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60_Species_Distribution_Modelling.Rmd
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# Species distribution modelling
Exercise scripts are at the bottom of this page.
## SDM introduction and review
What are species distribution models?
[Presentation (PDF)](./course_material/Course 1 Tuesday What_are_SDM.pdf)
### References
- [Araujo and Guisan 2006](./course_material/literature/Araujo _ Guisan2006.pdf)
- [Elith 2006](./course_material/literature/Elith 2006.pdf)
- [Elith and Leathwick 2009](./course_material/literature/Elith and Leathwick 2009.pdf)
- [Guisan and Zimmermann 2000](./course_material/literature/guisan and zimmermann 2000.pdf)
- [Peterson 2011](./course_material/literature/Peterson 2011.pdf)
- [Soberon and Peterson 2005](./course_material/literature/Soberon Peterson 2005.pdf)
## SDM outputs
Understand and generate SDM outputs.
[Presentation (PDF)](./course_material/Course 3 Tuesday_ SDM outputs.pdf)
### References
- [Elith et al. 2010](./course_material/literature/Elith_et_al-2010.pdf)
- [Guillaumot et al. 2018 Ecol & Evol](./course_material/literature/Guillaumot et al 2018-Ecology_and_Evolution.pdf)
- [Liu et al. 2013](./course_material/literature/liu 2013.pdf)
- [Torres 2015](./course_material/literature/Torres 2015.PDF)
## Calibration
What you should know before running a model.
[Presentation (PDF)](./course_material/Course 5 Calibration- all you should think about before running a model.pdf)
### References
- [Appendix S1 Elith 2008](./course_material/literature/Appendix S1 Elith 2008.pdf)
- [Barbet-Massin et al. 2012](./course_material/literature/Barbet-Massin_et_al-2012.pdf)
- [Barve 2011](./course_material/literature/Barve 2011.pdf)
- [Boria 2014](./course_material/literature/Boria 2014.pdf)
- [Brotons 2004](./course_material/literature/Brotons 2004.pdf)
- [Elith et al. 2008](./course_material/literature/Elith_et_al-2008.pdf)
- [Elith et al. 2010](./course_material/literature/Elith_et_al-2010.pdf)
- [Guillaumot et al. 2018 Ecol & Evol](./course_material/literature/Guillaumot et al 2018-Ecology_and_Evolution.pdf)
- [Guillaumot et al. 2019](./course_material/literature/Guillaumot et al. 2019_ Progress in Oceano.pdf)
- [Guillaumot et al. 2018 MEPS](./course_material/literature/Guillaumot et al 2018 MEPS final version.pdf)
- [Muscarella et al. 2014](./course_material/literature/Muscarella_et_al-2014-Methods_in_Ecology_and_Evolution.pdf)
- [Phillips et al. 2009](./course_material/literature/Phillips 2009.pdf)
- [Wisz and Guisan 2009](./course_material/literature/Wisz Guisan 2009.pdf)
## Exercise scripts
**Exercise - Run your first SDM**
[SDM_EXERCISE.pdf](./course_material/exercises/SDM_EXERCISE.pdf)
**Final practical work**
Run models, compare different model calibrations and compare your model outputs!
[SDM_FINAL.pdf](./course_material/exercises/SDM_FINAL.pdf)
**Other scripts**
[calibration_BRT.R](./course_material/exercises/scripts/calibration_BRT.R)
```{r eval = FALSE}
#### Open environmental data and occurrences (run_yOur_SDM.R file)
#---------------------------------------------------------
# compute there the MATRIX_OCC_ENVI variable (1 set)
# in the run_yOur_SDM.R file, run until the MyFold definition
# for set.seed(1) (j=1)
# run the model and compare the predictive deviance according to the set of parameters chosen
#=============================================================
source("scripts/Function_gbm.R")
tc=4 # tree complexity
lr=0.011 # learning rate
bf=0.8 # bag fraction
model.res<- gbm.step_v2 (data=MATRIX_OCC_ENVI,
gbm.x = 2:ncol(MATRIX_OCC_ENVI),
gbm.y = 1,
family = "bernoulli",
n.folds=4,
fold.vector = MyFold,
tree.complexity = tc,
learning.rate = lr,
bag.fraction =bf)
model1<-model.res # tc3 lr0.001 bf=0.8 nbt 10000
model2<-model.res # tc4 lr0.001 bf=0.8 nbt 10000
model3<-model.res # tc4 lr0.005 bf=0.8 nbt 10000
model4<-model.res # tc3 lr0.005 bf=0.8 nbt 10000
model5<-model.res # tc4 lr0.01 bf=0.8 nbt 10000
model6<-model.res # tc4 lr0.008 bf=0.8 nbt 10000
model7<-model.res # tc4 lr0.005 bf=0.9 nbt 10000
model8<-model.res # tc4 lr0.011 bf=0.8 nbt 10000
# GENERATE THE PLOTS
tree.list1 <- seq(100, model1$gbm.call$best.trees, by = 100)
tree.list2 <- seq(100, model2$gbm.call$best.trees, by = 100)
tree.list3 <- seq(100, model3$gbm.call$best.trees, by = 100)
tree.list4 <- seq(100, model4$gbm.call$best.trees, by = 100)
tree.list5 <- seq(100, model5$gbm.call$best.trees, by = 100)
tree.list6 <- seq(100, model6$gbm.call$best.trees, by = 100)
tree.list7 <- seq(100, model7$gbm.call$best.trees, by = 100)
tree.list8 <- seq(100, model8$gbm.call$best.trees, by = 100)
pred1 <- predict.gbm(model1,MATRIX_OCC_ENVI, n.trees = tree.list1, "response")
pred2 <- predict.gbm(model2,MATRIX_OCC_ENVI, n.trees = tree.list2, "response")
pred3 <- predict.gbm(model3,MATRIX_OCC_ENVI, n.trees = tree.list3, "response")
pred4 <- predict.gbm(model4,MATRIX_OCC_ENVI, n.trees = tree.list4, "response")
pred5 <- predict.gbm(model5,MATRIX_OCC_ENVI, n.trees = tree.list5, "response")
pred6 <- predict.gbm(model6,MATRIX_OCC_ENVI, n.trees = tree.list6, "response")
pred7 <- predict.gbm(model7,MATRIX_OCC_ENVI, n.trees = tree.list7, "response")
pred8 <- predict.gbm(model8,MATRIX_OCC_ENVI, n.trees = tree.list8, "response")
graphe.deviance1 <- rep(0,max(tree.list1)/100)
for (i in 1:length(graphe.deviance1)) {
graphe.deviance1 [i] <- calc.deviance(MATRIX_OCC_ENVI$id, pred1[,i],calc.mean=T)
}
graphe.deviance2 <- rep(0,max(tree.list2)/100)
for (i in 1:length(graphe.deviance2)) {
graphe.deviance2 [i] <- calc.deviance(MATRIX_OCC_ENVI$id, pred2[,i],calc.mean=T)
}
graphe.deviance3 <- rep(0,max(tree.list3)/100)
for (i in 1:length(graphe.deviance3)) {
graphe.deviance3 [i] <- calc.deviance(MATRIX_OCC_ENVI$id, pred3[,i],calc.mean=T)
}
graphe.deviance4 <- rep(0,max(tree.list4)/100)
for (i in 1:length(graphe.deviance4)) {
graphe.deviance4 [i] <- calc.deviance(MATRIX_OCC_ENVI$id, pred4[,i],calc.mean=T)
}
graphe.deviance5 <- rep(0,max(tree.list5)/100)
for (i in 1:length(graphe.deviance5)) {
graphe.deviance5 [i] <- calc.deviance(MATRIX_OCC_ENVI$id, pred5[,i],calc.mean=T)
}
graphe.deviance6 <- rep(0,max(tree.list6)/100)
for (i in 1:length(graphe.deviance6)) {
graphe.deviance6 [i] <- calc.deviance(MATRIX_OCC_ENVI$id, pred6[,i],calc.mean=T)
}
graphe.deviance7 <- rep(0,max(tree.list7)/100)
for (i in 1:length(graphe.deviance7)) {
graphe.deviance7 [i] <- calc.deviance(MATRIX_OCC_ENVI$id, pred7[,i],calc.mean=T)
}
graphe.deviance8 <- rep(0,max(tree.list8)/100)
for (i in 1:length(graphe.deviance8)) {
graphe.deviance8 [i] <- calc.deviance(MATRIX_OCC_ENVI$id, pred8[,i],calc.mean=T)
}
par(mai=c(0.5,0.5,0.5,0.5))
plot(tree.list1,graphe.deviance1,xlim = c(-100,4000), ylim=c(0,1),type='l', xlab = "number of trees",ylab = "predictive deviance", cex.lab = 1.5)
lines(tree.list2,graphe.deviance2,col="blue")
lines(tree.list3,graphe.deviance3,col="red")
lines(tree.list4,graphe.deviance4,col="green")
lines(tree.list5,graphe.deviance5,col="orange")
lines(tree.list6,graphe.deviance6,col="pink")
lines(tree.list7,graphe.deviance7,col="deepskyblue")
lines(tree.list8,graphe.deviance8,col="purple")
legend("topright",legend=c("tc3 lr0.001 bf=0.8","tc4 lr0.001 bf=0.8","tc4 lr0.005 bf=0.8 ","tc3 lr0.005 bf=0.8","tc4 lr0.01 bf=0.8","tc4 lr0.008 bf=0.8","tc4 lr0.005 bf=0.9","tc4 lr0.011 bf=0.8"),col=c("black","blue","red","green","orange","pink","deepskyblue","purple"),pch=16,cex=0.7)
```
[clock4_crossValidation.R](./course_material/exercises/scripts/clock4_crossValidation.R)
```{r eval = FALSE}
clock4 <- function(occ, bg.coords){
# the spatial sampling aims at defining areas containing either test or training data
# for the CLOCK-4 method, 4 triangle areas are defined, cutting the Southern Ocean circle into 4 equal areas. Three of these 4 areas contain the data that will be used to train the model, the other remaining one, the data that will be used to test the model after predictions
# the areas used to train and test the model are randomly defined at each loop step
#initialise vectors that are used to generate the spatial sampling structure
random_longA <- seq(0,179,1)
random_longB <- seq(-180,-1,1)
random_longC <- seq(0,180,1)
random_longD <- seq(-179,0,1)
random_long <- c(random_longA,random_longB,random_longC,random_longD)
# sample a number between -180 and 180 to define the random sampling transect
tirage <- sample(seq(181,541,1),1)
random_long_tirage <- random_long[tirage]
random_long_tirage_A1 <- random_long[tirage+90]
random_long_tirage_A2 <- random_long[tirage+180]
random_long_tirage_A3 <- random_long[tirage-90]
#random_long_tirage_A4 <- random_long[tirage-180]
## define training and test groups (composed of both presence and background data)
occ.grp <- rep(NA, nrow(occ))
bg.coords.grp <- rep(NA, nrow(bg.coords))
## define training and test groups (composed of both presence and background data)
presence_tot <- occ
background_data <- bg.coords
training_presences.occ1 <- NA;training_presences.occ3 <-NA
training_presences.occ1_part1 <- NA;training_presences.occ3_part1 <-NA
training_presences.occ1_part2 <- NA;training_presences.occ3_part2 <-NA
training_backgr.occ1 <- NA; training_backgr.occ3 <- NA
training_backgr.occ1_part1 <- NA; training_backgr.occ3_part1 <- NA
training_backgr.occ1_part2 <- NA; training_backgr.occ3_part2 <- NA
training_presences.occ2 <- NA;training_presences.occ4 <- NA
training_presences.occ2_part1 <- NA;training_presences.occ4_part1 <- NA
training_presences.occ2_part2 <- NA;training_presences.occ4_part2 <- NA
training_backgr.occ2 <- NA;training_backgr.occ4 <- NA
training_backgr.occ2_part1 <- NA;training_backgr.occ4_part1 <- NA
training_backgr.occ2_part2 <- NA;training_backgr.occ4_part2 <- NA
#---------------------
# TRAINING PRESENCES
#---------------------
### ZONE 1 ####
if (random_long_tirage <= 0 & random_long_tirage_A1 <=0){ # imply that A2 >= 0 and A3>=0
training_presences.occ1 <- which(presence_tot[,1] > random_long_tirage & presence_tot[,1] < random_long_tirage_A1)
training_backgr.occ1 <- which(background_data[,1] > random_long_tirage & background_data[,1] < random_long_tirage_A1)
}
if (random_long_tirage >= 0 & random_long_tirage_A1 >=0){
training_presences.occ1 <- which(presence_tot[,1] > random_long_tirage & presence_tot[,1] < random_long_tirage_A1)
training_backgr.occ1 <- which(background_data[,1] > random_long_tirage & background_data[,1] < random_long_tirage_A1)
}
if (random_long_tirage >= 0 & random_long_tirage_A1 <=0){
training_presences.occ1_part1 <- which(presence_tot[,1] > random_long_tirage & presence_tot[,1] < 180 )
training_presences.occ1_part2 <- which(presence_tot[,1] > -180 & presence_tot[,1] < random_long_tirage_A1 )
training_backgr.occ1_part1 <- which(background_data[,1] > random_long_tirage & background_data[,1] < 180 )
training_backgr.occ1_part2 <- which(background_data[,1] > -180 & background_data[,1] < random_long_tirage_A1 )
}
if (random_long_tirage <= 0 & random_long_tirage_A1 >=0){
training_presences.occ1_part1 <- which(presence_tot[,1] > random_long_tirage & presence_tot[,1] < 0 )
training_presences.occ1_part2 <- which(presence_tot[,1] > 0 & presence_tot[,1] < random_long_tirage_A1 )
training_backgr.occ1_part1 <- which(background_data[,1] > random_long_tirage & background_data[,1] < 0 )
training_backgr.occ1_part2 <- which(background_data[,1] > 0 & background_data[,1] < random_long_tirage_A1 )
}
### ZONE 2 ####
if (random_long_tirage_A1 <= 0 & random_long_tirage_A2 <=0){
training_presences.occ2 <- which(presence_tot[,1] > random_long_tirage_A1 & presence_tot[,1] < random_long_tirage_A2 )
training_backgr.occ2 <- which(background_data[,1] > random_long_tirage_A1 & background_data[,1] < random_long_tirage_A2)
}
if (random_long_tirage_A1 >= 0 & random_long_tirage_A2 >=0){
training_presences.occ2 <- which(presence_tot[,1] > random_long_tirage_A1 & presence_tot[,1] < random_long_tirage_A2 )
training_backgr.occ2 <- which(background_data[,1] > random_long_tirage_A1 & background_data[,1] < random_long_tirage_A2)
}
if (random_long_tirage_A1 >= 0 & random_long_tirage_A2 <=0){
training_presences.occ2_part1 <- which(presence_tot[,1] > random_long_tirage_A1 & presence_tot[,1] < 180)
training_presences.occ2_part2 <- which(presence_tot[,1] > -180 & presence_tot[,1] < random_long_tirage_A2)
training_backgr.occ2_part1 <- which(background_data[,1] > random_long_tirage_A1 & background_data[,1] < 180)
training_backgr.occ2_part2 <- which(background_data[,1] > -180 & background_data[,1] < random_long_tirage_A2)
}
if (random_long_tirage_A1 <= 0 & random_long_tirage_A2 >=0){
training_presences.occ2_part1 <- which(presence_tot[,1] > random_long_tirage_A1 & presence_tot[,1] < 0 )
training_presences.occ2_part2 <- which(presence_tot[,1] > 0 & presence_tot[,1] < random_long_tirage_A2 )
training_backgr.occ2_part1 <- which(background_data[,1] > random_long_tirage_A1 & background_data[,1] < 0 )
training_backgr.occ2_part2 <- which(background_data[,1] > 0 & background_data[,1] < random_long_tirage_A2 )
}
### ZONE 3 ####
if (random_long_tirage_A2 <= 0 & random_long_tirage_A3 <=0){
training_presences.occ3 <- which(presence_tot[,1] > random_long_tirage_A2 & presence_tot[,1] < random_long_tirage_A3 )
training_backgr.occ3 <- which(background_data[,1] > random_long_tirage_A2 & background_data[,1] < random_long_tirage_A3)
}
if (random_long_tirage_A2 >= 0 & random_long_tirage_A3 >=0){
training_presences.occ3 <- which(presence_tot[,1] > random_long_tirage_A2 & presence_tot[,1] < random_long_tirage_A3 )
training_backgr.occ3 <- which(background_data[,1] > random_long_tirage_A2 & background_data[,1] < random_long_tirage_A3)
}
if (random_long_tirage_A2 >= 0 & random_long_tirage_A3 <=0){
training_presences.occ3_part1 <- which(presence_tot[,1] > random_long_tirage_A2 & presence_tot[,1] < 180 )
training_presences.occ3_part2 <- which(presence_tot[,1] > -180 & presence_tot[,1] < random_long_tirage_A3 )
training_backgr.occ3_part1 <- which(background_data[,1] > random_long_tirage_A2 & background_data[,1] < 180 )
training_backgr.occ3_part2 <- which(background_data[,1] > -180 & background_data[,1] < random_long_tirage_A3 )
}
if (random_long_tirage_A2 <= 0 & random_long_tirage_A3 >=0){
training_presences.occ3_part1 <- which(presence_tot[,1] > random_long_tirage_A2 & presence_tot[,1] < 0 )
training_presences.occ3_part2 <- which(presence_tot[,1] > 0 & presence_tot[,1] < random_long_tirage_A3 )
training_backgr.occ3_part1 <- which(background_data[,1] > random_long_tirage_A2 & background_data[,1] < 0 )
training_backgr.occ3_part2 <- which(background_data[,1] > 0 & background_data[,1] < random_long_tirage_A3 )
}
### set the groups
training_presence_grp1_all <- as.vector(na.omit(c(training_presences.occ1,training_presences.occ1_part1,training_presences.occ1_part2)))
training_presence_grp2_all <- as.vector(na.omit(c(training_presences.occ2,training_presences.occ2_part1,training_presences.occ2_part2)))
training_presence_grp3_all <- as.vector(na.omit(c(training_presences.occ3,training_presences.occ3_part1,training_presences.occ3_part2)))
for (i in training_presence_grp1_all){
occ.grp[i] <- 1
}
for (i in training_presence_grp2_all){
occ.grp[i] <- 2
}
for (i in training_presence_grp3_all){
occ.grp[i] <- 3
}
occ.grp[which(is.na(occ.grp))]=4
training_backgr_grp1_all <- as.vector(na.omit(c(training_backgr.occ1,training_backgr.occ1_part1,training_backgr.occ1_part2)))
training_backgr_grp2_all <- as.vector(na.omit(c(training_backgr.occ2,training_backgr.occ2_part1,training_backgr.occ2_part2)))
training_backgr_grp3_all <- as.vector(na.omit(c(training_backgr.occ3,training_backgr.occ3_part1,training_backgr.occ3_part2)))
for (i in training_backgr_grp1_all){
bg.coords.grp[i] <- 1
}
for (i in training_backgr_grp2_all){
bg.coords.grp[i] <- 2
}
for (i in training_backgr_grp3_all){
bg.coords.grp[i] <- 3
}
bg.coords.grp[which(is.na(bg.coords.grp))]=4
out <- list(occ.grp=occ.grp,bg.coords.grp= bg.coords.grp, tirage=tirage)
return(out)
}
```
[Function_gbm.R](./course_material/exercises/scripts/Function_gbm.R)
```{r eval = FALSE}
### gbm.stepv2
.roc <-function (obsdat, preddat) {
# code adapted from Ferrier, Pearce and Watson's code, by J.Elith
#
# see:
# Hanley, J.A. & McNeil, B.J. (1982) The meaning and use of the area
# under a Receiver Operating Characteristic (ROC) curve.
# Radiology, 143, 29-36
#
# Pearce, J. & Ferrier, S. (2000) Evaluating the predictive performance
# of habitat models developed using logistic regression.
# Ecological Modelling, 133, 225-245.
# this is the non-parametric calculation for area under the ROC curve,
# using the fact that a MannWhitney U statistic is closely related to
# the area
#
# in dismo, this is used in the gbm routines, but not elsewhere (see evaluate).
if (length(obsdat) != length(preddat)) {
stop("obs and preds must be equal lengths")
}
n.x <- length(obsdat[obsdat == 0])
n.y <- length(obsdat[obsdat == 1])
xy <- c(preddat[obsdat == 0], preddat[obsdat == 1])
rnk <- rank(xy)
wilc <- ((n.x * n.y) + ((n.x * (n.x + 1))/2) - sum(rnk[1:n.x]))/(n.x * n.y)
return(round(wilc, 4))
}
.calibration <- function(obs, preds, family = "binomial") {
#
# j elith/j leathwick 17th March 2005
# calculates calibration statistics for either binomial or count data
# but the family argument must be specified for the latter
# a conditional test for the latter will catch most failures to specify
# the family
#
if (family == "bernoulli") {
family <- "binomial"
}
pred.range <- max(preds) - min(preds)
if(pred.range > 1.2 & family == "binomial") {
print(paste("range of response variable is ", round(pred.range, 2)), sep = "", quote = F)
print("check family specification", quote = F)
return()
}
if(family == "binomial") {
pred <- preds + 1e-005
pred[pred >= 1] <- 0.99999
mod <- glm(obs ~ log((pred)/(1 - (pred))), family = binomial)
lp <- log((pred)/(1 - (pred)))
a0b1 <- glm(obs ~ offset(lp) - 1, family = binomial)
miller1 <- 1 - pchisq(a0b1$deviance - mod$deviance, 2)
ab1 <- glm(obs ~ offset(lp), family = binomial)
miller2 <- 1 - pchisq(a0b1$deviance - ab1$deviance, 1)
miller3 <- 1 - pchisq(ab1$deviance - mod$deviance, 1)
} else if(family == "poisson") {
mod <- glm(obs ~ log(preds), family = poisson)
lp <- log(preds)
a0b1 <- glm(obs ~ offset(lp) - 1, family = poisson)
miller1 <- 1 - pchisq(a0b1$deviance - mod$deviance, 2)
ab1 <- glm(obs ~ offset(lp), family = poisson)
miller2 <- 1 - pchisq(a0b1$deviance - ab1$deviance, 1)
miller3 <- 1 - pchisq(ab1$deviance - mod$deviance, 1)
}
calibration.result <- c(mod$coef, miller1, miller2, miller3)
names(calibration.result) <- c("intercept", "slope", "testa0b1", "testa0|b1", "testb1|a")
return(calibration.result)
}
## VI.
gbm.step_v2 <- function (data, gbm.x, gbm.y, offset = NULL, fold.vector = NULL,
tree.complexity = 1, learning.rate = 0.01, bag.fraction = 0.75,
site.weights = rep(1, nrow(data)), var.monotone = rep(0,
length(gbm.x)),
n.folds = 10, prev.stratify = TRUE, family = "bernoulli",
n.trees = 50, step.size = n.trees, max.trees = 10000, tolerance.method = "auto",
tolerance = 0.001, plot.main = TRUE, plot.folds = FALSE,
verbose = TRUE, silent = FALSE, keep.fold.models = FALSE,
keep.fold.vector = FALSE, keep.fold.fit = FALSE, ...)
{
if (!requireNamespace("gbm")) {
stop("you need to install the gbm package to run this function")
}
requireNamespace("splines")
if (silent)
verbose <- FALSE
z1 <- Sys.time()
x.data <- data[, gbm.x, drop = FALSE]
y.data <- data[, gbm.y]
sp.name <- names(data)[gbm.y]
if (family == "bernoulli") {
prevalence <- mean(y.data)
}
n.cases <- nrow(data)
n.preds <- length(gbm.x)
if (!silent) {
cat("\n", "\n", "GBM STEP - version 2.9", "\n", "\n")
cat("Performing cross-validation optimisation of a boosted regression tree model \n")
cat("for", sp.name, "and using a family of", family,
"\n")
cat("Using", n.cases, "observations and", n.preds, "predictors \n")
}
if (is.null(fold.vector)) {
if (prev.stratify & family == "bernoulli") {
presence.mask <- data[, gbm.y] == 1
absence.mask <- data[, gbm.y] == 0
n.pres <- sum(presence.mask)
n.abs <- sum(absence.mask)
selector <- rep(0, n.cases)
temp <- rep(seq(1, n.folds, by = 1), length = n.pres)
temp <- temp[order(runif(n.pres, 1, 100))]
selector[presence.mask] <- temp
temp <- rep(seq(1, n.folds, by = 1), length = n.abs)
temp <- temp[order(runif(n.abs, 1, 100))]
selector[absence.mask] <- temp
}
else {
selector <- rep(seq(1, n.folds, by = 1), length = n.cases)
selector <- selector[order(runif(n.cases, 1, 100))]
}
} else {
if (length(fold.vector) != n.cases) {
stop("supplied fold vector is of wrong length")
}
cat("loading user-supplied fold vector \n")
selector <- fold.vector
}
pred.values <- rep(0, n.cases)
cv.loss.matrix <- matrix(0, nrow = n.folds, ncol = 1)
training.loss.matrix <- matrix(0, nrow = n.folds, ncol = 1)
trees.fitted <- n.trees
model.list <- list(paste("model", 1:n.folds, sep = ""))
if (is.null(offset)) {
gbm.call <- paste("gbm::gbm(y.subset ~ .,data=x.subset, n.trees = n.trees, interaction.depth = tree.complexity, shrinkage = learning.rate, bag.fraction = bag.fraction, weights = weight.subset, distribution = as.character(family), var.monotone = var.monotone, verbose = FALSE)",
sep = "")
} else {
gbm.call <- paste("gbm::gbm(y.subset ~ . + offset(offset.subset), data=x.subset, n.trees = n.trees, interaction.depth = tree.complexity, shrinkage = learning.rate, bag.fraction = bag.fraction, weights = weight.subset, distribution = as.character(family), var.monotone = var.monotone, verbose = FALSE)",
sep = "")
}
n.fitted <- n.trees
y_i <- y.data
u_i <- sum(y.data * site.weights)/sum(site.weights)
u_i <- rep(u_i, length(y_i))
total.deviance <- calc.deviance(y_i, u_i, weights = site.weights,
family = family, calc.mean = FALSE)
mean.total.deviance <- total.deviance/n.cases
tolerance.test <- tolerance
if (tolerance.method == "auto") {
tolerance.test <- mean.total.deviance * tolerance
}
if (!silent) {
cat("creating", n.folds, "initial models of", n.trees,
"trees", "\n")
if (prev.stratify & family == "bernoulli") {
cat("\n", "folds are stratified by prevalence", "\n")
} else {
cat("\n", "folds are unstratified", "\n")
}
cat("total mean deviance = ", round(mean.total.deviance,
4), "\n")
cat("tolerance is fixed at ", round(tolerance.test, 4),
"\n")
if (tolerance.method != "fixed" & tolerance.method !=
"auto") {
stop("invalid argument for tolerance method - should be auto or fixed")
}
}
if (verbose) {
cat("ntrees resid. dev.", "\n")
}
for (i in 1:n.folds) {
model.mask <- selector != i
pred.mask <- selector == i
y.subset <- y.data[model.mask]
x.subset <- x.data[model.mask, , drop = FALSE]
weight.subset <- site.weights[model.mask]
if (!is.null(offset)) {
offset.subset <- offset[model.mask]
}
else {
offset.subset <- NULL
}
model.list[[i]] <- eval(parse(text = gbm.call))
fitted.values <- model.list[[i]]$fit
if (!is.null(offset)) {
fitted.values <- fitted.values + offset[model.mask]
}
if (family == "bernoulli") {
fitted.values <- exp(fitted.values)/(1 + exp(fitted.values))
}
else if (family == "poisson") {
fitted.values <- exp(fitted.values)
}
pred.values[pred.mask] <- gbm::predict.gbm(model.list[[i]],
x.data[pred.mask, , drop = FALSE], n.trees = n.trees)
if (!is.null(offset)) {
pred.values[pred.mask] <- pred.values[pred.mask] +
offset[pred.mask]
}
if (family == "bernoulli") {
pred.values[pred.mask] <- exp(pred.values[pred.mask])/(1 +
exp(pred.values[pred.mask]))
}
else if (family == "poisson") {
pred.values[pred.mask] <- exp(pred.values[pred.mask])
}
y_i <- y.subset
u_i <- fitted.values
weight.fitted <- site.weights[model.mask]
training.loss.matrix[i, 1] <- calc.deviance(y_i, u_i,
weight.fitted, family = family)
y_i <- y.data[pred.mask]
u_i <- pred.values[pred.mask]
weight.preds <- site.weights[pred.mask]
cv.loss.matrix[i, 1] <- calc.deviance(y_i, u_i, weight.preds,
family = family)
}
delta.deviance <- 1
cv.loss.values <- apply(cv.loss.matrix, 2, mean)
if (verbose) {
cat(n.fitted, " ", round(cv.loss.values, 4), "\n")
}
if (!silent) {
cat("now adding trees...", "\n")
}
j <- 1
while (delta.deviance > tolerance.test & n.fitted < max.trees) {
training.loss.matrix <- cbind(training.loss.matrix, rep(0,
n.folds))
cv.loss.matrix <- cbind(cv.loss.matrix, rep(0, n.folds))
n.fitted <- n.fitted + step.size
trees.fitted <- c(trees.fitted, n.fitted)
j <- j + 1
for (i in 1:n.folds) {
model.mask <- selector != i
pred.mask <- selector == i
y.subset <- y.data[model.mask]
x.subset <- x.data[model.mask, , drop = FALSE]
weight.subset <- site.weights[model.mask]
if (!is.null(offset)) {
offset.subset <- offset[model.mask]
}
model.list[[i]] <- gbm::gbm.more(model.list[[i]],
weights = weight.subset, step.size)
fitted.values <- model.list[[i]]$fit
if (!is.null(offset)) {
fitted.values <- fitted.values + offset[model.mask]
}
if (family == "bernoulli") {
fitted.values <- exp(fitted.values)/(1 + exp(fitted.values))
}
else if (family == "poisson") {
fitted.values <- exp(fitted.values)
}
pred.values[pred.mask] <- gbm::predict.gbm(model.list[[i]],
x.data[pred.mask, , drop = FALSE], n.trees = n.fitted)
if (!is.null(offset)) {
pred.values[pred.mask] <- pred.values[pred.mask] +
offset[pred.mask]
}
if (family == "bernoulli") {
pred.values[pred.mask] <- exp(pred.values[pred.mask])/(1 +
exp(pred.values[pred.mask]))
}
else if (family == "poisson") {
pred.values[pred.mask] <- exp(pred.values[pred.mask])
}
y_i <- y.subset
u_i <- fitted.values
weight.fitted <- site.weights[model.mask]
training.loss.matrix[i, j] <- calc.deviance(y_i,
u_i, weight.fitted, family = family)
u_i <- pred.values[pred.mask]
y_i <- y.data[pred.mask]
weight.preds <- site.weights[pred.mask]
cv.loss.matrix[i, j] <- calc.deviance(y_i, u_i, weight.preds,
family = family)
}
cv.loss.values <- apply(cv.loss.matrix, 2, mean)
if (j < 5) {
if (cv.loss.values[j] > cv.loss.values[j - 1]) {
if (!silent) {
cat("restart model with a smaller learning rate or smaller step size...")
}
return()
}
}
if (j >= 20) {
test1 <- mean(cv.loss.values[(j - 9):j])
test2 <- mean(cv.loss.values[(j - 19):(j - 9)])
delta.deviance <- test2 - test1
}
if (verbose) {
cat(n.fitted, " ", round(cv.loss.values[j], 4), "\n")
flush.console()
}
}
training.loss.values <- apply(training.loss.matrix, 2, mean)
cv.loss.ses <- rep(0, length(cv.loss.values))
cv.loss.ses <- sqrt(apply(cv.loss.matrix, 2, var))/sqrt(n.folds)
y.bar <- min(cv.loss.values)
target.trees <- trees.fitted[match(TRUE, cv.loss.values ==
y.bar)]
if (plot.main) {
y.min <- min(cv.loss.values - cv.loss.ses)
y.max <- max(cv.loss.values + cv.loss.ses)
if (plot.folds) {
y.min <- min(cv.loss.matrix)
y.max <- max(cv.loss.matrix)
}
plot(trees.fitted, cv.loss.values, type = "l", ylab = "holdout deviance",
xlab = "no. of trees", ylim = c(y.min, y.max), ...)
abline(h = y.bar, col = 2)
lines(trees.fitted, cv.loss.values + cv.loss.ses, lty = 2)
lines(trees.fitted, cv.loss.values - cv.loss.ses, lty = 2)
if (plot.folds) {
for (i in 1:n.folds) {
lines(trees.fitted, cv.loss.matrix[i, ], lty = 3)
}
}
abline(v = target.trees, col = 3)
title(paste(sp.name, ", d - ", tree.complexity, ", lr - ",
learning.rate, sep = ""))
}
cv.deviance.stats <- rep(0, n.folds)
cv.roc.stats <- rep(0, n.folds)
cv.cor.stats <- rep(0, n.folds)
cv.calibration.stats <- matrix(0, ncol = 5, nrow = n.folds)
if (family == "bernoulli") {
threshold.stats <- rep(0, n.folds)
############################
## JA editions / 08/02/19 ##
############################
cv.corr.class <- rep(0, n.folds)
cv.length <- rep(0, n.folds)
tss.stat <- rep(0, n.folds)
####################
## End / 08/02/19 ##
####################
}
fitted.matrix <- matrix(NA, nrow = n.cases, ncol = n.folds)
fold.fit <- rep(0, n.cases)
for (i in 1:n.folds) {
pred.mask <- selector == i
model.mask <- selector != i
fits <- gbm::predict.gbm(model.list[[i]], x.data[model.mask,
, drop = FALSE], n.trees = target.trees)
if (!is.null(offset)) {
fits <- fits + offset[model.mask]
}
if (family == "bernoulli") {
fits <- exp(fits)/(1 + exp(fits))
} else if (family == "poisson") {
fits <- exp(fits)
}
fitted.matrix[model.mask, i] <- fits
fits <- gbm::predict.gbm(model.list[[i]], x.data[pred.mask,
, drop = FALSE], n.trees = target.trees)
if (!is.null(offset))
fits <- fits + offset[pred.mask]
fold.fit[pred.mask] <- fits
if (family == "bernoulli") {
fits <- exp(fits)/(1 + exp(fits))
}else if (family == "poisson") {
fits <- exp(fits)
}
fitted.matrix[pred.mask, i] <- fits
y_i <- y.data[pred.mask]
u_i <- fitted.matrix[pred.mask, i]
weight.preds <- site.weights[pred.mask]
cv.deviance.stats[i] <- calc.deviance(y_i, u_i, weight.preds,
family = family)
cv.cor.stats[i] <- cor(y_i, u_i)
if (family == "bernoulli") {
cv.roc.stats[i] <- .roc(y_i, u_i)
cv.calibration.stats[i, ] <- .calibration(y_i, u_i,
"binomial")
threshold.stats[i] <- approx(ppoints(u_i), sort(u_i,
decreasing = T), prevalence)$y
############################
## JA editions / 08/02/19 ##
############################
c_i <- c(1, 0)[as.factor(u_i <= threshold.stats[i])]
tab1 <- table(c_i, y_i)
# Correctly classified test data
cv.corr.class[i] <- sum(diag(tab1)) / sum(tab1)
# % cv / total data
cv.length[i] <- table(y_i)["1"] / table(y.data)["1"]
# TSS
# Sensitivity = TP/(TP + FN)
# Specificity = TN/(TN + FP)
tp <- tab1["1", "1"]
fn <- tab1["0", "1"]
tn <- tab1["0", "0"]
fp <- tab1["1", "0"]
sen <- tp/(tp + fn)
spe <- tn/(tn + fp)
# TSS
tss.stat[i] <- spe + sen -1
####################
## End / 08/02/19 ##
####################
}
if (family == "poisson") {
cv.calibration.stats[i, ] <- .calibration(y_i, u_i,
"poisson")
}
}
fitted.vars <- apply(fitted.matrix, 1, var, na.rm = TRUE)
cv.dev <- mean(cv.deviance.stats, na.rm = TRUE)
cv.dev.se <- sqrt(var(cv.deviance.stats))/sqrt(n.folds)
cv.cor <- mean(cv.cor.stats, na.rm = TRUE)
cv.cor.se <- sqrt(var(cv.cor.stats, use = "complete.obs"))/sqrt(n.folds)
cv.roc <- 0
cv.roc.se <- 0
if (family == "bernoulli") {
cv.roc <- mean(cv.roc.stats, na.rm = TRUE)
cv.roc.se <- sqrt(var(cv.roc.stats, use = "complete.obs"))/sqrt(n.folds)
cv.threshold <- mean(threshold.stats, na.rm = T)
cv.threshold.se <- sqrt(var(threshold.stats, use = "complete.obs"))/sqrt(n.folds)
}
cv.calibration <- 0
cv.calibration.se <- 0
if (family == "poisson" | family == "bernoulli") {
cv.calibration <- apply(cv.calibration.stats, 2, mean)
cv.calibration.se <- apply(cv.calibration.stats, 2, var)
cv.calibration.se <- sqrt(cv.calibration.se)/sqrt(n.folds)
}
if (is.null(offset)) {
gbm.call <- paste("gbm::gbm(y.data ~ .,data=x.data, n.trees = target.trees, interaction.depth = tree.complexity, shrinkage = learning.rate, bag.fraction = bag.fraction, weights = site.weights, distribution = as.character(family), var.monotone = var.monotone, verbose = FALSE)",
sep = "")
}
else {
gbm.call <- paste("gbm::gbm(y.data ~ . + offset(offset),data=x.data, n.trees = target.trees, interaction.depth = tree.complexity, shrinkage = learning.rate, bag.fraction = bag.fraction, weights = site.weights, distribution = as.character(family), var.monotone = var.monotone, verbose = FALSE)",
sep = "")
}
if (!silent) {
message("fitting final gbm model with a fixed number of ",
target.trees, " trees for ", sp.name)
}
gbm.object <- eval(parse(text = gbm.call))
best.trees <- target.trees
gbm.summary <- summary(gbm.object, n.trees = target.trees,
plotit = FALSE)
fits <- gbm::predict.gbm(gbm.object, x.data, n.trees = target.trees)
if (!is.null(offset))
fits <- fits + offset
if (family == "bernoulli") {
fits <- exp(fits)/(1 + exp(fits))
}
else if (family == "poisson") {
fits <- exp(fits)
}
fitted.values <- fits
y_i <- y.data
u_i <- fitted.values
resid.deviance <- calc.deviance(y_i, u_i, weights = site.weights,
family = family, calc.mean = FALSE)
self.cor <- cor(y_i, u_i)
self.calibration <- 0
self.roc <- 0
if (family == "bernoulli") {
deviance.contribs <- (y_i * log(u_i)) + ((1 - y_i) *
log(1 - u_i))
residuals <- sqrt(abs(deviance.contribs * 2))
residuals <- ifelse((y_i - u_i) < 0, 0 - residuals, residuals)
self.roc <- .roc(y_i, u_i)
self.calibration <- .calibration(y_i, u_i, "binomial")
############################
## JA editions / 08/02/19 ##
############################
self.th <- approx(ppoints(u_i), sort(u_i,
decreasing = T), prevalence)$y
####################
## End / 08/02/19 ##
####################
}
if (family == "poisson") {
deviance.contribs <- ifelse(y_i == 0, 0, (y_i * log(y_i/u_i))) -
(y_i - u_i)
residuals <- sqrt(abs(deviance.contribs * 2))
residuals <- ifelse((y_i - u_i) < 0, 0 - residuals, residuals)
self.calibration <- .calibration(y_i, u_i, "poisson")
}
if (family == "gaussian" | family == "laplace") {
residuals <- y_i - u_i
}
mean.resid.deviance <- resid.deviance/n.cases
z2 <- Sys.time()
elapsed.time.minutes <- round(as.numeric(z2 - z1)/60, 2)
if (verbose) {
cat("\n")
cat("mean total deviance =", round(mean.total.deviance,
3), "\n")
cat("mean residual deviance =", round(mean.resid.deviance,
3), "\n", "\n")
cat("estimated cv deviance =", round(cv.dev, 3), "; se =",
round(cv.dev.se, 3), "\n", "\n")
cat("training data correlation =", round(self.cor, 3),
"\n")
cat("cv correlation = ", round(cv.cor, 3), "; se =",
round(cv.cor.se, 3), "\n", "\n")
if (family == "bernoulli") {
cat("training data AUC score =", round(self.roc,
3), "\n")
cat("cv AUC score =", round(cv.roc, 3), "; se =",
round(cv.roc.se, 3), "\n", "\n")
}
cat("elapsed time - ", round(elapsed.time.minutes, 2),
"minutes", "\n")
}
if (n.fitted == max.trees & !silent) {
cat("\n", "########### warning ##########", "\n", "\n")
cat("maximum tree limit reached - results may not be optimal",
"\n")
cat(" - refit with faster learning rate or increase maximum number of trees",
"\n")
}
gbm.detail <- list(dataframe = data, gbm.x = gbm.x, predictor.names = names(x.data),
gbm.y = gbm.y, response.name = sp.name, offset = offset,
family = family, tree.complexity = tree.complexity, learning.rate = learning.rate,
bag.fraction = bag.fraction, cv.folds = n.folds, prev.stratification = prev.stratify,
max.fitted = n.fitted, n.trees = target.trees, best.trees = target.trees,
train.fraction = 1, tolerance.method = tolerance.method,
tolerance = tolerance, var.monotone = var.monotone, date = date(),
elapsed.time.minutes = elapsed.time.minutes)
training.stats <- list(null = total.deviance, mean.null = mean.total.deviance,
resid = resid.deviance, mean.resid = mean.resid.deviance,
correlation = self.cor, discrimination = self.roc, calibration = self.calibration)
cv.stats <- list(deviance.mean = cv.dev, deviance.se = cv.dev.se,
correlation.mean = cv.cor, correlation.se = cv.cor.se,
discrimination.mean = cv.roc, discrimination.se = cv.roc.se,
calibration.mean = cv.calibration, calibration.se = cv.calibration.se)
if (family == "bernoulli") {
cv.stats$cv.threshold <- cv.threshold
cv.stats$cv.threshold.se <- cv.threshold.se
}
gbm.object$gbm.call <- gbm.detail
gbm.object$fitted <- fitted.values
gbm.object$fitted.vars <- fitted.vars
gbm.object$residuals <- residuals
gbm.object$contributions <- gbm.summary
gbm.object$self.statistics <- training.stats
gbm.object$cv.statistics <- cv.stats
gbm.object$weights <- site.weights
gbm.object$trees.fitted <- trees.fitted
gbm.object$training.loss.values <- training.loss.values
gbm.object$cv.values <- cv.loss.values
gbm.object$cv.loss.ses <- cv.loss.ses
gbm.object$cv.loss.matrix <- cv.loss.matrix
gbm.object$cv.roc.matrix <- cv.roc.stats
############################
## JA editions / 08/02/19 ##
############################
gbm.object$cv.cor.matrix <- cv.cor.stats
gbm.object$cv.th.matrix <- threshold.stats
gbm.object$cv.corr.class <- cv.corr.class
gbm.object$self.th <- self.th
gbm.object$cv.length <- cv.length
gbm.object$tss.cv <- tss.stat
####################
## End / 08/02/19 ##
####################
if (keep.fold.models) {
gbm.object$fold.models <- model.list
}
else {
gbm.object$fold.models <- NULL
}
if (keep.fold.vector) {
gbm.object$fold.vector <- selector
}
else {
gbm.object$fold.vector <- NULL
}
if (keep.fold.fit) {
gbm.object$fold.fit <- fold.fit
}
else {
gbm.object$fold.fit <- NULL
}
return(gbm.object)
}
## II.
## https://github.com/cran/ENMeval/tree/master/R
#########################################################
######### MAKE BLOCK EVALUATION GROUPS #############
#########################################################
get.block <- function(occ, bg.coords){
# SPLIT OCC POINTS INTO FOUR SPATIAL GROUPS
noccs <- nrow(occ)
n1 <- ceiling(nrow(occ)/2)
n2 <- floor(nrow(occ)/2)
n3 <- ceiling(n1/2)
n4 <- ceiling(n2/2)
grpA <- occ[order(occ[, 2]),][1:n1,]
grpB <- occ[rev(order(occ[, 2])),][1:n2,]
grp1 <- grpA[order(grpA[, 1]),][1:(n3),]
grp2 <- grpA[!rownames(grpA)%in%rownames(grp1),]
grp3 <- grpB[order(grpB[, 1]),][1:(n4),]
grp4 <- grpB[!rownames(grpB)%in%rownames(grp3),]
# SPLIT BACKGROUND POINTS BASED ON SPATIAL GROUPS
bvert <- mean(max(grp1[, 1]), min(grp2[, 1])) + 0.5
tvert <- mean(max(grp3[, 1]), min(grp4[, 1])) + 0.5
horz <- mean(max(grpA[, 2]), min(grpB[, 2])) + 0.5
bggrp1 <- bg.coords[bg.coords[, 2] <= horz & bg.coords[, 1]<bvert,]
bggrp2 <- bg.coords[bg.coords[, 2] < horz & bg.coords[, 1]>=bvert,]
bggrp3 <- bg.coords[bg.coords[, 2] > horz & bg.coords[, 1]<=tvert,]
bggrp4 <- bg.coords[bg.coords[, 2] >= horz & bg.coords[, 1]>tvert,]
rr <- bg.coords[bg.coords[, 2] > horz & bg.coords[, 1] <= bvert & bg.coords[, 1] >= tvert,]
r <- data.frame()
if (nrow(grp1) > 0) grp1$grp <- 1; r <- rbind(r, grp1)
if (nrow(grp2) > 0) grp2$grp <- 2; r <- rbind(r, grp2)
if (nrow(grp3) > 0) grp3$grp <- 3; r <- rbind(r, grp3)
if (nrow(grp4) > 0) grp4$grp <- 4; r <- rbind(r, grp4)
occ.grp <- r[order(as.numeric(rownames(r))),]$grp