Introduction to the multiocc package
library(interp)
library(MCMCpack)
#> Loading required package: coda
#> Loading required package: MASS
#>
#> Attaching package: 'MASS'
#> The following object is masked from 'package:interp':
#>
#> area
#> ##
#> ## Markov Chain Monte Carlo Package (MCMCpack)
#> ## Copyright (C) 2003-2026 Andrew D. Martin, Kevin M. Quinn, and Jong Hee Park
#> ##
#> ## Support provided by the U.S. National Science Foundation
#> ## (Grants SES-0350646 and SES-0350613)
#> ##
library(tmvtnorm)
#> Loading required package: mvtnorm
#> Loading required package: Matrix
#> Loading required package: stats4
#> Loading required package: gmm
#> Loading required package: sandwich
library(truncnorm)
library(multiocc)
library(MASS)
library(corrplot)
#> corrplot 0.95 loaded
library(fields)
#> Loading required package: spam
#> Spam version 2.11-3 (2026-01-05) is loaded.
#> Type 'help( Spam)' or 'demo( spam)' for a short introduction
#> and overview of this package.
#> Help for individual functions is also obtained by adding the
#> suffix '.spam' to the function name, e.g. 'help( chol.spam)'.
#>
#> Attaching package: 'spam'
#> The following object is masked from 'package:stats4':
#>
#> mle
#> The following object is masked from 'package:Matrix':
#>
#> det
#> The following objects are masked from 'package:mvtnorm':
#>
#> rmvnorm, rmvt
#> The following objects are masked from 'package:base':
#>
#> backsolve, forwardsolve
#> Loading required package: viridisLite
#> Loading required package: RColorBrewer
#>
#> Try help(fields) to get started.data(detection)
data(occupancy)
data(coords)
DataNames <- list("species"=colnames(detection)[4:9],
"detection"=c("duration"),"occupancy"=c("forest","elev"))
model.input <- multioccbuild(detection, occupancy, coords, DataNames, threshold = 15000)
#> Warning: Rows in detection with missing covariates have been removed for purposes of fitting the model, but the site/season combination is retained in occupancy and therefore predictions will be outputted.Perform some exploratory data analysis
par(mfrow=c(1,3))
hist(occupancy$forest, main="", xlab="Forest")
hist(occupancy$elev, main="", xlab="Elevation")
hist(detection$duration, main="", xlab="Duration")
par(mfrow=c(3,2), mar=c(3,3,3,1))
quilt.plot(coords[,2:3], occupancy$forest[1:267], main="Forest Cover", zlim=c(-1.5,3))
fit <- Tps(coords[,2:3], occupancy$forest[1:267])
out <- predictSurface(fit, df=100)
image.plot(out, main="Forest Cover (interpolated)", zlim=c(-1.5,2))
quilt.plot(coords[,2:3], occupancy$elev[1:267], main="Elevation", zlim=c(-1.5,3.5))
fit <- Tps(coords[,2:3], occupancy$elev[1:267])
out <- predictSurface(fit, df=100)
image.plot(out, main="Elevation (interpolated)", zlim=c(-1.5,2))
quilt.plot(coords[,2:3], detection$duration[1:267], main="Duration", zlim=c(-2.5,3))
fit <- Tps(coords[,2:3], detection$duration[1:267])
out <- predictSurface(fit, df=100)
image.plot(out, main="Duration (Survey 1)", zlim=c(-2.5,2.5))
A short run for demonstration purposes
## Shorter run for demonstration purposes.
## library(tmvtnorm)
mcmc.out <- GibbsSampler(M.iter=10, M.burn=1, M.thin=1, model.input, q=10, sv=FALSE)
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%A longer run (not executed) for scientific results
Can summarize output
summary(mcmc.out$samples$alpha)
#>
#> Iterations = 1:9
#> Thinning interval = 1
#> Number of chains = 1
#> Sample size per chain = 9
#>
#> 1. Empirical mean and standard deviation for each variable,
#> plus standard error of the mean:
#>
#> Mean SD Naive SE Time-series SE
#> Great.tit Int 0.67685 0.08350 0.027834 0.054377
#> Great.tit forest -0.09610 0.02727 0.009090 0.009090
#> Great.tit elev -0.14975 0.04430 0.014768 0.026787
#> Blue.tit Int 0.44738 0.07733 0.025777 0.025777
#> Blue.tit forest -0.08451 0.02269 0.007565 0.007565
#> Blue.tit elev -0.18559 0.04679 0.015595 0.030371
#> Coal.tit Int 0.78209 0.11151 0.037170 0.074384
#> Coal.tit forest -0.01991 0.02047 0.006822 0.012722
#> Coal.tit elev -0.09226 0.03082 0.010273 0.020919
#> Crested.tit Int 0.55876 0.11075 0.036918 0.076343
#> Crested.tit forest -0.04567 0.04742 0.015807 0.032240
#> Crested.tit elev -0.07466 0.03652 0.012172 0.012172
#> Marsh.tit Int 0.31092 0.09203 0.030677 0.055269
#> Marsh.tit forest -0.04797 0.02279 0.007595 0.007595
#> Marsh.tit elev -0.22338 0.09767 0.032557 0.077301
#> Willow.tit Int 0.09057 0.06786 0.022620 0.039116
#> Willow.tit forest 0.08367 0.01744 0.005814 0.005814
#> Willow.tit elev 0.03986 0.03580 0.011933 0.015008
#>
#> 2. Quantiles for each variable:
#>
#> 2.5% 25% 50% 75% 97.5%
#> Great.tit Int 0.52131 0.66320 0.70977 0.7223741 0.75723
#> Great.tit forest -0.13706 -0.11002 -0.09497 -0.0904783 -0.04947
#> Great.tit elev -0.20130 -0.18542 -0.15813 -0.1252374 -0.07509
#> Blue.tit Int 0.31764 0.38962 0.46177 0.4889005 0.55158
#> Blue.tit forest -0.11226 -0.09740 -0.09009 -0.0827571 -0.04213
#> Blue.tit elev -0.23439 -0.21441 -0.20894 -0.1549234 -0.10154
#> Coal.tit Int 0.59039 0.73418 0.79962 0.8481661 0.91982
#> Coal.tit forest -0.04620 -0.03326 -0.02437 0.0005934 0.01026
#> Coal.tit elev -0.13625 -0.10871 -0.10199 -0.0758144 -0.04674
#> Crested.tit Int 0.38245 0.50706 0.57020 0.6231967 0.70578
#> Crested.tit forest -0.09056 -0.07926 -0.06161 -0.0402808 0.03736
#> Crested.tit elev -0.11693 -0.10264 -0.07998 -0.0646828 -0.00937
#> Marsh.tit Int 0.15356 0.26180 0.33033 0.3781374 0.41793
#> Marsh.tit forest -0.07886 -0.06423 -0.04814 -0.0331432 -0.01516
#> Marsh.tit elev -0.30610 -0.29629 -0.27002 -0.1567000 -0.05583
#> Willow.tit Int -0.03889 0.05858 0.11954 0.1231798 0.15621
#> Willow.tit forest 0.05963 0.07481 0.08266 0.0911714 0.10975
#> Willow.tit elev -0.01934 0.02520 0.05027 0.0631018 0.08047
summary(mcmc.out$samples$rho)
#>
#> Iterations = 1:9
#> Thinning interval = 1
#> Number of chains = 1
#> Sample size per chain = 9
#>
#> 1. Empirical mean and standard deviation for each variable,
#> plus standard error of the mean:
#>
#> Mean SD Naive SE Time-series SE
#> Great.tit rho 0.8322 0.17105 0.05702 0.09978
#> Blue.tit rho 0.8293 0.10245 0.03415 0.03415
#> Coal.tit rho 0.5962 0.13438 0.04479 0.05355
#> Crested.tit rho 0.9193 0.05637 0.01879 0.01879
#> Marsh.tit rho 0.9147 0.06801 0.02267 0.04032
#> Willow.tit rho 0.9380 0.06482 0.02161 0.05126
#>
#> 2. Quantiles for each variable:
#>
#> 2.5% 25% 50% 75% 97.5%
#> Great.tit rho 0.5122 0.7274 0.8913 0.9218 0.9946
#> Blue.tit rho 0.6311 0.7990 0.8527 0.8943 0.9251
#> Coal.tit rho 0.3718 0.5063 0.6233 0.7094 0.7308
#> Crested.tit rho 0.8176 0.8951 0.9380 0.9445 0.9823
#> Marsh.tit rho 0.7882 0.8831 0.9365 0.9542 0.9819
#> Willow.tit rho 0.8284 0.8954 0.9770 0.9874 0.9894Visualize correlation matrix
par(mfrow=c(1,1), mar=c(3,3,3,1))
sigout <- mcmc.out$samples$sig
Sig <- matrix(colMeans(sigout),6,6)
SpeciesCor <- cov2cor(Sig)
rownames(SpeciesCor) <- DataNames$species
colnames(SpeciesCor) <- DataNames$species
corrplot::corrplot(SpeciesCor)
Make predictions from fitted model
y.agg1 <- aggregate(model.input$y[,1], by=list(model.input$detection.info$siteID,
model.input$detection.info$season), FUN=sum, na.rm=TRUE)
y.plot1 <- 1*(y.agg1$x>0)
y.agg2 <- aggregate(model.input$y[,2], by=list(model.input$detection.info$siteID,
model.input$detection.info$season), FUN=sum, na.rm=TRUE)
y.plot2 <- 1*(y.agg2$x>0)
y.agg3 <- aggregate(model.input$y[,3], by=list(model.input$detection.info$siteID,
model.input$detection.info$season), FUN=sum, na.rm=TRUE)
y.plot3 <- 1*(y.agg3$x>0)
y.agg4 <- aggregate(model.input$y[,4], by=list(model.input$detection.info$siteID,
model.input$detection.info$season), FUN=sum, na.rm=TRUE)
y.plot4 <- 1*(y.agg4$x>0)
y.agg5 <- aggregate(model.input$y[,5], by=list(model.input$detection.info$siteID,
model.input$detection.info$season), FUN=sum, na.rm=TRUE)
y.plot5 <- 1*(y.agg5$x>0)
y.agg6 <- aggregate(model.input$y[,6], by=list(model.input$detection.info$siteID,
model.input$detection.info$season), FUN=sum, na.rm=TRUE)
y.plot6 <- 1*(y.agg6$x>0)
for (yr in c(1,4,7,10)){
print(yr)
range <- which(model.input$occupancy.info$season == yr)
psiout <- mcmc.out$samples$psi
#pout <- mcmc.out$p
dim(psiout)
psi1 <- apply(psiout[,0*2670+range],2,mean)
psi2 <- apply(psiout[,1*2670+range],2,mean)
psi3 <- apply(psiout[,2*2670+range],2,mean)
psi4 <- apply(psiout[,3*2670+range],2,mean)
psi5 <- apply(psiout[,4*2670+range],2,mean)
psi6 <- apply(psiout[,5*2670+range],2,mean)
par(mfrow=c(3,2), mar=c(1,3,3,1))
fit <- Tps(coords[1:267,2:3], psi1)
out <- predictSurface(fit, df=100)
image.plot(out, main="Great Tit", zlim=c(-0.01,1.01))
mtext(paste("Year",yr), side=3, line=-2, outer=TRUE)
y.plot1.in <- y.plot1[which(model.input$occupancy.info$season ==yr)]
points(coords[which(y.plot1.in==1),2:3])
fit <- Tps(coords[1:267,2:3], psi2)
out <- predictSurface(fit, df=100)
image.plot(out, main="Blue Tit", zlim=c(-0.01,1.01))
y.plot2.in <- y.plot2[which(model.input$occupancy.info$season ==yr)]
points(coords[which(y.plot2.in==1),2:3])
fit <- Tps(coords[1:267,2:3], psi3)
out <- predictSurface(fit, df=100)
image.plot(out, main="Coal Tit", zlim=c(-0.01,1.01))
y.plot3.in <- y.plot3[which(model.input$occupancy.info$season ==yr)]
points(coords[which(y.plot3.in==1),2:3])
fit <- Tps(coords[1:267,2:3], psi4)
out <- predictSurface(fit, df=100)
image.plot(out, main="Crested Tit", zlim=c(-0.01,1.01))
y.plot4.in <- y.plot4[which(model.input$occupancy.info$season ==yr)]
points(coords[which(y.plot4.in==1),2:3])
fit <- Tps(coords[1:267,2:3], psi5)
out <- predictSurface(fit, df=100)
image.plot(out, main="Marsh Tit", zlim=c(-0.01,1.01))
y.plot5.in <- y.plot5[which(model.input$occupancy.info$season ==yr)]
points(coords[which(y.plot5.in==1),2:3])
fit <- Tps(coords[1:267,2:3], psi6)
out <- predictSurface(fit, df=100)
image.plot(out, main="Willow Tit", zlim=c(-0.01,1.01))
y.plot6.in <- y.plot6[which(model.input$occupancy.info$season ==yr)]
points(coords[which(y.plot6.in==1),2:3])
}
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