R/compare_apsim.R

In apsimx: Inspect, Read, Edit and Run 'APSIM' "Next Generation" and 'APSIM' Classic

#' 
#' @title Compare two or more apsim output objects
#' @name compare_apsim
#' @rdname compare_apsim
#' @description Function which allows for a simple comparison between APSIM output objects
#' @param ... data frames with APSIM output or observed data. 
#' @param variable specific variable to compare. By default all common ones are compared.
#' @param index index for merging objects. Default is \sQuote{Date}
#' @param by factor for splitting the comparison, such as a treatment effect.
#' @param labels labels for plotting and identification of objects.
#' @param cRSS compute (weighted) combined residual sum of squares using some or all variables
#' @param weights optional weights for computing the (weighted) combined sum of squares
#' @param verbose whether to print indexes to console (default is FALSE).
#' @note \sQuote{Con Corr} is the concordance correlation coefficient (https://en.wikipedia.org/wiki/Concordance_correlation_coefficient);
#' \sQuote{ME} is the model efficiency (https://en.wikipedia.org/wiki/Nash%E2%80%93Sutcliffe_model_efficiency_coefficient)
#' @export
#' @return object of class \sQuote{out_mrg}, which can be used for further plotting
#' @examples 
#' \donttest{
#' ## Directory with files
#' extd.dir <- system.file("extdata", package = "apsimx")
#' ## Comparing observed and simulated for Wheat
#' data(obsWheat)
#' sim.opt <- read.csv(file.path(extd.dir, "wheat-sim-opt.csv"))
#' sim.opt$Date <- as.Date(sim.opt$Date)
#'
#' cap <- compare_apsim(obsWheat, sim.opt, labels = c("obs", "sim"))
#'
#' plot(cap)
#' plot(cap, plot.type = "diff")
#' plot(cap, plot.type = "resid")
#' plot(cap, plot.type = "ts")
#'
#' plot(cap, variable = "AboveGround")
#' plot(cap, variable = "AboveGround", plot.type = "diff")
#' plot(cap, variable = "AboveGround", plot.type = "ts")
#' 
#' ## Selecting a variable
#' cap <- compare_apsim(obsWheat, sim.opt, variable = "AboveGround", 
#'                      labels = c("obs", "sim"))
#'                      
#' ## Using id
#' plot(cap, variable = "AboveGround", id = 0.05)
#'                      
#' 
#' 
#' }
#' 

compare_apsim <- function(..., 
                          variable,
                          index = "Date",
                          by,
                          labels, 
                          cRSS = FALSE,
                          weights,
                          verbose = FALSE){
  
  outs <- list(...)
  
  n.outs <- length(outs)
  
  if(n.outs < 2) stop("you should provide at least two data frames")
  
  out1 <- as.data.frame(outs[[1]])
  
  o.nms <- NULL
  if(!missing(labels)){
    o.nms <- labels
    if(length(labels) != n.outs)
      stop(" 'labels' lenght should be the same as the number of 'output' objects", call. = FALSE)
  } 
  
  if(!inherits(out1, "data.frame")) stop("object should be of class 'data.frame' ", call. = FALSE)
  
  if(!missing(variable)){
    if(length(variable) > 1) 
      stop("Only one variable can be selected", call. = FALSE)    
  }

  ## Process out1
  nms1 <- names(out1)
  
  if(!all(index %in% nms1)) 
    stop("index not found in first data.frame")
  
  if(!all(index %in% names(outs[[2]]))) 
    stop("index not found in second data.frame")
  
  nms1.i <- intersect(nms1, names(outs[[2]])) ## Variables in common

  if(all(c("report", "Date") %in% nms1) && length(index) == 1){
    stop("'report' and 'Date' found in first data frame but index length is equal to 1.
         Maybe index should be c('report', 'Date')?", call. = FALSE)
  }
  
  if(all(c("outfile", "Date") %in% nms1) && length(index) == 1){
    stop("'outfile' and 'Date' found in first data frame but index length is equal to 1.
         Maybe index should be c('outfile', 'Date')?", call. = FALSE)
  }
  
  if(all(c("SimulationName", "Date") %in% nms1) && length(index) == 1){
    stop("'SimulationName' and 'Date' found in first data frame but index length is equal to 1.
         Maybe index should be c('SimulationName', 'Date')?", call. = FALSE)
  }

  if(length(index) == 1){
    if(length(nms1.i) < 2) 
      stop("No names in common between the data.frames")    
  }else{
    if(length(nms1.i) < 3) 
      stop("No names in common between the data.frames")    
  }

  ## The line below drops irrelevant columns and brings index to the first column
  ##out1 <- subset(out1, select = c(index, nms1.i[-which(nms1 %in% index)]))
  out1 <- subset(out1, select = c(index, setdiff(nms1.i, index)))

  ### Drop character or factor variables which are not in index
  which.var.not.numeric <- sapply(subset(out1, select = setdiff(nms1.i, index)), is.numeric) 
  ### Remove non-numeric variables and throw warning if verbose
  if(any(isFALSE(which.var.not.numeric))){
    out1 <- out1[, -c(which(which.var.not.numeric == 0) + length(index))]
    if(verbose) warning("Removed non-numeric non-index variables from first data.frame")
  }
  
  new.nms1 <- paste0(names(out1), ".1") ## This simply adds a 1
  if(length(index) == 1){
    out1.new.names <- gsub(paste0(index, ".1"), index, new.nms1) ## Rename Date.1 to Date  
  }else{
    out1.new.names <- gsub(paste0(index[1], ".1"), index[1], new.nms1) ## Rename report.1 to report
    out1.new.names <- gsub(paste0(index[2], ".1"), index[2], out1.new.names) ## Rename Date.1 to Date
  }
  
  out.mrg <- stats::setNames(out1, out1.new.names) 
  
  for(i in 2:n.outs){
    
    ## This selects only those columns present in the first object
    out.i <- subset(outs[[i]], 
                    select = c(index, nms1.i[-which(nms1.i %in% index)])) 
    nms.i <- names(out.i)
    new.nms.i <- paste0(nms.i, ".", i)
    if(length(index) == 1){
      names(out.i) <- gsub(paste0(index, ".", i), index, new.nms.i)  
    }else{
      names.out.i <- gsub(paste0(index[1], ".", i), index[1], new.nms.i)  
      names(out.i) <- gsub(paste0(index[2], ".", i), index[2], names.out.i)  
    }
    
    out.mrg <- merge(out.mrg, out.i, by = index)
    
    if(nrow(out.mrg) < 1){
      stop("No data in common between data frames")
    }
  }

  if(length(index) == 1){
    ans.out.length <- ifelse(missing(variable), length(nms1.i) - 1, 1)  
  }else{
    ans.out.length <- ifelse(missing(variable), length(nms1.i) - 2, 1)  
  }
  
  ans <- data.frame(variable = rep(NA, ans.out.length), vs = NA, labels = NA, bias = NA,
                    intercept = NA, slope = NA, rss = NA, rmse = NA, r2 = NA, concorr = NA,
                    mod.eff = NA)
  k <- 1
  ## Calculate statistics for all variables
  resid.matrix <- NULL
  crss <- NA
  
  if(missing(variable)){
    var.sel <- setdiff(nms1.i, index) ## All variables except index
    gvar.sel <- paste0(var.sel, collapse = "|")
    idx.out.mrg <- grep(gvar.sel, names(out.mrg))
    out.mrg.s <- out.mrg[, idx.out.mrg]
    ## Compute Bias matrix
    for(i in var.sel){
      if(verbose) cat("Variable: ", i, "\n")
      tmp <- out.mrg.s[, grep(i, names(out.mrg.s))]
      if(ncol(tmp) < 2) stop("merged selected variables should be at least of length 2", call. = FALSE)
      if(ncol(tmp) > 2){
        ### This means that the variable matched more than one target in the dataframes
        ### I need an exact match
        wvm1 <- which(paste0(i, ".1") == names(out.mrg.s))
        wvm2 <- which(paste0(i, ".2") == names(out.mrg.s))
        tmp <- out.mrg.s[, c(wvm1, wvm2)]
      }
      ans$variable[k] <- i
   
      for(j in 2:ncol(tmp)){
        if(verbose) cat(names(tmp)[j - 1], " vs. ", names(tmp)[j], "\n")
        ans$vs[k] <- c(paste(names(tmp)[j - 1], "vs.", names(tmp)[j]))
        if(!missing(labels)){
          if(verbose) cat("labels:", labels[j - 1], " vs. ", labels[j], "\n")
          ans$labels[k] <- paste(labels[j - 1], " vs. ", labels[j])
        }
        fm0 <- lm(tmp[, j] ~ tmp[, j - 1], na.action = "na.exclude")
        ### Store residuals
        resid.matrix <- cbind(resid.matrix, stats::residuals(fm0, type = "pearson"))
        if(verbose) cat(" \t Bias: ", sum(tmp[, j - 1] - tmp[, j]), "\n")
        ans$bias[k] <- sum(tmp[, j - 1] - tmp[, j])
        if(verbose) cat(" \t Intercept: ", coef(fm0)[1], "\n")
        ans$intercept[k] <- coef(fm0)[1]
        if(verbose) cat(" \t Slope: ", coef(fm0)[2], "\n")
        ans$slope[k] <- coef(fm0)[2]
        if(verbose) cat(" \t RSS: ", deviance(fm0), "\n")
        ans$rss[k] <- deviance(fm0)
        if(verbose) cat(" \t RMSE: ", sigma(fm0), "\n")
        ans$rmse[k] <- sigma(fm0)
        if(verbose) cat(" \t R^2: ", summary(fm0)$r.squared, "\n")
        ans$r2[k] <- summary(fm0)$r.squared
        if(verbose) cat(" \t Corr: ", cor(tmp[, j - 1], tmp[, j]), "\n")
        ans$corr[k] <- cor(tmp[, j - 1], tmp[, j])
        if(verbose) cat(" \t Con. Corr: ", con_cor(tmp[, j - 1], tmp[, j]), "\n")
        ans$concorr[k] <- con_cor(tmp[, j - 1], tmp[, j])
        if(verbose) cat(" \t ME: ", mod_eff(tmp[, j - 1], tmp[, j]), "\n")
        ans$mod.eff[k] <- mod_eff(tmp[, j - 1], tmp[, j])
      }
      k <- k + 1
    }
    #### Compute cRSS (combined Residual Sum of Squares) ----
    if(cRSS){
      sndout1 <- grep(".1", names(out.mrg), fixed = TRUE, value = TRUE)
      sndout2 <- grep(".2", names(out.mrg), fixed = TRUE, value = TRUE)
      dout1 <- subset(out.mrg, select = sndout1)
      dout2 <- subset(out.mrg, select = sndout2)
      diffs <- as.matrix(dout1) - as.matrix(dout2)
      if(missing(weights)) weights <- rep(1, ncol(diffs))
      crss <- sum(weights * colSums(diffs^2, na.rm = TRUE)) 
    }
    ### Need to assign names to residual matrix
    ## browser()
    colnames(resid.matrix) <- var.sel
  }
  
  if(!missing(variable)){
    ## Just select the appropriate variable
    idx.out.mrg <- grep(variable, names(out.mrg))  
    out.mrg.s <- out.mrg[, idx.out.mrg]
    
    if(verbose) cat("Variable:", variable, "\n")
    ans$variable[k] <- i
    tmp <- out.mrg.s
    for(j in 2:ncol(tmp)){
      if(verbose) cat(names(tmp)[j - 1], " vs. ", names(tmp)[j], "\n")
      ans$vs[k] <- c(paste(names(tmp)[j - 1], "vs.", names(tmp)[j]))
      if(!missing(labels)){
        if(verbose) cat("labels", labels[j - 1], " vs. ", labels[j], "\n")
        ans$labels[k] <- paste(labels[j - 1], " vs. ", labels[j])
      }
      fm0 <- lm(tmp[, j - 1] ~ tmp[, j])
      ### Store residuals
      resid.matrix <- cbind(resid.matrix, stats::residuals(fm0, type = "pearson"))
      if(verbose) cat(" \t Bias: ", sum(tmp[, j - 1] - tmp[, j]), "\n")
      ans$bias[k] <- sum(tmp[, j - 1] - tmp[, j])
      if(verbose) cat(" \t Intercept: ", coef(fm0)[1], "\n")
      ans$intercept[k] <- coef(fm0)[1]
      if(verbose) cat(" \t Slope: ", coef(fm0)[2], "\n")
      ans$slope[k] <- coef(fm0)[2]
      if(verbose) cat(" \t RSS: ", deviance(fm0), "\n")
      ans$rss[k] <- deviance(fm0)
      if(verbose) cat(" \t RMSE: ", sigma(fm0), "\n")
      ans$rmse[k] <- sigma(fm0)
      if(verbose) cat(" \t R^2: ", summary(fm0)$r.squared, "\n")
      ans$r2[k] <- summary(fm0)$r.squared
      if(verbose) cat(" \t Corr: ", cor(tmp[,j - 1], tmp[, j]), "\n")
      ans$corr[k] <- cor(tmp[, j - 1], tmp[, j])
      if(verbose) cat(" \t Con. Corr: ", con_cor(tmp[, j - 1], tmp[, j]), "\n")
      ans$concorr[k] <- con_cor(tmp[, j - 1], tmp[, j])
      if(verbose) cat(" \t ME: ", mod_eff(tmp[, j-1], tmp[, j]), "\n")
      ans$mod.eff[k] <- mod_eff(tmp[, j - 1], tmp[, j])
    }
    clnm <- gsub(".1", "", grep(variable, names(out.mrg), value = TRUE)[1], fixed = TRUE) 
    colnames(resid.matrix) <- clnm
  }

  attr(out.mrg, "out.names") <- o.nms
  attr(out.mrg, "length.outs") <- n.outs
  attr(out.mrg, "index") <- index
  out.mrg <- structure(list(out.mrg = out.mrg, index.table = ans, cRSS = crss, resid.matrix = resid.matrix),
                       class = "out_mrg")
  invisible(out.mrg)
}

#' print method for out_mrg
#' @rdname compare_apsim
#' @description print method for \sQuote{out_mrg}
#' @param x object of class \sQuote{out_mrg}
#' @param ... additional arguments passed to print
#' @param digits digits to print (default is 2)
#' @export
#' @return it prints the index.table data.frame
print.out_mrg <- function(x, ..., digits = 2){
  print(x$index.table, digits = digits)
}

#' The by and facet arguments are only available for plot.type vs and ts for now
#' 
#' Plotting function for observed and simulated data
#' @rdname compare_apsim
#' @description plotting function for compare_apsim, it requires ggplot2
#' @param x object of class \sQuote{out_mrg}
#' @param ... data frames with APSIM output or observed data. 
#' @param plot.type either \sQuote{vs}, \sQuote{diff}, \sQuote{ts} - for time series or \sQuote{density}
#' @param pairs pair of objects to compare, defaults to 1 and 2 but others are possible
#' @param cumulative whether to plot cumulative values (default FALSE)
#' @param variable variable to plot 
#' @param id identification. Useful for finding extreme values. If this values is equal to 
#' 1 and no id.label is provided all observations are labeled by the row number. If it is 
#' less than one points are labeled if their probability is equal or less than the id value.
#' For example, a value of 0.05 will label values that have a probability of 0.05 (or less)
#' under a normal distribution.
#' @param id.label optional label for the id
#' @param by variable in \sQuote{index} used for plotting
#' @param facet whether to facet or use color for the by variable (default is FALSE, meaning \sQuote{color})
#' @param span argument passed to \sQuote{geom_smooth}
#' @param dodge.width optional argument to control the \sQuote{dodge} for the \sQuote{id.label}
#' @return it produces a plot
#' @export
#' 
plot.out_mrg <- function(x, ..., plot.type = c("vs", "diff", "resid", "ts", "density"),
                         pairs = c(1, 2),
                         cumulative = FALSE, ## Might not make sense for these type of graphs...
                         variable,
                         id,
                         id.label,
                         by,
                         facet = FALSE,
                         span = 0.75,
                         dodge.width = NULL){
  
  if(!requireNamespace("ggplot2", quietly = TRUE)){
    warning("ggplot2 is required for this plotting function")
    return(NULL)
  }
  
  x.resid <- x$resid.matrix
  colnames(x.resid) <- paste0("resid.", colnames(x.resid))
  x <- x$out.mrg
  
  o.nms <- attr(x, "out.names")
  if(max(pairs) > attr(x, "length.outs")) stop("pairs index larger than length of outs")
  
  index <- attr(x, "index") ## This is normally 'Date'
  x <- as.data.frame(unclass(x))

  if(!missing(by) && length(index) == 1)
    stop("'by' is only available when index length is equal to 2.")
  
  if(missing(variable)){
    vnms <- setdiff(names(x), index)[1]
    variable <- gsub(".1", "", vnms, fixed = TRUE)
  }else{
    variable <- gsub(".1", "", grep(variable, names(x), value = TRUE)[1], fixed = TRUE)
  } 
  
  if(is.na(variable) || length(variable) == 0) stop("variable not found")
  
  ### If I'm guaranteed to have a variable then I need to subset residuals
  x.resid <- x.resid[, grep(variable, colnames(x.resid), value = TRUE), drop = FALSE]
  
  plot.type <- match.arg(plot.type)
  
  if(cumulative && plot.type != "ts") 
    stop("cumulative is only available for plot.type = 'ts' ")
  
  ### id and label ----
  ### If id and label are missing
  if(missing(id) && missing(id.label)){
    id.lbs <- rep("", nrow(x))
    if(is.null(dodge.width)) dodge.width <- 0
  }
    
  if(missing(id) && !missing(id.label))
    stop("'id' should be specified if 'id.label' is not missing", call. = FALSE)
  
  ### I should be able to add the label to all plots and not need the
  ### duplication
  prs0 <- paste0(variable, ".", pairs)
  prs <- paste0(prs0, collapse = "|")
  tmp <- x[, grep(prs, names(x))]
  ## Add residuals
  tmpr <- cbind(tmp, x.resid)
  if(!missing(id)){
    if(is.null(dodge.width)){
      dodge.width <- diff(range(tmp[[prs0[1]]])) * (1/10)  
    }
    if(missing(id.label) && id == 1){
      id.lbs <- seq_len(nrow(tmp))
    }
    if(missing(id.label) && id < 1){
      ### Probability of residuals under the normal distribution
      p.vls <- stats::pnorm(-abs(x.resid))
      w.pvls <- !c(p.vls <= id)
      id.lbs <- seq_len(nrow(tmp))
      id.lbs[w.pvls] <- ""
    }
    if(!missing(id.label) && id == 1){
      if(length(id.label) != nrow(tmp))
        stop("length of id.label whould be equal to the number of observations", call. = FALSE)
      id.lbs <- id.label
    }
    if(!missing(id.label) && id < 1){
      if(length(id.label) != nrow(tmp))
        stop("length of id.label should be equal to the number of observations", call. = FALSE)
      id.lbs <- id.label
      p.vls <- stats::pnorm(-abs(x.resid))
      w.pvls <- !c(p.vls <= id)
      id.lbs[w.pvls] <- ""
    }    
  }

  #### plot.type = "vs" ----
  if(plot.type == "vs" && !cumulative && (length(index) == 1 || missing(by))){
    tmp <- x[, grep(variable, names(x))]
    prs <- paste0(variable, ".", pairs)
    gp1 <- ggplot2::ggplot(data = tmp, ggplot2::aes(x = eval(parse(text = eval(prs[1]))), 
                                                    y = eval(parse(text = eval(prs[2]))))) +
      ggplot2::geom_point() + 
      ggplot2::xlab(paste(o.nms[pairs[1]], prs[1])) + 
      ggplot2::ylab(paste(o.nms[pairs[2]], prs[2])) + 
      ggplot2::geom_smooth(method = "lm", ...) + 
      ggplot2::geom_abline(intercept = 0, slope = 1, color = "orange") + 
      ggplot2::geom_text(ggplot2::aes(label = id.lbs),
                         position = ggplot2::position_dodge2(dodge.width))
    
    print(gp1)
    
  }
  
  if(plot.type == "vs" && !cumulative && length(index) == 2 && !missing(by)){
    if(!facet){
      tmp <- x[, c(by, grep(variable, names(x), value = TRUE))]
      prs <- paste0(variable, ".", pairs)
      gp1 <- ggplot2::ggplot(data = tmp, ggplot2::aes(x = eval(parse(text = eval(prs[1]))), 
                                                      y = eval(parse(text = eval(prs[2]))),
                                                      color = eval(parse(text = eval(by))))) +
        ggplot2::geom_point() + 
        ggplot2::xlab(paste(o.nms[pairs[1]], prs[1])) + 
        ggplot2::ylab(paste(o.nms[pairs[2]], prs[2])) + 
        ggplot2::geom_smooth(method = "lm", ...) + 
        ggplot2::geom_abline(intercept = 0, slope = 1, color = "orange") + 
        ggplot2::guides(color=ggplot2::guide_legend(title=by)) + 
        ggplot2::geom_text(ggplot2::aes(label = id.lbs),
                           position = ggplot2::position_dodge2(dodge.width))
      
      print(gp1)      
    }else{
      tmp <- x[, c(by, grep(variable, names(x), value = TRUE))]
      prs <- paste0(variable, ".", pairs)
      gp1 <- ggplot2::ggplot(data = tmp, ggplot2::aes(x = eval(parse(text = eval(prs[1]))), 
                                                      y = eval(parse(text = eval(prs[2]))))) +
        ggplot2::facet_wrap(~eval(parse(text = eval(by)))) + 
        ggplot2::geom_point() + 
        ggplot2::xlab(paste(o.nms[pairs[1]], prs[1])) + 
        ggplot2::ylab(paste(o.nms[pairs[2]], prs[2])) + 
        ggplot2::geom_smooth(method = "lm", ...) + 
        ggplot2::geom_abline(intercept = 0, slope = 1, color = "orange") + 
        ggplot2::geom_text(ggplot2::aes(label = id.lbs),
                           position = ggplot2::position_dodge2(dodge.width))
      
      print(gp1)
    }
  }
  
  #### plot.type = "diff" ----
  if(plot.type == "diff" && !cumulative){
    
    prs0 <- paste0(variable, ".", pairs)
    prs <- paste0(prs0, collapse = "|")
    tmp <- x[, grep(prs, names(x))]
    
    ## x Variable is prs[1]
    ## y Variable is prs[2] - prs[1]
    dff <- tmp[,prs0[2]] - tmp[,prs0[1]]
    
    gp1 <- ggplot2::ggplot(data = tmp, ggplot2::aes(x = eval(parse(text = eval(prs0[1]))), 
                                                    y = dff)) +
      ggplot2::geom_point() + 
      ggplot2::xlab(paste(o.nms[pairs[1]], prs0[1])) + 
      ggplot2::ylab(paste("Difference", prs0[2], "-", prs0[1])) + 
      ggplot2::geom_smooth(method = "lm", ...) + 
      ggplot2::geom_hline(yintercept = 0, color = "orange") + 
      ggplot2::geom_text(ggplot2::aes(label = id.lbs),
                         position = ggplot2::position_dodge2(dodge.width))
    
    print(gp1)   
  }

  #### plot.type = "resid" ----
  if(plot.type == "resid" && !cumulative){
    
    if(is.null(dodge.width)) dodge.width <- 0
    
    resid.name <- grep("resid", names(tmpr), value = TRUE)
    
    gp1 <- ggplot2::ggplot(data = tmpr, ggplot2::aes(x = eval(parse(text = eval(prs0[1]))), 
                                                     y = eval(parse(text = eval(resid.name))))) +
      ggplot2::geom_point() + 
      ggplot2::xlab(paste(o.nms[pairs[1]], prs0[1])) + 
      ggplot2::ylab(paste("Pearson ", resid.name)) + 
      ggplot2::geom_smooth(method = "lm", ...) + 
      ggplot2::geom_hline(yintercept = 0, color = "orange") + 
      ggplot2::geom_text(ggplot2::aes(label = id.lbs),
                           position = ggplot2::position_dodge2(dodge.width))
    print(gp1)   
  }
  
    
  if(plot.type == "ts" && !cumulative && (length(index) == 1 || missing(by))){
  
    prs0 <- paste0(variable, ".", pairs)
    prs <- paste0(prs0, collapse = "|")
    tmp <- x[, grep(prs, names(x))]
    if(length(index) == 1){
      tmp[[index]] <- x[[index]] ## Put it back in - kinda dumb   
    }else{
      if(index[2] == 'Date'){
        tmp[[index[2]]] <- x[[index[2]]] ## Put it back in - kinda dumb   
      }else{
        stop("I have not implemented this yet", call. = FALSE)
      }
    }
    
    gp1 <- ggplot2::ggplot(data = tmp, ggplot2::aes(x = .data[[index[1]]], 
                                                    y = eval(parse(text = eval(prs0[1]))),
                                                    color = paste(o.nms[pairs[1]], prs0[1]))) +
      
      ggplot2::geom_point() + 
      ggplot2::geom_smooth(span = span, ...) + 
      ggplot2::geom_point(ggplot2::aes(y = eval(parse(text = eval(prs0[2]))),
                                       color = paste(o.nms[pairs[2]], prs0[2]))) + 
      ggplot2::geom_smooth(ggplot2::aes(y = eval(parse(text = eval(prs0[2]))),
                                        color = paste(o.nms[pairs[2]], prs0[2])),
                           span = span, ...) + 
      ggplot2::xlab(index) + 
      ggplot2::ylab(variable) + 
      ggplot2::guides(color=ggplot2::guide_legend(title="")) + 
      ggplot2::geom_text(ggplot2::aes(label = id.lbs),
                         position = ggplot2::position_dodge2(dodge.width))
    
    print(gp1)   
  }

  
  #### plot.type = "ts" ----
  if(plot.type == "ts" && !cumulative && length(index) == 2 && !missing(by)){
    
    if(facet){
      prs0 <- paste0(variable, ".", pairs)
      prs <- paste0(prs0, collapse = "|")
      tmp <- x[, c(index, grep(prs, names(x), value = TRUE))]

      gp1 <- ggplot2::ggplot(data = tmp, ggplot2::aes(x = .data[[index[2]]], 
                                                      y = eval(parse(text = eval(prs0[1]))),
                                                      color = paste(o.nms[pairs[1]], prs0[1]))) +
        ggplot2::facet_wrap(~eval(parse(text = eval(by)))) + 
        ggplot2::geom_point() + 
        ggplot2::geom_smooth(span = span, ...) + 
        ggplot2::geom_point(ggplot2::aes(y = eval(parse(text = eval(prs0[2]))),
                                         color = paste(o.nms[pairs[2]], prs0[2]))) + 
        ggplot2::geom_smooth(ggplot2::aes(y = eval(parse(text = eval(prs0[2]))),
                                          color = paste(o.nms[pairs[2]], prs0[2])),
                             span = span, ...) + 
        ggplot2::xlab(index[2]) + 
        ggplot2::ylab(variable) + 
        ggplot2::guides(color=ggplot2::guide_legend(title="")) + 
        ggplot2::geom_text(ggplot2::aes(label = id.lbs),
                           position = ggplot2::position_dodge2(dodge.width))
      
      print(gp1)         
    }else{
      stop("Set 'facet' to TRUE for this type of graph", call. = FALSE)
    }

  }
    
  if(plot.type == "ts" && cumulative){
    
    if(length(index) != 1)
      stop("I have only implemented this when 'index' length is equal to 1")
    
    prs0 <- paste0(variable, ".", pairs)
    prs <- paste0(prs0, collapse = "|")
    tmp <- x[, grep(prs, names(x))]
    tmp[[index]] <- x[[index]]
    tmp$cum_var1 <- cumsum(tmp[, prs0[1]])
    tmp$cum_var2 <- cumsum(tmp[, prs0[2]])
    
    gp1 <- ggplot2::ggplot(data = tmp, ggplot2::aes(x = .data[[index]], 
                                                    y = .data[["cum_var1"]],
                                                    color = paste(o.nms[pairs[1]], prs0[1]))) +
      
      ggplot2::geom_line() + 
      ggplot2::geom_line(ggplot2::aes(y = .data[["cum_var2"]],
                                      color = paste(o.nms[pairs[2]], prs0[2]))) + 
      ggplot2::xlab(index) + 
      ggplot2::ylab(paste("Cumulative ", variable)) + 
      ggplot2::theme(legend.title = ggplot2::element_blank()) + 
      ggplot2::geom_text(ggplot2::aes(label = id.lbs),
                         position = ggplot2::position_dodge2(dodge.width))
    
    print(gp1)   
  }
  
  if(plot.type == "density"){
    
    prs0 <- paste0(variable, ".", pairs)
    prs <- paste0(prs0, collapse = "|")
    tmp <- x[, grep(prs, names(x))]
    
    gp1 <- ggplot2::ggplot(data = tmp, ggplot2::aes(x = eval(parse(text = eval(prs0[1]))),
                                                    color = paste(o.nms[pairs[1]], prs0[1]))) + 
      ggplot2::geom_density() + 
      ggplot2::geom_density(ggplot2::aes(x = eval(parse(text = eval(prs0[2]))),
                                         color = paste(o.nms[pairs[2]], prs0[2]))) +
      ggplot2::xlab(variable) + 
      ggplot2::theme(legend.title = ggplot2::element_blank())
    
    print(gp1)
  }
  invisible(gp1)
}

## Model efficiency
## https://en.wikipedia.org/wiki/Nash%E2%80%93Sutcliffe_model_efficiency_coefficient
mod_eff <- function(x, y){
  sse <- sum((x - y)^2)
  ssx <- sum((x - mean(x))^2)
  ans <- 1 - sse / ssx
  ans
}

## Concordance correlation
## https://en.wikipedia.org/wiki/Concordance_correlation_coefficient
con_cor <- function(x, y){
  num <- 2 * cor(x, y) * sd(x) * sd(y)
  den <- var(x) + var(y) + (mean(x) - mean(y))^2
  ans <- num/den
  ans
}