#####################################################################
# R code to the manuscript
# "Right on track? Performance of satellite telemetry in terrestrial wildlife research"
# by M.P.G. Hofman, M.W. Hayward, N. Balkenhol, et al.
# 
# March 2019
# 
# For more details, contact mpghofman@gmail.com
#
# This script runs a beta gamboostLSS model for the Overall fix Success Rate (OSR),
# calculates the empirical point-wise confidence intervals, 
# and plots the variables with their confidence intervals.
#####################################################################
library(dplyr)
library(stringr)
library(ggplot2)
library(mboost)
library(gamboostLSS)
library(lubridate)

### load overall dataframe and subset for OSR calculation ####
overallFrame<- as.data.frame(read.csv("S10 Data.csv"))

### set filter, weighting and predictor variables for the OSR model ##
OSRfilters <- c("oneBrand")
OSRweights <- "numTag"
OSRpredictors <- c("qualCovLab","forDen2","terRug", "wmTTF", "forTyp","wmYop", "quanCov", "speBurHib", "speHeight", "mquanTri", "mainRet2") # add "mainRet2" for the Overall Fix Succcess Rate
OSRresponse <- "adjOSR"
OSRrandomeffect <- c("mainBrand5")

### subset the overall dataframe for OSR analysis and further preparations
OSRframe <- overallFrame[,c(OSRfilters, OSRweights, OSRpredictors, OSRresponse,OSRrandomeffect)]
OSRframe <- OSRframe[-(which(is.na(OSRframe$adjOSR))),]
OSRframe <- OSRframe[(which(!is.na(OSRframe$numTag))),]

### other adjustments
OSRframe$logspeHeight <- log(OSRframe$speHeight) # log-transform species heigth
OSRframe$mainBrand5 <- as.factor(OSRframe$mainBrand5)
OSRframe$speBurHib <- as.factor(OSRframe$speBurHib)
OSRframe$forTyp <- as.factor(OSRframe$forTyp)
OSRframe$forDen2 <- as.factor(OSRframe$forDen2)
OSRframe$qualCovLab <- as.factor(OSRframe$qualCovLab)
OSRframe$terRug <- as.factor(OSRframe$terRug)
OSRframe$wmYop <- as.numeric(OSRframe$wmYop)
OSRframe$mquanTri <- as.numeric(OSRframe$mquanTri)

### FUNCTION: Run a gambooslss model and cut it off at the optimised mstop determined by cross-validation ####
full.beta.gamboostLSS <- function(data,formula,weights,control) {
  ## run model
  # weights <- OSR.weights; formula <- OSR.mA; control <- OSR.boostControl; data <- OSR.dat
  mod <- gamboostLSS(formula, weights = weights, control = control, families = BetaLSS(stabilization = "MAD"), data = data)
  ## find the optimal mstop value
  ## set up the cross validation runs
  densegrid <- make.grid(max = c(mu = 100, phi = 100), min = 10, 
                         length.out = 10, dense_mu_grid = TRUE)
  cores <- ifelse(grepl("linux|apple", R.Version()$platform), 2, 1)
  folds <- cv(model.weights(mod), type = "subsampling", prob = .75)
  ## run cross validation
  cvr <- cvrisk(mod, grid = densegrid, folds = folds, mc.cores = cores) 
  ## extract mstop and set the model results to it
  mstop(mod) <- mstop(cvr)
  return(mod)
}

### model preparation ####
### (manually mean-center continuous variables when using bols() without intercept)!!
theSeed <- 3
set.seed(theSeed)
### the model 
## change OSR to OSR when running analysis for OSR, and
## add "mainRet2" 
OSR.incl <- c("forTyp", "qualCovLab","forDen2","terRug", "mainRet2",
  "speBurHib", "wmTTF","wmYop", "logspeHeight", "mainBrand5", "quanCov",
  "mquanTri","numTag","adjOSR") 
OSR.dat <- na.omit(OSRframe[,OSR.incl])
OSR.weights <- OSR.dat$numTag
OSR.mA <- as.formula(adjOSR ~ bols(forTyp) + bols(qualCovLab) + bols(forDen2) + bols(mainRet2) + # Change OSR to OSR when running analysis for OSR
                       bols(terRug) + bols(speBurHib) + brandom(mainBrand5) + 
                       mquanTri +  quanCov + logspeHeight + wmTTF + wmYop)
OSR.boostControl <- boost_control(mstop = c(100,100), risk = "inbag", trace = T)
OSR.mod <- full.beta.gamboostLSS(OSR.dat,OSR.mA,OSR.weights,OSR.boostControl)
summary(OSR.mod)
emp_risk <- risk(OSR.mod, merge = TRUE) 
tail(emp_risk, n = 1)

### store final model results: 
# final.OSR.model.fit <- OSR.mod
# final.OSR.model <- OSR.mA

### FUNCTION: randomly subsample a data frame (without replacement)####
## (source: https://gist.github.com/ramhiser/1421185 )
boot_subsample <- function(x, subsample_size) {
  x[sample(x = seq_len(nrow(x)), size = subsample_size), ]
}

### calculation of confidence bands ####
## create an empty list to store the bootstrap models
set.seed(theSeed)
boot.out <- list()
## set global model parameters (should be the same as the full test model)
## we keep the mstop values the same to avoid the subsampling needed for the cross validation
tboostControl <- boost_control(mstop = mstop(OSR.mod), risk = "inbag", trace = T)
## run the bootraps. 
## change OSR for OSR when Running the OSR analysis
fileConnc <- sink(paste0("OSR_Log_",str_replace_all(today(),"\\D", ""), "_", theSeed,".txt")) # start a basic log file
print(paste0("The seed was set to ", theSeed));print(OSR.mA);print(summary(OSR.mod))
boot.n <- 999; print(paste0("Number of bootstraps = ",boot.n))
sub_size <- floor(nrow(OSR.dat)*.75)
for (i in 1:boot.n) {
  strt <- Sys.time(); print(paste0("bootstrap ",i," started at ", strt))
  ## subsample dataset (75% of the data) without replacement
  idat <- boot_subsample(OSR.dat,sub_size)
  ## set local weights
  iweights <- idat$numTag
  boot.out[[i]] <- gamboostLSS(OSR.mA, weights = iweights, control = tboostControl, families = BetaLSS(stabilization = "MAD"), data = idat)
  bend <- Sys.time(); print(paste0("bootstrap ",i," took")); print(bend-strt); print("")
}
sink(fileConnc)

## Create a list of dataframes for each covariate in the models for both distribution parameters)
## the first column being the fitted values of the original model (OSR.mod)
## the other columns will contain the predicted values using the bootstrap models
## first: get covariate names used in the model
cov.names <- names(OSR.dat)[-c(match("adjOSR",names(OSR.dat)),match("numTag",names(OSR.dat)))]
## create lists for mu and phi data frames
mu.list <- list()
phi.list <- list()
## populate lists with single column data frames (fitted OSR.mod values) for each variable
for (i in 1:length(cov.names)) {
  name=cov.names[i]; muname <- paste0(name,".mu"); phiname <- paste0(name,".phi")
  mu.list[[i]] <- assign(muname, as.data.frame(fitted(OSR.mod$mu, which = name)))
  names(mu.list)[i] <- muname
  phi.list[[i]] <- assign(phiname, as.data.frame(fitted(OSR.mod$phi, which = name)))
  names(phi.list)[i] <- phiname
}
## predict partial effects for the original data using the bootstrap models
## and attach predictions for each bootstrap model to the dataframes
for (i in 1:length(boot.out)) {
  for (j in 1:length(cov.names)) {
    ijpred <- predict(boot.out[[i]], newdata = OSR.dat, which = cov.names[j])
    mu.list[[paste0(cov.names[j],".mu")]] <- cbind(mu.list[[paste0(cov.names[j],".mu")]], ijpred$mu)
    names(mu.list[[paste0(cov.names[j],".mu")]])[ncol(mu.list[[paste0(cov.names[j],".mu")]])] <- paste0("run",i)
    phi.list[[paste0(cov.names[j],".phi")]] <- cbind(phi.list[[paste0(cov.names[j],".phi")]], ijpred$phi)
    names(phi.list[[paste0(cov.names[j],".phi")]])[ncol(phi.list[[paste0(cov.names[j],".phi")]])] <- paste0("run",i)
  }
}

### FUNCTION: Calculate the percentiles per row in each data frame and add to data frames ####
addQuants <- function(x) {
  newCols <- data.frame("lower" = numeric(),
                        "upper" = numeric())
  for (j in 1:nrow(x)) {
    quant <- quantile(x[j,], c(.025, .975))
    newCols <- rbind(newCols,quant)
  }
  result <- cbind(x,newCols)
  return(result)
}


### apply addQuants function ####
mu.list <- lapply(mu.list, function(x) addQuants(x))
# for phi we had to exclude phi.list[[5]] (=speBurHib) from the operation as it did not have any predictions
for (i in 1:length(phi.list)) {
  if (i == 6) {next} else {phi.list[[i]] <- addQuants(phi.list[[i]])}
}


### FUNCTION: Multiple plots ####
#
# source: http://www.cookbook-r.com/Graphs/Multiple_graphs_on_one_page_(ggplot2)/
# 
# ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects)
# - cols:   Number of columns in layout
# - layout: A matrix specifying the layout. If present, 'cols' is ignored.
#
# If the layout is something like matrix(c(1,2,3,3), nrow=2, byrow=TRUE),
# then plot 1 will go in the upper left, 2 will go in the upper right, and
# 3 will go all the way across the bottom.
#
multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {
  library(grid)
  
  # Make a list from the ... arguments and plotlist
  plots <- c(list(...), plotlist)
  
  numPlots = length(plots)
  
  # If layout is NULL, then use 'cols' to determine layout
  if (is.null(layout)) {
    # Make the panel
    # ncol: Number of columns of plots
    # nrow: Number of rows needed, calculated from # of cols
    layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),
                     ncol = cols, nrow = ceiling(numPlots/cols), byrow = T)
  }
  
  if (numPlots==1) {
    print(plots[[1]])
    
  } else {
    # Set up the page
    grid.newpage()
    pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))
    
    # Make each plot, in the correct location
    for (i in 1:numPlots) {
      # Get the i,j matrix positions of the regions that contain this subplot
      matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))
      
      print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,
                                      layout.pos.col = matchidx$col))
    }
  }
}




### create list of mu.plots ####
mu.plots <- list()
for (i in 1:length(mu.list)) {
  x <- mu.list[[i]]
  xname <- str_replace(names(mu.list[i]),".mu","")
  if (is.factor(OSR.dat[,xname])) {
    ## for categoricals
    pldf.x <- data.frame(var = OSR.dat[,xname],
                         fpartial = x[,1],
                         low = x[,ncol(x)-1],
                         high = x[,ncol(x)])
    mu.plots[[i]] <- ggplot(data=pldf.x) + 
      xlab(paste0(xname, ".mu")) +
      geom_boxplot(aes(x = var, y = fpartial)) +
      geom_boxplot(aes(x = var, y = low), colour = "darkgrey") +
      geom_boxplot(aes(x = var, y = high), colour = "darkgrey") +
      # theme(panel.grid.minor = element_blank(), panel.background = element_blank())
      theme_classic()
  } else {
    ## for continuous
    pldf.x <- data.frame(var = OSR.dat[,xname],
                         fpartial = x[,1],
                         low = x[,ncol(x)-1],
                         high = x[,ncol(x)])
    mu.plots[[i]] <- ggplot(data=pldf.x) + 
      xlab(paste0(xname, ".mu")) +
      geom_ribbon(aes(x = var, ymin=low, ymax = high), fill = "grey")  + 
      geom_line(aes(x = var, y = fpartial))# + 
    #geom_point(aes(x = var, y = fpartial))
    #geom_line(aes(x = var, y = low), colour = "grey") + 
    #geom_line(aes(x = var, y = high), colour = "grey") + 
  }
}
png(filename=paste0("OSR_mu",str_replace_all(today(),"\\D", ""), "_", theSeed,".png"), width = 900, height = 900)
multiplot(plotlist = mu.plots, cols = ifelse(length(mu.list)<7, 2,3))
dev.off()

### create list of phi.plots ####
phi.plots <- list()
for (i in 1:length(phi.list)) { if (i == 6) {next} else { # exclude plotting phi.list[[5]] (speBurHib) as it did not produce any perdictions
  x <- phi.list[[i]]
  xname <- str_replace(names(phi.list[i]),".phi","")
  if (is.factor(OSR.dat[,xname])) {
    ## for categoricals
    pldf.x <- data.frame(var = OSR.dat[,xname],
                         fpartial = x[,1],
                         low = x[,ncol(x)-1],
                         high = x[,ncol(x)])
    phi.plots[[i]] <- ggplot(data=pldf.x) + 
      xlab(paste0(xname, ".phi")) +
      geom_boxplot(aes(x = var, y = fpartial)) +
      geom_boxplot(aes(x = var, y = low), colour = "grey") +
      geom_boxplot(aes(x = var, y = high), colour = "grey")
  } else {
    ## for continuous
    pldf.x <- data.frame(var = OSR.dat[,xname],
                         fpartial = x[,1],
                         low = x[,ncol(x)-1],
                         high = x[,ncol(x)])
    phi.plots[[i]] <- ggplot(data=pldf.x) + 
      xlab(paste0(xname, ".phi")) +
      geom_ribbon(aes(x = var, ymin=low, ymax = high), fill = "grey")  + 
      geom_line(aes(x = var, y = fpartial))# + 
    #geom_point(aes(x = var, y = fpartial))
    #geom_line(aes(x = var, y = low), colour = "grey") + 
    #geom_line(aes(x = var, y = high), colour = "grey") + 
  }
}
}
png(filename=paste0("OSR_phi",str_replace_all(today(),"\\D", ""), "_", theSeed,".png"), width = 900, height = 900)
multiplot(plotlist = phi.plots, cols = ifelse(length(mu.list)<7, 2,3))
dev.off()


### Code to produce the plots as in PlosONE publication ####

### mu graphs ###
names(mu.list)
# mainBrand - mu.list[9]
xplots <- list()
varNamList <- c("Main brand", "Time to fix (sec)", "Forest density", "Burrowing/Hibernating", "Species height (mm)","Forest type", "Forest cover (%)")
forDenLabs <- c("No forest","","","Medium","","","Dense")
forTypLabs <- c("NF","TE","TD","TM", "SE",  "SD", "SM")
qualCovLabs <- c("0-25", "25-50","50-75","75-100")
speBurHibLabs <- c("No","Yes")
terRugLabs <- c("Rugged", "","", "Flat" )
mainBrand5Labs <- c(LETTERS[1:8])

for (i in c(10,7,3,6,9,1,2)) {
  x <- mu.list[[i]]
  xname <- str_replace(names(mu.list[i]),".mu","")
  seqIndex <- as.numeric(match(i,c(10,7,3,6,9,1,2)))
  if (is.factor(OSR.dat[,xname])) {
    pldf.x <- data.frame(var = OSR.dat[,xname],
                         fpartial = x[,1],
                         low = x[,ncol(x)-.5],
                         high = x[,ncol(x)])
    if(i == 3) {
      xplots[[seqIndex]] <- ggplot(data=pldf.x) + 
        geom_boxplot(aes(x = var, y = fpartial)) +
        geom_boxplot(aes(x = var, y = low), colour = "grey") +
        geom_boxplot(aes(x = var, y = high), colour = "grey") +
        ylim(-.6,.6) +
        labs(x=varNamList[seqIndex]) + 
        scale_x_discrete(labels =  forDenLabs) + 
        theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
              axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
              panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
    } else {
      if(i == 1) {
        xplots[[seqIndex]] <-ggplot(data=pldf.x) + 
          geom_boxplot(aes(x = var, y = fpartial)) +
          geom_boxplot(aes(x = var, y = low), colour = "grey") +
          geom_boxplot(aes(x = var, y = high), colour = "grey") +
          ylim(-.6,.6) +
          labs(x=varNamList[seqIndex]) + 
          scale_x_discrete(labels =  forTypLabs) + 
          theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
                panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
      } else {
        if(i == 6) {
          xplots[[seqIndex]] <-ggplot(data=pldf.x) + 
            geom_boxplot(aes(x = var, y = fpartial)) +
            geom_boxplot(aes(x = var, y = low), colour = "grey") +
            geom_boxplot(aes(x = var, y = high), colour = "grey") +
            ylim(-.6,.6) +
            labs(x=varNamList[seqIndex], y="Partial effect") + 
            scale_x_discrete(labels = speBurHibLabs) + 
            theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                  axis.text.y  = element_text(colour = "black"), axis.title.y=element_text(),
                  panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
        } else {
          if(i == 2) {
            xplots[[seqIndex]] <-ggplot(data=pldf.x) + 
              geom_boxplot(aes(x = var, y = fpartial)) +
              geom_boxplot(aes(x = var, y = low), colour = "grey") +
              geom_boxplot(aes(x = var, y = high), colour = "grey") +
              ylim(-.6,.6) +
              labs(x=varNamList[seqIndex], y="Partial effect") + 
              scale_x_discrete(labels = qualCovLabs) + 
              theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                    axis.text.y  = element_text(colour = "black"), axis.title.y=element_text(),
                    panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
          } else {
            xplots[[seqIndex]] <- ggplot(data=pldf.x) + 
              geom_boxplot(aes(x = var, y = fpartial)) +
              geom_boxplot(aes(x = var, y = low), colour = "grey") +
              geom_boxplot(aes(x = var, y = high), colour = "grey") +
              ylim(-.6,.6) +
              labs(x=varNamList[seqIndex], y="Partial effect") + 
              scale_x_discrete(labels = mainBrand5Labs) + 
              theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                    axis.text.y  = element_text(colour = "black"), axis.title.y=element_text(),
                    panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
          }}}}
  } else {
    ## for continuous
    pldf.x <- data.frame(var = OSR.dat[,xname],
                         fpartial = x[,1],
                         low = x[,ncol(x)-.5],
                         high = x[,ncol(x)])
    if (i == 9) {
      xplots[[seqIndex]] <- ggplot(data=pldf.x) + 
        labs(x=varNamList[seqIndex]) +
        geom_ribbon(aes(x = exp(var), ymin=low, ymax = high), fill = "grey")  + 
        geom_line(aes(x = exp(var), y = fpartial)) +
        ylim(-.6,.6) +
        # coord_trans(xtrans = "exp") +
        # scale_x_exp() + 
        theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
              axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
              panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
    } else {
      if(i == 7) {
        xplots[[seqIndex]] <- ggplot(data=pldf.x) +
          labs(x=varNamList[seqIndex]) +
          geom_ribbon(aes(x = var, ymin=low, ymax = high), fill = "grey")  +
          geom_line(aes(x = var, y = fpartial)) +
          ylim(-.6,.6) +
          # coord_trans(xtrans = "exp") +
          # scale_x_exp() +
          theme(axis.text.x  = element_text(colour = "black", hjust = .75), axis.title.x=element_text(face="bold", vjust = -.5), 
                axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
                panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
      } else {
        xplots[[seqIndex]] <- ggplot(data=pldf.x) + 
          labs(x=varNamList[seqIndex], y="Partial effect") +
          geom_ribbon(aes(x = var, ymin=low, ymax = high), fill = "grey")  + 
          geom_line(aes(x = var, y = fpartial)) + 
          ylim(-.6,.6) +
          #geom_text(aes(x=min(var), y=max(high)), label=plotLabs[seqIndex]) +
          theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                axis.text.y  = element_text(colour = "black"), axis.title.y=element_text(),
                panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
      }
    }
  } }

tiff(filename=paste0("OSRmuplots_", str_replace_all(today(),"\\D", ""), "_s", theSeed,".tiff"), width = 2250, height = 2250, res = 300, compression = "lzw")
multiplot(plotlist = xplots, cols = ifelse(length(xplots)<7, 2,3))
dev.off()

#### Graphs for publication (phi) #####
### phi graphs ###
names(phi.list)
# mainBrand - phi.list[9]
yplots <- list()
varNamList <- c("Main brand","Forest type", "Forest cover (%)", "Forest density", "Terrain Ruggedness Index", "Time to fix (sec)", "Year of Purchase")
forDenLabs <- c("No forest","","","Medium","","","Dense")
forTypLabs <- c("NF","TE","TD","TM", "SE",  "SD", "SM")
speBurHibLabs <- c("No","Yes")
terRugLabs <- c("Rugged", "","", "Flat" )
mainBrand5Labs <- c(LETTERS[1:8])

for (i in c(10,1,11,3,12,7,8)) {
  y <- phi.list[[i]]
  yname <- str_replace(names(phi.list[i]),".phi","")
  seqIndex <- as.numeric(match(i,c(10,1,11,3,12,7,8)))
  if (is.factor(OSR.dat[,yname])) {
    pldf.y <- data.frame(var = OSR.dat[,yname],
                         fpartial = y[,1],
                         low = y[,ncol(y)-.5],
                         high = y[,ncol(y)])
    if(i == 3) {
      yplots[[seqIndex]] <- ggplot(data=pldf.y) + 
        geom_boxplot(aes(x = var, y = fpartial)) +
        geom_boxplot(aes(x = var, y = low), colour = "grey") +
        geom_boxplot(aes(x = var, y = high), colour = "grey") +
        ylim(-1,.9) +
        labs(x=varNamList[seqIndex], y="Partial effect") + 
        scale_x_discrete(labels =  forDenLabs) + 
        theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
              axis.text.y  = element_text(colour = "black"), axis.title.y=element_text(),
              panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
    } else {
      if(i == 1) {
        yplots[[seqIndex]] <-ggplot(data=pldf.y) + 
          geom_boxplot(aes(x = var, y = fpartial)) +
          geom_boxplot(aes(x = var, y = low), colour = "grey") +
          geom_boxplot(aes(x = var, y = high), colour = "grey") +
          ylim(-1,.9) +
          labs(x=varNamList[seqIndex]) + 
          scale_x_discrete(labels =  forTypLabs) + 
          theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
                panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
      } else {
        if(i == 6) {
          yplots[[seqIndex]] <-ggplot(data=pldf.y) + 
            geom_boxplot(aes(x = var, y = fpartial)) +
            geom_boxplot(aes(x = var, y = low), colour = "grey") +
            geom_boxplot(aes(x = var, y = high), colour = "grey") +
            ylim(-1,.9) +
            labs(x=varNamList[seqIndex]) + 
            scale_x_discrete(labels = speBurHibLabs) + 
            theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                  axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
                  panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
        } else {
          if(i == 4) {
            yplots[[seqIndex]] <-ggplot(data=pldf.y) + 
              geom_boxplot(aes(x = var, y = fpartial)) +
              geom_boxplot(aes(x = var, y = low), colour = "grey") +
              geom_boxplot(aes(x = var, y = high), colour = "grey") +
              ylim(-1,.9) +
              labs(x=varNamList[seqIndex]) + 
              scale_x_discrete(labels = terRugLabs) + 
              theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                    axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
                    panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
          } else {
            yplots[[seqIndex]] <- ggplot(data=pldf.y) + 
              geom_boxplot(aes(x = var, y = fpartial)) +
              geom_boxplot(aes(x = var, y = low), colour = "grey") +
              geom_boxplot(aes(x = var, y = high), colour = "grey") +
              ylim(-1,.9) +
              labs(x=varNamList[seqIndex], y="Partial effect") + 
              scale_x_discrete(labels = mainBrand5Labs) + 
              theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                    axis.text.y  = element_text(colour = "black"), axis.title.y=element_text(),
                    panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
          }}}}
  } else {
    ## for continuous
    pldf.y <- data.frame(var = OSR.dat[,yname],
                         fpartial = y[,1],
                         low = y[,ncol(y)-.5],
                         high = y[,ncol(y)])
    if (i == 7) {
      yplots[[seqIndex]] <- ggplot(data=pldf.y) + 
        labs(x=varNamList[seqIndex]) +
        geom_ribbon(aes(x = var, ymin=low, ymax = high), fill = "grey")  + 
        geom_line(aes(x = var, y = fpartial)) +
        ylim(-1,.9) +
        theme(axis.text.x  = element_text(colour = "black", hjust = .75), axis.title.x=element_text(face="bold", vjust = -.5), 
              axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
              panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
    } else {
      if(i == 12) {
        yplots[[seqIndex]] <- ggplot(data=pldf.y) +
          labs(x=varNamList[seqIndex]) +
          geom_ribbon(aes(x = var, ymin=low, ymax = high), fill = "grey")  +
          geom_line(aes(x = var, y = fpartial)) +
          ylim(-1,.9) +
          theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
                panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
      } else {
        if(i == 11) {
          yplots[[seqIndex]] <- ggplot(data=pldf.y) +
            labs(x=varNamList[seqIndex]) +
            geom_ribbon(aes(x = var*100, ymin=low, ymax = high), fill = "grey")  +
            geom_line(aes(x = var*100, y = fpartial)) +
            ylim(-1,.9) +
            theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                  axis.text.y  = element_text(colour = "black"), axis.title.y=element_blank(),
                  panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
        } else {
          yplots[[seqIndex]] <- ggplot(data=pldf.y) + 
            labs(x=varNamList[seqIndex], y="Partial effect") +
            geom_ribbon(aes(x = var, ymin=low, ymax = high), fill = "grey")  + 
            geom_line(aes(x = var, y = fpartial)) + 
            ylim(-1,.9) +
            #geom_text(aes(y=min(var), y=max(high)), label=plotLabs[seqIndex]) +
            theme(axis.text.x  = element_text(colour = "black"), axis.title.x=element_text(face="bold", vjust = -.5), 
                  axis.text.y  = element_text(colour = "black"), axis.title.y=element_text(),
                  panel.grid.major = element_blank(), panel.grid.minor = element_blank(), panel.background = element_blank(), axis.line = element_line(colour = "grey"))
        }}
    }
  } }

tiff(filename=paste0("OSRphiplots_", str_replace_all(today(),"\\D", ""), "_s", theSeed,".tiff"), width = 2250, height = 2250, res = 300, compression = "lzw")
multiplot(plotlist = yplots, cols = ifelse(length(yplots)<7, 2,3))
dev.off()