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###########################################################
##Authors: Andreas Alfons, Bernd Prantner, Matthias Templ
## and Daniel Schopfhauser
## Vienna University of Technology
###########################################################
#' Aggregations for missing/imputed values
#'
#' Calculate or plot the amount of missing/imputed values in each variable and
#' the amount of missing/imputed values in certain combinations of variables.
#'
#' Often it is of interest how many missing/imputed values are contained in
#' each variable. Even more interesting, there may be certain combinations of
#' variables with a high number of missing/imputed values.
#'
#' If `combined` is `FALSE`, two separate plots are drawn for the
#' missing/imputed values in each variable and the combinations of
#' missing/imputed and non-missing values. The barplot on the left hand side
#' shows the amount of missing/imputed values in each variable. In the
#' *aggregation plot* on the right hand side, all existing combinations of
#' missing/imputed and non-missing values in the observations are visualized.
#' Available, missing and imputed data are color coded as given by `col`.
#' Additionally, there are two possibilities to represent the frequencies of
#' occurrence of the different combinations. The first option is to visualize
#' the proportions or frequencies by a small bar plot and/or numbers. The
#' second option is to let the cell heights be given by the frequencies of the
#' corresponding combinations. Furthermore, variables may be sorted by the
#' number of missing/imputed values and combinations by the frequency of
#' occurrence to give more power to finding the structure of missing/imputed
#' values.
#'
#' If `combined` is `TRUE`, a small version of the barplot showing
#' the amount of missing/imputed values in each variable is drawn on top of the
#' aggregation plot.
#'
#' The graphical parameter `oma` will be set unless supplied as an
#' argument.
#'
#' @aliases aggr plot.aggr print.aggr summary.aggr print.summary.aggr
#' @param x a vector, matrix or `data.frame`.
#' @param delimiter a character-vector to distinguish between variables and
#' imputation-indices for imputed variables (therefore, `x` needs to have
#' [colnames()]). If given, it is used to determine the corresponding
#' imputation-index for any imputed variable (a logical-vector indicating which
#' values of the variable have been imputed). If such imputation-indices are
#' found, they are used for highlighting and the colors are adjusted according
#' to the given colors for imputed variables (see `col`).
#'
#' @return for `aggr`, a list of class `"aggr"` containing the
#' following components:
#' - x the data used.
#' - combinations a character vector representing the combinations of
#' variables.
#' - count the frequencies of these combinations.
#' - percent the percentage of these combinations.
#' - missings a `data.frame` containing the amount of
#' missing/imputed values in each variable.
#' - tabcomb the indicator matrix for the combinations of variables.
#' @note Some of the argument names and positions have changed with version 1.3
#' due to extended functionality and for more consistency with other plot
#' functions in `VIM`. For back compatibility, the arguments `labs`
#' and `names.arg` can still be supplied to \code{\dots{}} and are handled
#' correctly. Nevertheless, they are deprecated and no longer documented. Use
#' `ylabs` and `labels` instead.
#' @author Andreas Alfons, Matthias Templ, modifications for displaying imputed
#' values by Bernd Prantner
#' @seealso [print.aggr()], [summary.aggr()]
#' @references M. Templ, A. Alfons, P. Filzmoser (2012) Exploring incomplete
#' data using visualization tools. *Journal of Advances in Data Analysis
#' and Classification*, Online first. DOI: 10.1007/s11634-011-0102-y.
#' @keywords hplot
#' @family plotting functions
#' @examples
#'
#' data(sleep, package="VIM")
#' ## for missing values
#' a <- aggr(sleep)
#' a
#' summary(a)
#'
#' ## for imputed values
#' sleep_IMPUTED <- kNN(sleep)
#' a <- aggr(sleep_IMPUTED, delimiter="_imp")
#' a
#' summary(a)
#'
#' @export
aggr <- function(x, delimiter = NULL, plot = TRUE, ...) {
check_data(x)
x <- as.data.frame(x)
imputed <- FALSE # indicates if there are Variables with missing-index
if(is.null(dim(x))) {
n <- length(x)
imp <- FALSE
cn <- defaultNames(1)
nNA <- countNA(x)
tab <- table(as.numeric(is.na(x)))
tabcomb <- as.matrix(as.integer(names(tab)))
} else {
## delimiter ##
if(!is.null(delimiter)) {
tmp <- grep(delimiter, colnames(x)) # Position of the missing-index
if(length(tmp) > 0) {
imp_var <- x[, tmp, drop=FALSE]
x <- x[, -tmp, drop=FALSE]
if(ncol(x) == 0) stop("Only the missing-index is given")
if(is.matrix(imp_var) && range(imp_var) == c(0,1)) imp_var <- apply(imp_var,2,as.logical)
if(is.null(dim(imp_var))) {
if(!is.logical(imp_var)) stop("The missing-index of imputed variables must be of the type logical")
} else {
if(!any(as.logical(lapply(imp_var,is.logical)))) stop("The missing-index of imputed variables must be of the type logical")
}
imputed <- TRUE
} else {
warning("'delimiter' is given, but no missing-index variable is found", call. = FALSE)
}
}
n <- nrow(x)
cn <- colnames(x)
if(is.null(cn)) cn <- defaultNames(ncol(x))
nNA <- apply(x, 2, countNA)
imp <- rep(FALSE,ncol(x))
# Combine imputed and Missing Values
if(imputed) {
nNA_imp <-countImp(x, delimiter, imp_var)
imp <- nNA_imp > 0
nNA <- nNA + nNA_imp
}
# Combine imputed and Missing Values
tmp <- ifelse(is.na(x), 1, 0) # 'ifelse' does not omit 'dim' attribute
if(imputed) {
tmp_imp <- isImp(x, pos = NULL, delimiter = delimiter, imp_var = imp_var, selection = "none")[["missh"]]
tmp_imp <- ifelse(tmp_imp, 2,0)
tmp[,colnames(tmp_imp)] <- tmp_imp
}
tab <- table(apply(tmp, 1, paste, collapse=":"))
tabcomb <- sapply(names(tab),
function(x) as.integer(unlist(strsplit(x, ":", fixed=TRUE))),
USE.NAMES=FALSE)
tabcomb <- if(is.null(dim(tabcomb))) as.matrix(tabcomb) else t(tabcomb)
}
miss <- data.frame(Variable=cn, Count=nNA, stringsAsFactors=FALSE)
count <- as.integer(tab) # frequency of combinations
res <- list(x=x, combinations=names(tab), count=count,
percent=count*100/n, missings=miss, tabcomb=tabcomb, imputed = imp)
class(res) <- "aggr"
if(plot) {
plot(res, ...)
invisible(res)
} else res
}
# plot method
# TODO: interactive sorting of variables or combinations
# FIXME: sortVars = TRUE bei nur missings
#' @rdname aggr
#' @method plot aggr
#' @param plot a logical indicating whether the results should be plotted (the
#' default is `TRUE`).
#' @param col a vector of length three giving the colors to be used for
#' observed, missing and imputed data. If only one color is supplied, it is
#' used for missing and imputed data and observed data is transparent. If only
#' two colors are supplied, the first one is used for observed data and the
#' second color is used for missing and imputed data.
#' @param bars a logical indicating whether a small barplot for the frequencies
#' of the different combinations should be drawn.
#' @param numbers a logical indicating whether the proportion or frequencies of
#' the different combinations should be represented by numbers.
#' @param prop a logical indicating whether the proportion of missing/imputed
#' values and combinations should be used rather than the total amount.
#' @param combined a logical indicating whether the two plots should be
#' combined. If `FALSE`, a separate barplot on the left hand side shows
#' the amount of missing/imputed values in each variable. If `TRUE`, a
#' small version of this barplot is drawn on top of the plot for the
#' combinations of missing/imputed and non-missing values. See
#' \dQuote{Details} for more information.
#' @param varheight a logical indicating whether the cell heights are given by
#' the frequencies of occurrence of the corresponding combinations.
#' @param only.miss a logical indicating whether the small barplot for the
#' frequencies of the combinations should only be drawn for combinations
#' including missing/imputed values (if `bars` is `TRUE`). This is
#' useful if most observations are complete, in which case the corresponding
#' bar would dominate the barplot such that the remaining bars are too
#' compressed. The proportion or frequency of complete observations (as
#' determined by `prop`) is then represented by a number instead of a bar.
#' @param border the color to be used for the border of the bars and
#' rectangles. Use `border=NA` to omit borders.
#' @param sortVars a logical indicating whether the variables should be sorted
#' by the number of missing/imputed values.
#' @param sortCombs a logical indicating whether the combinations should be
#' sorted by the frequency of occurrence.
#' @param ylabs if `combined` is `TRUE`, a character string giving
#' the y-axis label of the combined plot, otherwise a character vector of
#' length two giving the y-axis labels for the two plots.
#' @param axes a logical indicating whether axes should be drawn.
#' @param labels either a logical indicating whether labels should be plotted
#' on the x-axis, or a character vector giving the labels.
#' @param cex.lab the character expansion factor to be used for the axis
#' labels.
#' @param cex.axis the character expansion factor to be used for the axis
#' annotation.
#' @param cex.numbers the character expansion factor to be used for the
#' proportion or frequencies of the different combinations
#' @param gap if `combined` is `FALSE`, a numeric value giving the
#' distance between the two plots in margin lines.
#' @param \dots for `aggr` and `TKRaggr`, further arguments and
#' graphical parameters to be passed to [plot.aggr()]. For
#' `plot.aggr`, further graphical parameters to be passed down.
#' `par("oma")` will be set appropriately unless supplied (see
#' [graphics::par()]).
#' @export
plot.aggr <- function(x, col = c("skyblue","red","orange"), bars = TRUE,
numbers = FALSE, prop = TRUE, combined = FALSE, varheight = FALSE,
only.miss = FALSE, border = par("fg"), sortVars = FALSE,
sortCombs = TRUE, ylabs = NULL, axes = TRUE, labels = axes,
cex.lab = 1.2, cex.axis = par("cex"), cex.numbers = par("cex"),
gap = 4,
#interactive=TRUE,
...) {
# back compatibility
dots <- list(...)
nmdots <- names(dots)
if(missing(ylabs) && "labs" %in% nmdots) ylabs <- dots$labs
if(missing(labels) && "names.arg" %in% nmdots) labels <- dots$names.arg
# are there imputed variables in the dataset
imputed <- x$imputed
# are there imputed and missing variables in the dataset
miss_imp <- any(x$missings[,2] > 0 & !imputed)
imputed <- any(x$imputed)
# error messages and initializations
if(length(col) == 0) col <- c("skyblue","red","orange")
else if(length(col) == 1) col <- c("transparent", rep(col,2))
else if(length(col) == 2) col <- rep(col,1:2)
else if(length(col) != 3) col <- rep(col, length.out=3)
if(!is.logical(prop) || length(prop) == 0) prop <- TRUE
if(combined) {
prop <- rep.int(isTRUE(prop[1]), 2)
if(varheight) bars <- FALSE
# numbers <- FALSE
if(is.null(ylabs)) ylabs <- "Combinations"
} else {
if(length(prop) == 1) prop <- rep.int(isTRUE(prop), 2)
else prop <- c(isTRUE(prop[1]), isTRUE(prop[2]))
if(varheight) {
bars <- FALSE
numbers <- FALSE
}
if(is.null(ylabs)) {
if(!imputed) ylabs <- if(prop[1]) "Proportion of missings" else "Number of missings"
else if (!miss_imp) ylabs <- if(prop[1]) "Proportion of imputed missings" else "Number of imputed missings"
else ylabs <- if(prop[1]) "Proportion of missings or imputed missings" else "Number of missings or imputed missings"
ylabs <- c(ylabs, "Combinations")
} else if(length(ylabs) != 2) stop("'ylabs' must be a vector of length 2")
}
# dimensions of the data
if(is.null(dim(x$x))) {
nx <- length(x$x)
px <- 1
if(nx == 0) stop("'x' must have positive length")
} else {
nx <- nrow(x$x)
px <- ncol(x$x)
if(nx == 0) stop("'x' has no rows")
else if(px == 0) stop("'x' has no columns")
}
# graphical parameters for resetting
op <- par(no.readonly=TRUE)
on.exit(par(op))
# some parameters
if(is.null(dots$oma)) {
oma.left <- if(combined) 2.5 else 4.5
oma <- c(5, oma.left, 1.5, 1)+0.1
} else oma <- dots$oma
par(mar=rep(0, 4), oma=oma, xpd=NA)
csi <- par("csi") # margin line height in inches
gap.inch <- gap * csi # gap in inches
gap.cm <- gap.inch * 2.54 # gap in centimeters
p.bars <- 0.1
p.numbers <- if(combined) 0.1 else 0.15
p.gap <- 0.05 # gap before bars and numbers
if(is.null(dots$las)) {
las <- par("las")
if(las == 0) las <- 3
else if(las == 1) las <- 2
} else las <- dots$las
# combinations
tc <- x$tabcomb
count <- x$count
nc <- nrow(tc)
pc <- ncol(tc)
# if desired, check if numbers can be plotted
if(numbers) {
num <- if(prop[2]) format(x$percent/100, digits=2) else count
num.height <- strheight(num, units="inches", cex=cex.numbers)
space.vert <- par("pin")[2]/nc
if(all(num.height < space.vert)) {
plot.width <- par("pin")[1] - gap.inch
p.sum <- 2 + p.bars + p.numbers + 2*p.gap
num.width <- strwidth(num, units="inches", cex=cex.numbers)
space.horiz <- plot.width*p.numbers/p.sum + oma[4]*csi
num.width.ok <- num.width < space.horiz
if(!any(num.width.ok)) {
numbers <- FALSE
warning("not enough horizontal space to display frequencies")
}
} else {
numbers <- FALSE
warning("not enough vertical space to display ",
"frequencies (too many combinations)")
}
}
if(combined) {
if(numbers) {
if(bars) {
l.mat <- matrix(c(1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 4), 3, 5)
l.widths <- c(1, p.gap, p.bars, p.gap, p.numbers)
} else {
l.mat <- matrix(c(1, 0, 2, 0, 0, 0, 0, 0, 3), 3, 3)
l.widths <- c(1, p.gap, p.numbers)
}
} else {
if(bars) {
l.mat <- matrix(c(1, 0, 2, 0, 0, 0, 0, 0, 3), 3, 3)
l.widths <- c(1, p.gap, p.bars)
} else {
l.mat <- matrix(c(1, 0, 2), 3, 1)
l.widths <- 1
}
}
l.heights <- c(p.bars, p.gap, 1)
layout(l.mat, widths=l.widths, heights=l.heights)
} else {
if(numbers) {
if(bars) {
l.mat <- t(c(1, 0, 2, 0, 3, 0, 4))
l.widths <- c(1, lcm(gap.cm), 1, p.gap, p.bars, p.gap, p.numbers)
} else {
l.mat <- t(c(1, 0, 2, 0, 3))
l.widths <- c(1, lcm(gap.cm), 1, p.gap, p.numbers)
}
} else {
if(bars) {
l.mat <- t(c(1, 0, 2, 0, 3))
l.widths <- c(1, lcm(gap.cm), 1, p.gap, p.bars)
} else {
l.mat <- t(c(1, 0, 2))
l.widths <- c(1, lcm(gap.cm), 1)
}
}
layout(l.mat, widths=l.widths)
}
par(cex=op$cex, mex=op$mex)
# check if x-axis should be plotted and get labels
x.axis <- TRUE
if(is.logical(labels)) {
if(!is.na(labels) && labels) labels <- NULL
else x.axis <- FALSE
}
if(is.null(labels)) {
if(is.null(dim(x$x))) cn <- ""
else {
cn <- colnames(x$x)
if(is.null(cn)) cn <- defaultNames(ncol(x$x))
}
}
else cn <- rep(labels, length.out=px)
# barplot
miss <- x$missings[, 2]
if(!combined && prop[1]) miss <- miss/nx
if(!imputed) color <- rep(col[2],px)
else color <- ifelse(x$imputed,col[3],col[2])
if(sortVars) {
ordVars <- order(miss, decreasing=TRUE)
miss <- miss[ordVars]
cn <- cn[ordVars]
color <- color[ordVars]
}
if(all(miss == 0)) {
ylim <- if(!combined && prop[1]) c(0,1) else c(0, nx)
} else ylim <- c(0, max(miss))
if(x.axis) {
space.vert <- (oma[1]-1)*csi
}
if(combined) {
xlim <- c(0, pc)
barplot(miss, col=color, border=border, axes=FALSE,
xlim=0.1+1.2*xlim, ylim=ylim, xaxs="i", yaxs="i", xpd=NA)
} else {
if(las %in% 2:3) {
mp <- barplot(miss, col=color, border=border, ylab=ylabs[1],
ylim=ylim, xpd=NA, axes=axes, axisnames=FALSE, cex.axis=cex.axis,
cex.lab=cex.lab, las=las)
if(x.axis) {
cn.ok <- prettyLabels(cn, as.vector(mp), space.vert, cex.axis)
axis(side=1, at=mp[cn.ok], labels=cn[cn.ok],
lty=0, las=las, cex.axis=cex.axis)
}
} else {
barplot(miss, col=color, names.arg=cn, border=border,
ylab=ylabs[1], ylim=ylim, xpd=NA, axes=axes, axisnames=x.axis,
cex.axis=cex.axis, cex.names=cex.axis, cex.lab=cex.lab, las=las)
}
}
# combinations plot
if(sortVars) tc <- tc[, ordVars, drop=FALSE]
if(sortCombs) {
ordCombs <- order(count, decreasing=TRUE)
count <- count[ordCombs]
tc <- tc[ordCombs, , drop=FALSE]
if(numbers) num <- num[ordCombs]
}
# axis limits
xlim <- c(0, pc)
# ylim <- c(0, nc)
# define rectangles
xleft <- 0:(pc-1)
xright <- 1:pc
if(varheight) {
cs <- cumsum(count)
ybottom <- c(0, cs[-nc])
ytop <- cs
ylim <- c(0, cs[nc])
} else {
ybottom <- 0:(nc-1)
ytop <- 1:nc
ylim <- c(0, nc)
}
rects <- merge(data.frame(ybottom,ytop), data.frame(xleft,xright))
# initialize plot
initializePlot(xlim, ylim)
# match the colors
color <- matrix(nrow = nrow(tc), ncol = ncol(tc))
color[which(tc == 0)] <- col[1]
color[which(tc == 1)] <- col[2]
color[which(tc == 2)] <- col[3]
# plot rectangles
rect(rects$xleft, rects$ybottom, rects$xright, rects$ytop,
col=color, border=border)
title(ylab=ylabs[2-combined], line=1, cex.lab = cex.lab)
if(x.axis) {
at <- (xleft+xright)/2
if(las %in% 2:3) {
cn.ok <- prettyLabels(cn, at, space.vert, cex.axis)
axis(side=1, at=at[cn.ok], labels=cn[cn.ok],
lty=0, las=las, cex.axis=cex.axis)
} else {
axis(side=1, at=at, labels=cn, lty=0, las=las, cex.axis=cex.axis)
}
}
if(bars) { # add barplot
# cols <- ifelse(rowSums(tc) == 0, col[1], col[2])
# cols[unique(which(tc == 2, arr.ind = TRUE)[,1])] <- col[3]
# barplot(count, horiz=TRUE, col=cols, border=border,
# axes=FALSE, ylim=0.1+1.2*ylim, xaxs="i", yaxs="i", xpd=NA)
which.complete <- rowSums(tc) == 0
if(only.miss && any(which.complete)) {
# set count of bar for complete observations to 0
countPlot <- count
countPlot[which.complete] <- 0
# transparent color and border of bar for complete observations
cols <- ifelse(which.complete, NA, col[2])
cols[unique(which(tc == 2, arr.ind = TRUE)[,1])] <- col[3]
border <- rep(border, length.out=length(count))
border[which.complete] <- NA
# plot bars
barplot(countPlot, horiz=TRUE, col=cols, border=border,
axes=FALSE, ylim=0.1+1.2*ylim, xaxs="i", yaxs="i", xpd=NA)
# when numbers are not plotted, plot amount of complete observations
if(!numbers) {
if(prop[2]) {
num <- x$percent/100
if(sortCombs) num <- num[ordCombs]
num <- format(num[which.complete], digits=2)
} else num <- count[which.complete]
text(0, 0.1+1.2*(ybottom[which.complete]+ytop[which.complete])/2,
labels=num, adj=0, cex=cex.numbers)
}
} else {
cols <- ifelse(which.complete, col[1], col[2])
cols[unique(which(tc == 2, arr.ind = TRUE)[,1])] <- col[3]
barplot(count, horiz=TRUE, col=cols, border=border,
axes=FALSE, ylim=0.1+1.2*ylim, xaxs="i", yaxs="i", xpd=NA)
}
}
if(numbers) { # plot number of combinations
initializePlot(c(0, 1), ylim)
num[!num.width.ok] <- ""
text(0, (ybottom+ytop)/2, labels=num, adj=0, cex=cex.numbers)
}
# labels may not have been plotted, if we sorted the variables, we
# should print out their order, otherwise plot is not very useful
if(sortVars) {
if(!imputed) cat("\n Variables sorted by number of missings: \n")
else if (!miss_imp) cat("\n Variables sorted by number of imputed missings: \n")
else cat("\n Variables sorted by number of missings or imputed missings: \n")
tmp <- data.frame(Variable=cn, Count=miss)
print(tmp, row.names=FALSE)
}
invisible()
}
# print method
#' Print method for objects of class aggr
#'
#' Print method for objects of class `"aggr"`.
#'
#'
#' @param digits the minimum number of significant digits to be used (see
#' [print.default()]).
#' @author Matthias Templ, modifications by Andreas Alfons and Bernd Prantner
#' @seealso [aggr()]
#' @keywords print
#' @examples
#'
#' data(sleep, package = "VIM")
#' a <- aggr(sleep, plot=FALSE)
#' a
#'
#' @rdname aggr
#' @method print aggr
#' @export
print.aggr <- function(x, ..., digits = NULL) {
i <- x$missings[,2] > 0
imputed <- x$imputed
if(!any(imputed)) cat("\n Missings in variables:\n")
else if(any(i & !imputed)) cat("\n Missings or imputed missings in variables:\n")
else if(any(i)) cat("\n Imputed missings in variables:\n")
else cat("No missings.\n")
print(x$missings[i, ], digits=digits, row.names=FALSE)
}
#' Summary method for objects of class aggr
#'
#' Summary method for objects of class `"aggr"`.
#'
#'
#' @param object an object of class `"aggr"`.
#' @return a list of class `"summary.aggr"` containing the following
#' components:
#' - missings a `data.frame` containing the amount of missing or
#' imputed values in each variable.
#' - combinations a `data.frame` containing a character vector
#' representing the combinations of variables along with their frequencies and
#' percentages.
#' @author Matthias Templ, modifications by Andreas Alfons
#' @seealso [print.summary.aggr()], [aggr()]
#' @keywords print
#' @examples
#'
#' data(sleep, package = "VIM")
#' summary(aggr(sleep, plot=FALSE))
#'
#' @rdname aggr
#' @export
#' @method summary aggr
summary.aggr <- function(object, ...) {
res <- list(missings=object$missings,
combinations=data.frame(Combinations=object$combinations,
Count=object$count, Percent=object$percent), imputed = object$imputed)
class(res) <- "summary.aggr"
res
}
#' Print method for objects of class summary.aggr
#'
#' Print method for objects of class `"summary.aggr"`.
#'
#'
#' @param x an object of class `"summary.aggr"`.
#' @param \dots Further arguments, currently ignored.
#' @author Andreas Alfons, modifications by Bernd Prantner
#' @seealso [summary.aggr()], [aggr()]
#' @keywords print
#' @examples
#'
#' data(sleep, package = "VIM")
#' s <- summary(aggr(sleep, plot=FALSE))
#' s
#'
#' @rdname aggr
#' @export
#' @method print summary.aggr
print.summary.aggr <- function(x, ...) {
i <- x$missings[,2] > 0
imputed <- x$imputed
if(!any(imputed)) cat("\n Missings per variable: \n")
else if(any(i & !imputed)) cat("\n Missings or imputed missings per variables:\n")
else cat("\n Imputed missings per variables:\n")
print(x$missings, row.names=FALSE)
if(!any(imputed)) cat("\n Missings in combinations of variables: \n")
else if(any(i & !imputed)) cat("\n Missings or imputed missings in combinations of variables:\n")
else cat("\n Imputed missings in combinations of variables:\n")
print(x$combinations, row.names=FALSE)
}
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