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m_Section 16 (INLA)
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######################## Install inla
###### Inlaのインストールについては下記も参照ください：
## https://www.r-inla.org/download-install
install.packages("INLA",repos=c(getOption("repos"),INLA="https://inla.r-inla-download.org/R/stable"), dep=TRUE)
### or install.packages("INLA",repos=c(getOption("repos"),INLA="https://inla.r-inla-download.org/R/testing"), dep=TRUE)
### For Windows
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install(c("graph", "Rgraphviz"), dep=TRUE)
########################
library(INLA)
names(inla.models()$likelihood)
names(inla.models()$latent)
inla.list.models()
####################################################
########### example 1: disease mapping #############
####################################################
#install.packages( c( "spdep", "CARBayesdata", "sf", "RColorBrewer", fmesher ) )
library(spdep);library(CARBayesdata);library(RColorBrewer);library(fmesher)
##### pollutionhealth data
data(pollutionhealthdata)
##### Adjacency matrix
data(GGHB.IZ)
W.nb <- poly2nb(GGHB.IZ)
W <- nb2mat(W.nb, style = "B")
#### Poisson regression
formula <- observed ~ offset(log(expected)) + jsa + price + pm10
res <- inla(formula=formula, data=pollutionhealthdata, family="poisson",
control.compute = list(dic = TRUE))
summary(res)
#### Poisson CAR model with group effects
pollutionhealthdata$ID <- as.integer(pollutionhealthdata$IZ) # zone ID
formula <- observed ~ pm10 + jsa + offset(log(expected)) +
f(ID, model = "besag", graph= W) + f(year, model="iid")
res <- inla(formula=formula, data=pollutionhealthdata, family="nbinomial",
control.compute = list(dic = TRUE))
summary(res)
#### Estimated group effects
res$summary.random[[1]][1:4,]
res$summary.random[[2]]
#### Predicted values
pred <-res$summary.fitted.values
pred[1:4,]
#### Plot the predicted value (posterior mean)
year <- 2011
dat2011 <- pollutionhealthdata[pollutionhealthdata$year==year,]
dat2011$pred<- pred$mean[pollutionhealthdata$year==year]
data(GGHB.IZ)
dat <- merge(x=GGHB.IZ, y=dat2011, by="IZ", all.x=FALSE, duplicateGeoms = TRUE)
dat2 <- st_as_sf(dat)
nc <- 11
breaks <- seq(10, 200, len=nc+1)
pal <- rev(brewer.pal(nc, "RdYlBu"))
plot(dat2[, c("observed", "pred")], pal=pal, breaks=breaks, axes=TRUE, lwd=0.1)
####################################################
########### example 2: spatial prediction ##########
####################################################
# install.packages( c("gstat", "sf") )
library(sf); library(sp)#library(gstat);
##### Meuse data
data(meuse)
data(meuse.grid)
y <- meuse[,c("zinc")]
x <- meuse[,c("dist","ffreq")]
coords <- as.matrix( meuse[,c("x","y")] )
x0 <- meuse.grid[,c("dist","ffreq")]
coords0 <- as.matrix( meuse.grid[,c("x","y")] )
##### Generate mesh
# This part is updated because use of fm_mesh_2d is now recommended
mesh1 <- fm_mesh_2d( loc=coords, max.edge = c(1000,1000))
mesh2 <- fm_mesh_2d( loc=coords, max.edge = c(300,1000))
mesh3 <- fm_mesh_2d( loc=coords, max.edge = c(300,300))
mesh4 <- fm_mesh_2d( loc=coords, max.edge = c(300,1000),cutoff=200)
mesh5 <- fm_mesh_2d( loc=coords, max.edge = c(300,1000),offset=c(-0.3,-0.1))
mesh6 <- fm_mesh_2d( loc=coords, max.edge = c(300,1000),offset=c(-0.1,-0.3))
### or
#mesh1 <- inla.mesh.2d( loc=coords, max.edge = c(1000,1000))
#mesh2 <- inla.mesh.2d( loc=coords, max.edge = c(300,1000))
#mesh3 <- inla.mesh.2d( loc=coords, max.edge = c(300,300))
#mesh4 <- inla.mesh.2d( loc=coords, max.edge = c(300,1000),cutoff=200)
#mesh5 <- inla.mesh.2d( loc=coords, max.edge = c(300,1000),offset=c(-0.3,-0.1))
#mesh6 <- inla.mesh.2d( loc=coords, max.edge = c(300,1000),offset=c(-0.1,-0.3))
plot(mesh1, asp=1);points(coords, col="red",pch=20,cex=0.7)
plot(mesh2, asp=1);points(coords, col="red",pch=20,cex=0.7)
plot(mesh3, asp=1);points(coords, col="red",pch=20,cex=0.7)
plot(mesh4, asp=1);points(coords, col="red",pch=20,cex=0.7)
plot(mesh5, asp=1);points(coords, col="red",pch=20,cex=0.7)
plot(mesh6, asp=1);points(coords, col="red",pch=20,cex=0.7)
##########################################################
##### Conventional geostatistical modeling ###############
##### Pre-processing
spde <- inla.spde2.matern(mesh=mesh2, alpha=0.5)
A <- inla.spde.make.A( mesh=mesh2, loc=coords )
stk <- inla.stack(data=list(y=y), A=list(1, A), tag="obs",
effects=list(data.frame(intercept=1, dist=x$dist, ffreq=x$ffreq), s=1:spde$n.spde))
A0 <- inla.spde.make.A(mesh=mesh2, loc=coords0)
stk0 <- inla.stack(data=list(y=NA), A=list(1, A0), tag="mis",
effects=list( data.frame(intercept=1, dist=x0$dist, ffreq=x0$ffreq),s=1:spde$n.spde))
stk.full<- inla.stack(stk, stk0)
stk.data<- inla.stack.data(stk.full)
stk.A <- inla.stack.A(stk.full)
##### Geostatistical modeling and prediction
mod <- inla( log(y) ~ 0 + intercept + dist + ffreq + f(s, model=spde), data=stk.data,
control.predictor=list( A=stk.A ), family="gaussian")
mis.ind <- inla.stack.index(stk.full, tag="mis")$data
pred <- mod$summary.fitted.values[mis.ind, "mean"]
pred_sd <- mod$summary.fitted.values[mis.ind, "sd"]
##### Plot the predicted values
meuse.grid_sf <- st_as_sf(meuse.grid, coords = c("x", "y"), crs = 28992)
meuse.grid_sf$pred <-pred
meuse.grid_sf$pred_sd<-pred_sd
plot(meuse.grid_sf[, "pred"], axes=TRUE, pch=15)
plot(meuse.grid_sf[, "pred_sd"], axes=TRUE, pch=15)
########################################################################
##### Geostatistical modeling considering physical barrier #############
##### [a] Constrained by the Meuse river
data(meuse.riv)
xlim <- c(min(meuse.grid[,1])-100, max(meuse.grid[,1])+100)
ylim <- c(min(meuse.grid[,2])-100, max(meuse.grid[,2])+100)
meuse.riv<- meuse.riv[meuse.riv[,1]>xlim[1] & meuse.riv[,1]<xlim[2] & meuse.riv[,2]>ylim[1] & meuse.riv[,2]<ylim[2],]
meuse.lst<- list(Polygons(list(Polygon(meuse.riv)),"meuse.riv"))
meuse.sr <- SpatialPolygons(meuse.lst)
segment <- inla.sp2segment(meuse.sr)
mesh_b1 <- fm_mesh_2d( loc=coords, max.edge = 300, interior =segment)
#or mesh_b1 <- inla.mesh.2d( loc=coords, max.edge = 300, interior =segment)
##### [b] Constrained by the study area
# This part is uodated because rgeos package is retired
meuse.grid_sp<-meuse.grid
coordinates(meuse.grid_sp) = c("x", "y")
gridded(meuse.grid_sp) <- TRUE
meuse.grid_sp <- as(meuse.grid_sp, "SpatialPolygons")
meuse.grid_sf <- st_as_sf(meuse.grid_sp)
meuse.area_sf <- st_union(meuse.grid_sf)
mesh_b2 <- fm_mesh_2d(loc = coords, max.edge = 300, boundary = fm_segm(meuse.area_sf))
##### Spatial prediction under [a] or [b] ##########
##### Pre-processing
mesh2 <-mesh_b2 ## or mesh_b2
plot(mesh2, asp=1);points(coords, col="red",pch=20,cex=0.7)
spde<- inla.spde2.matern(mesh=mesh2, alpha=1.5)
A <- inla.spde.make.A( mesh=mesh2, loc=coords)
stk <- inla.stack(data=list(y=y), A=list(1, A), tag="obs",
effects=list(data.frame(intercept=1,dist=x$dist, ffreq=x$ffreq), s=1:spde$n.spde))
A0 <- inla.spde.make.A(mesh=mesh2, loc=coords0)
stk0 <- inla.stack(data=list(y=NA), A=list(1, A0), tag="mis",
effects=list( data.frame(intercept=1,dist=x0$dist, ffreq=x0$ffreq), s=1:spde$n.spde))
stk.full <- inla.stack(stk, stk0)
stk.data <- inla.stack.data(stk.full)
stk.A <- inla.stack.A(stk.full)
##### Geostatistical modeling and prediction
mod <- inla( log(y) ~ 0 + intercept + dist + ffreq + f(s, model=spde), data=stk.data,
control.predictor=list( A=stk.A),family="gaussian")
mis.ind<- inla.stack.index(stk.full, tag="mis")$data
pred <- mod$summary.fitted.values[mis.ind, "mean"]
pred_sd<- mod$summary.fitted.values[mis.ind, "sd"]
meuse.grid_sf$pred2 <-pred
meuse.grid_sf$pred2_sd<-pred_sd
##### Plot the predicted values
plot(meuse.grid_sf[, "pred2"], axes=TRUE, pch=15,border=NA)
plot(meuse.grid_sf[, "pred2_sd"], axes=TRUE, pch=15,border=NA)