <- 1
plot(barrier)
TL.all=get.TL(stack(int,cov.ras,barrier))
##
## sampling locations
##
nsamps=150
set.seed(4567)
samp.xy=cbind(runif(nsamps,0,30),runif(nsamps,0,30))
## samp.xy=samp.xy[rep(1:nsamps,times=5),]
samp.locs=cellFromXY(int,samp.xy)
samp.cells=unique(samp.locs)
nsamps=nrow(samp.xy)
plot(cov.ras)
points(samp.xy)
K=matrix(0,nrow=nsamps,ncol=length(samp.cells))
for(i in 1:nsamps){
K[i,which(samp.cells==samp.locs[i])]=1
}
image(K)
##
## beta values
##
betas=c(-2,-1)
tau=.01
Q=get.Q(TL,betas)
Phi=get.Phi(Q,samp.cells)
## simulate from ibr model
D.rand.ibr=rGenWish(df=20,Sigma=K%*%ginv(as.matrix(Phi))%*%t(K) + diag(nsamps)*tau)
image(D.rand.ibr)
## crude plot of geographic distance vs genetic distance
plot(as.numeric(as.matrix(dist(xyFromCell(ras,samp.locs)))),as.numeric(D.rand.ibr))
###################################
##
##
## fitting using optim
##
##
nll.gen.wish.icar <- function(theta,D,df,TL,obs.idx){
## get K
cells.idx=unique(obs.idx)
n.cells=length(cells.idx)
n.obs=length(obs.idx)
K <- matrix(0, nrow = n.obs, ncol = n.cells)
for (i in 1:n.obs){
K[i, which(cells.idx == obs.idx[i])] <- 1
}
## get precision matrix of whole graph
tau=exp(theta[1])
beta=theta[-1]
Q=get.Q(TL,beta)
## get precision matrix of observed nodes
max.diag=max(diag(Q))
Q=Q/max.diag
Phi=get.Phi(Q,cells.idx)
## get covariance matrix of observations
Sigma.nodes=ginv(as.matrix(Phi))
Sigma.nodes=Sigma.nodes/max.diag
Psi=K%*%Sigma.nodes%*%t(K)+tau*diag(nrow(K))
## get nll
nll=-dGenWish(D,Psi,df,log=TRUE)
nll
}
fit=optim(c(log(tau),betas),nll.gen.wish.icar,D=D.rand.ibr,df=20,TL=TL,
obs.idx=samp.locs,control=list(trace=10),hessian=TRUE)
fit.all=optim(c(log(tau),betas,0),nll.gen.wish.icar,D=D.rand.ibr,df=20,TL=TL.all,
obs.idx=samp.locs,control=list(trace=10),hessian=FALSE)
fit.ibd=optim(c(log(tau),0),nll.gen.wish.icar,D=D.rand.ibr,df=20,TL=TL.int,
obs.idx=samp.locs,control=list(trace=10),hessian=FALSE)
## model selection using AIC
aic.ibr=2*fit$value + 2*length(fit$par)
aic.all=2*fit.all$value + 2*length(fit.all$par)
aic.ibd=2*fit.ibd$value + 2*length(fit.ibd$par)
aic.ibr
aic.all
aic.ibd
## se's for best fit
str(fit)
## get standard errors from optim
H=fit$hessian
S=solve(H)
se=sqrt(diag(S))
se
## CI's for best fit
CImat=matrix(NA,3,4)
rownames(CImat) <- c("log(tau)","intercept","resistance")
colnames(CImat) <- c("truth","estimate","lower95CI","upper95CI")
CImat[,1]=c(log(tau),betas)
CImat[,2]=fit$par
CImat[,3]=fit$par-1.96*se
CImat[,4]=fit$par+1.96*se
CImat
## End(Not run)
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