R/plot.IWTaov.R

In alessiapini/fdatest: Interval Wise Testing for Functional Data

#' @title Plot method for IWT results on functional ANOVA
#' 
#' @description \code{plot} method for class "\code{IWTaov}".
#' Plotting function creating a graphical output of the IWT for the test on a functional analysis of variance: 
#' functional data, and IWT-adjusted p-values of the F-tests on the whole model and on each factor are plotted.
#' 
#' @param x  The object to be plotted. An object of class "\code{IWTaov}", usually, a result of a call 
#' to \code{\link{IWTaov}}.
#' 
#' @param xrange Range of the \code{x} axis.
#' 
#' @param alpha1 First level of significance used to select and display significant effects. Default is \code{alpha1 = 0.05}.
#' 
#' @param alpha2 Second level of significance used to select and display significant effects. Default is \code{alpha1 = 0.01}. 
#' \code{alpha1} and \code{alpha2} are s.t. \code{alpha2 < alpha1}. Otherwise the two values are switched.
#' 
#' @param plot_adjpval A logical indicating wether the plots of adjusted p-values have to be done. Default is \code{plot_adjpval = FALSE}.
#' 
#' @param ylim Range of the \code{y} axis. Default is \code{NULL}, giving a plot with authomatic range for functional data.
#' 
#' @param col Colors for the plot of functional data. Default is \code{col = 1}.
#' 
#' @param ylab Label of \code{y} axis of the plot of functional data. Default is "\code{Functional Data}".
#' 
#' @param main An overall title for the plots (it will be pasted to "Functional Data and F-test" for the first plot and to factor names for the other plots).
#' 
#' @param lwd Line width for the plot of the adjusted p-value function. Default is \code{lwd=1}.
#' 
#' @param type line type for the plot of the adjusted p-value function. Default is type='l'.
#' 
#' @param ... Additional plotting arguments that can be used with function \code{plot}, 
#' such as \code{\link{graphical parameters}} (see \code{\link{par}}).
#' 
#' @return No value returned. 
#' The function produces a graphical output of the IWT results:  the plot of the functional data and the one of the adjusted p-values. 
#' The portions of the domain selected as significant by the test at level \code{alpha1} and \code{alpha2} are highlighted in the plot of the adjusted p-value function and in the one of functional data by gray areas (light and dark gray, respectively). 
#' The first plot reports the gray areas corresponding to a significant F-test on the whole model. The remaining plots report the gray areas corresponding to significant F-tests on each factor (with colors corresponding to the levels of the factor).
#' 
#' @seealso \code{\link{IWTimage}} for the plot of p-values heatmaps. 
#' See also \code{\link{IWT1}}, \code{\link{IWT2}} to perform the ITP to test on the mean of one population and test of differences between two populations. 
#' See \code{\link{ITPaovbspline}} for functional ANOVA based on B-spline basis representation
#' 
#' @examples 
#' # Importing the NASA temperatures data set
#' data(NASAtemp)
#' 
#' temperature <- rbind(NASAtemp$milan,NASAtemp$paris)
#' groups <- c(rep(0,22),rep(1,22))
#' 
#' # Performing the IWT
#' IWT.result <- IWTaov(temperature ~ groups,B=1000)
#' 
#' # Summary of the IWT results
#' summary(IWT.result)
#' 
#' # Plot of the IWT results
#' layout(1)
#' plot(IWT.result)
#' 
#' # All graphics on the same device
#' layout(matrix(1:4,nrow=2,byrow=FALSE))
#' plot(IWT.result,main='NASA data', plot_adjpval = TRUE,xlab='Day',xrange=c(1,365))
#' 
#' @references
#' Pini, A., & Vantini, S. (2017). Interval-wise testing for functional data. \emph{Journal of Nonparametric Statistics}, 29(2), 407-424
#'
#' Pini, A., Vantini, S., Colosimo, B. M., & Grasso, M. (2018). Domain‐selective functional analysis of variance for supervised statistical profile monitoring of signal data. \emph{Journal of the Royal Statistical Society: Series C (Applied Statistics)} 67(1), 55-81.
#'
#' Abramowicz, K., Hager, C. K., Pini, A., Schelin, L., Sjostedt de Luna, S., & Vantini, S. (2018).
#' Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament. \emph{Scandinavian Journal of Statistics} 45(4), 1036-1061.
#'
#' @export

plot.IWTaov <- function(x, xrange = c(0,1), 
                        alpha1 = 0.05, alpha2 = 0.01, 
                        plot_adjpval = FALSE,
                        ylim = NULL, col = 1,
                        ylab = 'Functional Data', 
                        main = NULL, lwd = 0.5, type='l', ...) {
  if (class(x) != "IWTaov") stop("x should be an object of the class IWTaov")
  if (alpha1 < alpha2) {
    temp <- alpha1
    alpha1 <- alpha2
    alpha2 <- temp
  }
  object <- x
  nvar <- dim(object$adjusted_pval_factors)[1]
  p <- length(object$unadjusted_pval_F)
  n <- dim(t(object$data.eval))[1]
  xmin <- xrange[1]
  xmax <- xrange[2]
  abscissa_pval = seq(xmin, xmax, len = p)
  devAskNewPage(ask = TRUE)  
  main_f <- paste(main, ': Functional Data and F-test')
  main_f <- sub("^ : +", "", main_f)
  
  if (is.null(ylim)) ylim <- range(object$data.eval)
  
  if(nvar>1){
    matplot(abscissa_pval, t(object$data.eval), type = 'l', col = col, main = main_f, 
            ylab = ylab, ylim = ylim, lwd = lwd, ...)
    difference1 <- which(object$adjusted_pval_F < alpha1)
    if (length(difference1) > 0) {
      for (j in 1:length(difference1)) {
        min_rect <- abscissa_pval[difference1[j]] - (abscissa_pval[2] - abscissa_pval[1])/2
        max_rect <- min_rect + (abscissa_pval[2] - abscissa_pval[1])
        rect(min_rect, par("usr")[3], max_rect, par("usr")[4], col = "gray90", 
             density = -2, border = NA)
      }
      rect(par("usr")[1], par("usr")[3], par("usr")[2],par("usr")[4], col = NULL,
           border = "black")
    }
    difference2 <- which(object$adjusted_pval_F < alpha2)
    if (length(difference2) > 0) {
      for (j in 1:length(difference2)) {
        min_rect <- abscissa_pval[difference2[j]] - (abscissa_pval[2] - abscissa_pval[1])/2
        max_rect <- min_rect + (abscissa_pval[2] - abscissa_pval[1])
        rect(min_rect, par("usr")[3], max_rect, par("usr")[4], col = "gray80", 
             density = -2, border = NA)
      }
      rect(par("usr")[1], par("usr")[3], par("usr")[2],par("usr")[4], col = NULL,
           border = "black")
    }
    matplot(abscissa_pval, t(object$data.eval), type = 'l', 
            col = col, add = TRUE, lwd = lwd, ...)
    
  }
  
  
  names_all <- colnames(object$design_matrix)
  interaz <- grep(':', names_all)
  for (var in 1:(dim(object$adjusted_pval_factors)[1])) {
    var_name <- rownames(object$adjusted_pval_factors)[var]
    main_t <- paste(main, ': factor', var_name, sep = ' ')
    main_t <- sub("^ : +", "", main_t)
    if (length(grep(':', var_name)) > 0) { # Plot interaction
      var12 <- strsplit(var_name, ':')
      var1 <- var12[[1]][1]
      var2 <- var12[[1]][2]
      dummy_test1 <- grep(var1, names_all)
      dummy_test2 <- grep(var2, names_all)
      dummy_test <- intersect(dummy_test1, dummy_test2)
      colors <- object$design_matrix[, dummy_test]
      if (length(dim(colors)) > 1) {
        colors <- (apply(colors, 1, paste, collapse = ''))
      }
      colors <- as.factor(colors)
    } else { # Plot of a factor
      dummy_test <- grep(var_name, names_all)
      dummy_test <- setdiff(dummy_test, interaz)
      colors <- object$design_matrix[, dummy_test]
      if (length(dim(colors)) > 1) {
        colors <- (apply(colors, 1, paste, collapse = ''))
      }
      colors <- as.factor(colors)
    }
    matplot(abscissa_pval, t(object$data.eval),type = 'l', col = colors, ylim = ylim,
            lwd = 1, main = main_t, ylab = ylab, ...)
    difference1 <- which(object$adjusted_pval_factors[var,] < alpha1)
    if (length(difference1) > 0) {
      for (j in 1:length(difference1)) {
        min_rect <- abscissa_pval[difference1[j]] - (abscissa_pval[2] - abscissa_pval[1])/2
        max_rect <- min_rect + (abscissa_pval[2] - abscissa_pval[1])
        rect(min_rect, par("usr")[3], max_rect, par("usr")[4], col = "gray90", 
             density = -2, border = NA)
      }
      rect(par("usr")[1], par("usr")[3], par("usr")[2],par("usr")[4], 
           col = NULL, border = "black")
    }
    difference2 <- which(object$adjusted_pval_factors[var,] < alpha2)
    if (length(difference2) > 0) {
      for (j in 1:length(difference2)) {
        min_rect <- abscissa_pval[difference2[j]] - (abscissa_pval[2] - abscissa_pval[1])/2
        max_rect <- min_rect + (abscissa_pval[2] - abscissa_pval[1])
        rect(min_rect, par("usr")[3], max_rect, par("usr")[4], col = "gray80", 
             density = -2, border = NA)
      }
      rect(par("usr")[1], par("usr")[3], par("usr")[2],par("usr")[4], 
           col = NULL, border = "black")
    }
    matlines(abscissa_pval, t(object$data.eval), type='l', col=colors, ...)
    abline(h = 0, lty = 2, col = 1)
  }
  # Plot adjusted p-values
  if (plot_adjpval == TRUE) {
    main_p <- paste(main, ': Adjusted p-values - F-test')
    main_p <- sub("^ : +", "", main_p)
    plot(abscissa_pval, object$adjusted_pval_F, ylim = c(0, 1),
         main = main_p, ylab = 'p-value',type=type,lwd=2, ...)
    difference1 <- which(object$adjusted_pval_F < alpha1)
    if (length(difference1) > 0) {
      for (j in 1:length(difference1)) {
        min_rect <- abscissa_pval[difference1[j]] - (abscissa_pval[2] - abscissa_pval[1])/2
        max_rect <- min_rect + (abscissa_pval[2] - abscissa_pval[1])
        rect(min_rect, par("usr")[3], max_rect, par("usr")[4], col = "gray90", 
             density = -2, border = NA)
      }
      rect(par("usr")[1], par("usr")[3], par("usr")[2],par("usr")[4], 
           col = NULL, border = "black")
    }
    difference2 <- which(object$adjusted_pval_F < alpha2)
    if (length(difference2) > 0) {
      for (j in 1:length(difference2)) {
        min_rect <- abscissa_pval[difference2[j]] - (abscissa_pval[2] - abscissa_pval[1])/2
        max_rect <- min_rect + (abscissa_pval[2] - abscissa_pval[1])
        rect(min_rect, par("usr")[3], max_rect, par("usr")[4], col = "gray80", 
             density = -2, border = NA)
      }
      rect(par("usr")[1], par("usr")[3], par("usr")[2],par("usr")[4], 
           col = NULL, border = "black")
    }
    for (j in 0:10) {
      abline(h = j / 10, col = 'lightgray', lty = "dotted")
    }
    lines(abscissa_pval, object$adjusted_pval_F, lwd=2, type=type,...)
    for (var in 1:(dim(object$adjusted_pval_factors)[1])) {
      var_name <- rownames(object$adjusted_pval_factors)[var]
      main_p <- paste(main, ': Adjusted p-values - factor', var_name)
      main_p <- sub("^ : +", "", main_p)
      plot(abscissa_pval, object$adjusted_pval_factors[var, ],
           ylim = c(0, 1), main = main_p, ylab = 'p-value',lwd=2,type=type, ...)
      difference1 <- which(object$adjusted_pval_factors[var,] < alpha1)
      if (length(difference1) > 0) {
        for (j in 1:length(difference1)) {
          min_rect <- abscissa_pval[difference1[j]] - (abscissa_pval[2] - abscissa_pval[1])/2
          max_rect <- min_rect + (abscissa_pval[2] - abscissa_pval[1])
          rect(min_rect, par("usr")[3], max_rect, par("usr")[4], col = "gray90", 
               density = -2, border = NA)
        }
        rect(par("usr")[1], par("usr")[3], par("usr")[2],par("usr")[4], 
             col = NULL, border = "black")
      }
      difference2 <- which(object$adjusted_pval_factors[var,] < alpha2)
      if (length(difference2) > 0) {
        for (j in 1:length(difference2)) {
          min_rect <- abscissa_pval[difference2[j]] - (abscissa_pval[2] - abscissa_pval[1])/2
          max_rect <- min_rect + (abscissa_pval[2] - abscissa_pval[1])
          rect(min_rect, par("usr")[3], max_rect, par("usr")[4], col = "gray80", 
               density = -2, border = NA)
        }
        rect(par("usr")[1], par("usr")[3], par("usr")[2],par("usr")[4], 
             col = NULL, border = "black")
      }
      for (j in 0:10) {
        abline(h = j / 10, col = 'lightgray', lty = "dotted")
      }
      lines(abscissa_pval, object$adjusted_pval_factors[var,],type=type,lwd=2, ...)
    }
  }
  devAskNewPage(ask = FALSE)  
}