One-Dimensional Scatter Diagram, Spike Histogram, or Density

scat1d adds tick marks (bar codes. rug plot) on any of the four sides of an existing plot, corresponding with non-missing values of a vector x. This is used to show the data density. Can also place the tick marks along a curve by specifying y-coordinates to go along with the x values.

If any two values of x are within $\code{eps}*w$ of each other, where eps defaults to .001 and w is the span of the intended axis, values of x are jittered by adding a value uniformly distributed in $[-\code{jitfrac}*w, \code{jitfrac}*w]$, where jitfrac defaults to .008. Specifying preserve=TRUE invokes jitter2 with a different logic of jittering. Allows plotting random sub-segments to handle very large x vectors (seetfrac).

jitter2 is a generic method for jittering, which does not add random noise. It retains unique values and ranks, and randomly spreads duplicate values at equidistant positions within limits of enclosing values. jitter2 is especially useful for numeric variables with discrete values, like rating scales. Missing values are allowed and are returned. Currently implemented methods are jitter2.default for vectors and jitter2.data.frame which returns a data.frame with each numeric column jittered.

datadensity is a generic method used to show data densities in more complex situations. Here, another datadensity method is defined for data frames. Depending on the which argument, some or all of the variables in a data frame will be displayed, with scat1d used to display continuous variables and, by default, bars used to display frequencies of categorical, character, or discrete numeric variables. For such variables, when the total length of value labels exceeds 200, only the first few characters from each level are used. By default, datadensity.data.frame will construct one axis (i.e., one strip) per variable in the data frame. Variable names appear to the left of the axes, and the number of missing values (if greater than zero) appear to the right of the axes. An optional group variable can be used for stratification, where the different strata are depicted using different colors. If the q vector is specified, the desired quantiles (over all groups) are displayed with solid triangles below each axis.

When the sample size exceeds 2000 (this value may be modified using the nhistSpike argument, datadensity calls histSpike instead of scat1d to show the data density for numeric variables. This results in a histogram-like display that makes the resulting graphics file much smaller. In this case, datadensity uses the minf argument (see below) so that very infrequent data values will not be lost on the variable's axis, although this will slightly distortthe histogram.

histSpike is another method for showing a high-resolution data distribution that is particularly good for very large datasets (say $\code{n} > 1000$). By default, histSpike bins the continuous x variable into 100 equal-width bins and then computes the frequency counts within bins (if n does not exceed 10, no binning is done). If add=FALSE (the default), the function displays either proportions or frequencies as in a vertical histogram. Instead of bars, spikes are used to depict the frequencies. If add=FALSE, the function assumes you are adding small density displays that are intended to take up a small amount of space in the margins of the overall plot. The frac argument is used as with scat1d to determine the relative length of the whole plot that is used to represent the maximum frequency. No jittering is done by histSpike.

histSpike can also graph a kernel density estimate for x, or add a small density curve to any of 4 sides of an existing plot. When y or curve is specified, the density or spikes are drawn with respect to the curve rather than the x-axis.

histSpikeg is similar to histSpike but is for adding layers to a ggplot2 graphics object or traces to a plotly object. histSpikeg can also add lowess curves to the plot.

ecdfpM makes a plotly graph or series of graphs showing possibly superposed empirical cumulative distribution functions.

Usage

scat1d(x, side=3, frac=0.02, jitfrac=0.008, tfrac,
       eps=ifelse(preserve,0,.001),
       lwd=0.1, col=par("col"),
       y=NULL, curve=NULL,
       bottom.align=FALSE,
       preserve=FALSE, fill=1/3, limit=TRUE, nhistSpike=2000, nint=100,
       type=c('proportion','count','density'), grid=FALSE, ...)

jitter2(x, ...)

# Default S3 method
jitter2(x, fill=1/3, limit=TRUE, eps=0,
        presorted=FALSE, ...)

# S3 method for class 'data.frame'
jitter2(x, ...)

datadensity(object, ...)

# S3 method for class 'data.frame'
datadensity(object, group,
            which=c("all","continuous","categorical"),
            method.cat=c("bar","freq"),
            col.group=1:10,
            n.unique=10, show.na=TRUE, nint=1, naxes,
            q, bottom.align=nint>1,
            cex.axis=sc(.5,.3), cex.var=sc(.8,.3),
            lmgp=NULL, tck=sc(-.009,-.002),
            ranges=NULL, labels=NULL, ...)
# sc(a,b) means default to a if number of axes <= 3, b if >=50, use
# linear interpolation within 3-50

histSpike(x, side=1, nint=100, bins=NULL, frac=.05, minf=NULL, mult.width=1,
          type=c('proportion','count','density'),
          xlim=range(x), ylim=c(0,max(f)), xlab=deparse(substitute(x)), 
          ylab=switch(type,proportion='Proportion',
                           count     ='Frequency',
                           density   ='Density'),
          y=NULL, curve=NULL, add=FALSE, minimal=FALSE,
          bottom.align=type=='density', col=par('col'), lwd=par('lwd'),
          grid=FALSE, ...)

histSpikeg(formula=NULL, predictions=NULL, data, plotly=NULL,
           lowess=FALSE, xlim=NULL, ylim=NULL,
           side=1, nint=100,
           frac=function(f) 0.01 + 0.02*sqrt(f-1)/sqrt(max(f,2)-1),
           span=3/4, histcol='black', showlegend=TRUE)

ecdfpM(x, group=NULL, what=c('F','1-F','f','1-f'), q=NULL,
       extra=c(0.025, 0.025), xlab=NULL, ylab=NULL, height=NULL, width=NULL,
       colors=NULL, nrows=NULL, ncols=NULL, ...)

Arguments

x: a vector of numeric data, or a data frame (for jitter2 or ecdfpM)
object: a data frame or list (even with unequal number of observations per variable, as long as group is notspecified)
side: axis side to use (1=bottom (default for histSpike), 2=left, 3=top (default for scat1d), 4=right)
frac: fraction of smaller of vertical and horizontal axes for tick mark lengths. Can be negative to move tick marks outside of plot. For histSpike, this is the relative y-direction length to be used for the largest frequency. When scat1d calls histSpike, it multiplies its frac argument by 2.5. For histSpikeg, frac is a function of f, the vector of all frequencies. The default function scales tick marks so that they are between 0.01 and 0.03 of the y range, linearly scaled in the square root of the frequency less one.
jitfrac: fraction of axis for jittering. If $\code{jitfrac} \le 0$, no jittering is done. If preserve=TRUE, the amount of jittering is independent of jitfrac.
tfrac: Fraction of tick mark to actually draw. If $\code{tfrac}<1$, will draw a random fraction tfrac of the line segment at each point. This is useful for very large samples or ones with some very dense points. The default value is 1 if the number of non-missing observations n is less than 125, and $\max{(.1, 125/n)}$ otherwise.
eps: fraction of axis for determining overlapping points in x. For preserve=TRUE the default is 0 and original unique values are retained, bigger values of eps tends to bias observations from dense to sparse regions, but ranks are still preserved.
lwd: line width for tick marks, passed to segments
col: color for tick marks, passed to segments
y: specify a vector the same length as x to draw tick marks along a curve instead of by one of the axes. The y values are often predicted values from a model. The side argument is ignored when y is given. If the curve is already represented as a table look-up, you may specify it using the curve argument instead. y may be a scalar to use a constant verticalplacement.
curve: a list containing elements x and y for which linear interpolation is used to derive y values corresponding to values of x. This results in tick marks being drawn along the curve. For histSpike, interpolated y values are derived for binmidpoints.
minimal: for histSpike set minimal=TRUE to draw a minimalist spike histogram with no y-axis. This works best when produce graphics images that are short, e.g., have a height of two inches. add is forced to be FALSE in this case so that a standalone graph is produced. Only base graphics are used.
bottom.align: set to TRUE to have the bottoms of tick marks (for side=1 or side=3) aligned at the y-coordinate. The default behavior is to center the tick marks. For datadensity.data.frame, bottom.align defaults to TRUE if nint>1. In other words, if you are only labeling the first and last axis tick mark, the scat1d tick marks are centered on the variable's axis.
preserve: set to TRUE to invoke jitter2
fill: maximum fraction of the axis filled by jittered values. If d are duplicated values between a lower value l and upper value u, then d will be spread within $\pm \code{fill}*\min{(u-d,d-l)}/2$.
limit: specifies a limit for maximum shift in jittered values. Duplicate values will be spread within $\pm\code{fill}*\min{(u-d,d-l)}/2$. The default TRUE restricts jittering to the smallest $\min{(u-d,d-l)}/2$ observed and results in equal amount of jittering for all d. Setting to FALSE allows for locally different amount of jittering, using maximum space available.
nhistSpike: If the number of observations exceeds or equals nhistSpike, scat1d will automatically call histSpike to draw the data density, to prevent the graphics file from being too large.
type: used by or passed to histSpike. Set to "count" to display frequency counts rather than relative frequencies, or "density" to display a kernel density estimate computed using the density function.
grid: set to TRUE if the R grid package is in effect for the current plot
nint: number of intervals to divide each continuous variable's axis for datadensity. For histSpike, is the number of equal-width intervals for which to bin x, and if instead nint is a character string (e.g.,nint="all"), the frequency tabulation is done with no binning. In other words, frequencies for all unique values of x are derived and plotted. For histSpikeg, if x has no more than nint unique values, all observed values are used, otherwise the data are rounded before tabulation so that there are no more than nint intervals. For histSpike, nint is ignored if bins is given.
bins: for histSpike specifies the actual cutpoints to use for binning x. The default is to use nint in conjunction with xlim.
...: optional arguments passed to scat1d from datadensity or to histSpike from scat1d. For histSpikep are passed to the lines list to add_trace. For ecdfpM these arguments are passed to add_lines.
presorted: set to TRUE to prevent from sorting for determining the order $l<d<u$. This is usefull if an existing meaningfull local order would be destroyed by sorting, as in $\sin{(\pi*\code{sort}(\code{round}(\code{runif}(1000,0,10),1)))}$.
group: an optional stratification variable, which is converted to a factor vector if it is not one already
which: set which="continuous" to only plot continuous variables, or which="categorical" to only plot categorical, character, or discrete numeric ones. By default, all types of variables are depicted.
method.cat: set method.cat="freq" to depict frequencies of categorical variables with digits representing the cell frequencies, with size proportional to the square root of the frequency. By default, vertical bars are used.
col.group: colors representing the group strata. The vector of colors is recycled to be the same length as the levels of group.
n.unique: number of unique values a numeric variable must have before it is considered to be a continuous variable
show.na: set to FALSE to suppress drawing the number of NAs to the right of each axis
naxes: number of axes to draw on each page before starting a new plot. You can set naxes larger than the number of variables in the data frame if you want to compress the plot vertically.
q: a vector of quantiles to display. By default, quantiles are not shown.
extra: a two-vector specifying the fraction of the x range to add on the left and the fraction to add on the right
cex.axis: character size for draw labels for axis tick marks
cex.var: character size for variable names and frequence of NAs
lmgp: spacing between numeric axis labels and axis (see par for mgp)
tck: see tck under par
ranges: a list containing ranges for some or all of the numeric variables. If ranges is not given or if a certain variable is not found in the list, the empirical range, modified by pretty, is used. Example: ranges=list(age=c(10,100), pressure=c(50,150)).
labels: a vector of labels to use in labeling the axes for datadensity.data.frame. Default is to use the names of the variable in the input data frame. Note: margin widths computed for setting aside names of variables use the names, and not these labels.
minf: For histSpike, if minf is specified low bin frequencies are set to a minimum value of minf times the maximum bin frequency, so that rare data points will remain visible. A good choice of minf is 0.075. datadensity.data.frame passes minf=0.075 to scat1d to pass to histSpike. Note that specifying minf will cause the shape of the histogram to be distorted somewhat.
mult.width: multiplier for the smoothing window width computed by histSpike when type="density"
xlim: a 2-vector specifying the outer limits of x for binning (and plotting, if add=FALSE and nint is a number). For histSpikeg, observations outside the xlim range are ignored.
ylim: y-axis range for plotting (if add=FALSE). Often needed for histSpikeg to help scale the tick mark line segments.
xlab: x-axis label (add=FALSE or for ecdfpM); default is name of input argument, or for ecdfpM comes from label and units attributes of the analysis variable. For ecdfpM xlab may be a vector if there is more than one analysis variable.
ylab: y-axis label (add=FALSE or for ecdfpM)
add: set to TRUE to add the spike-histogram to an existing plot, to show marginal data densities
formula: a formula of the form y ~ x1 or y ~ x1 + ... where y is the name of the y-axis variable being plotted with ggplot, x1 is the name of the x-axis variable, and optional ... are variables used by ggplot to produce multiple curves on a panel and/or facets.
predictions: the data frame being plotted by ggplot, containing x and y coordinates of curves. If omitted, spike histograms are drawn at the bottom (default) or top of the plot according to side.
data: for histSpikeg is a mandatory data frame containing raw data whose frequency distribution is to be summarized, using variables in formula.
plotly: an existing plotly object. If not NULL, histSpikeg uses plotly instead of ggplot.
lowess: set to TRUE to have histSpikeg add a geom_line layer to the ggplot2 graphic, containing lowess() nonparametric smoothers. This causes the returned value of histSpikeg to be a list with two components: "hist" and "lowess" each containing a layer. Fortunately, ggplot2 plots both layers automatically. If the dependent variable is binary, iter=0 is passed to lowess so that outlier detection is turned off; otherwise iter=3 is passed.
span: passed to lowess as the f argument
histcol: color of line segments (tick marks) for histSpikeg. Default is black. Set to any color or to "default" to use the prevailing colors for the graphic.
showlegend: set to FALSE too have the added plotly traces not have entries in the plot legend
what: set to "1-F" to plot 1 minus the ECDF instead of the ECDF, "f" to plot cumulative frequency, or "1-f" to plot the inverse cumulative frequency
height,width: passed to plot_ly
colors: a vector of colors to pas to add_lines
nrows,ncols: passed to plotly::subplot

Value

histSpike returns the actual range of x used in its binning. histSpikeg returns a list of ggplot2 layers that ggplot2 will easily add with +.

Side Effects

scat1d adds line segments to plot. datadensity.data.frame draws a complete plot. histSpike draws a complete plot or adds to an existing plot.

Details

For scat1d the length of line segments used is frac*min(par()$pin)/par()$uin[opp] data units, where opp is the index of the opposite axis and frac defaults to .02. Assumes that plot has already been called. Current par("usr") is used to determine the range of data for the axis of the current plot. This range is used in jittering and in constructing line segments.

Author

Frank Harrell
Department of Biostatistics
Vanderbilt University
Nashville TN, USA
fh@fharrell.com

Martin Maechler (improved scat1d)
Seminar fuer Statistik
ETH Zurich SWITZERLAND
maechler@stat.math.ethz.ch

Jens Oehlschlaegel-Akiyoshi (wrote jitter2)
Center for Psychotherapy Research
Christian-Belser-Strasse 79a
D-70597 Stuttgart Germany
oehl@psyres-stuttgart.de

Examples

plot(x <- rnorm(50), y <- 3*x + rnorm(50)/2 )
scat1d(x)                 # density bars on top of graph
scat1d(y, 4)              # density bars at right
histSpike(x, add=TRUE)       # histogram instead, 100 bins
histSpike(y, 4, add=TRUE)
histSpike(x, type='density', add=TRUE)  # smooth density at bottom
histSpike(y, 4, type='density', add=TRUE)


smooth <- lowess(x, y)    # add nonparametric regression curve
lines(smooth)             # Note: plsmo() does this
scat1d(x, y=approx(smooth, xout=x)$y) # data density on curve
scat1d(x, curve=smooth)   # same effect as previous command
histSpike(x, curve=smooth, add=TRUE) # same as previous but with histogram
histSpike(x, curve=smooth, type='density', add=TRUE)  

# same but smooth density over curve


plot(x <- rnorm(250), y <- 3*x + rnorm(250)/2)
scat1d(x, tfrac=0)        # dots randomly spaced from axis
scat1d(y, 4, frac=-.03)   # bars outside axis
scat1d(y, 2, tfrac=.2)    # same bars with smaller random fraction



x <- c(0:3,rep(4,3),5,rep(7,10),9)
plot(x, jitter2(x))       # original versus jittered values
abline(0,1)               # unique values unjittered on abline
points(x+0.1, jitter2(x, limit=FALSE), col=2)
                          # allow locally maximum jittering
points(x+0.2, jitter2(x, fill=1), col=3); abline(h=seq(0.5,9,1), lty=2)

                          # fill 3/3 instead of 1/3
x <- rnorm(200,0,2)+1; y <- x^2
x2 <- round((x+rnorm(200))/2)*2
x3 <- round((x+rnorm(200))/4)*4
dfram <- data.frame(y,x,x2,x3)
plot(dfram$x2, dfram$y)   # jitter2 via scat1d
scat1d(dfram$x2, y=dfram$y, preserve=TRUE, col=2)
scat1d(dfram$x2, preserve=TRUE, frac=-0.02, col=2)
scat1d(dfram$y, 4, preserve=TRUE, frac=-0.02, col=2)



pairs(jitter2(dfram))     # pairs for jittered data.frame

# This gets reasonable pairwise scatter plots for all combinations of
# variables where
#
# - continuous variables (with unique values) are not jittered at all, thus
#   all relations between continuous variables are shown as they are,
#   extreme values have exact positions.
#
# - discrete variables get a reasonable amount of jittering, whether they
#   have 2, 3, 5, 10, 20 \dots levels
#
# - different from adding noise, jitter2() will use the available space
#   optimally and no value will randomly mask another
#
# If you want a scatterplot with lowess smooths on the *exact* values and
# the point clouds shown jittered, you just need
#
pairs( dfram ,panel=function(x,y) { points(jitter2(x),jitter2(y))
                                    lines(lowess(x,y)) } )





datadensity(dfram)     # graphical snapshot of entire data frame

datadensity(dfram, group=cut2(dfram$x2,g=3))

                          # stratify points and frequencies by
                          # x2 tertiles and use 3 colors


# datadensity.data.frame(split(x, grouping.variable))
# need to explicitly invoke datadensity.data.frame when the
# first argument is a list

if (FALSE) { # \dontrun{
require(rms)
require(ggplot2)
f <- lrm(y ~ blood.pressure + sex * (age + rcs(cholesterol,4)),
         data=d)
p <- Predict(f, cholesterol, sex)
g <- ggplot(p, aes(x=cholesterol, y=yhat, color=sex)) + geom_line() +
  xlab(xl2) + ylim(-1, 1)
g <- g + geom_ribbon(data=p, aes(ymin=lower, ymax=upper), alpha=0.2,
                linetype=0, show_guide=FALSE)
g + histSpikeg(yhat ~ cholesterol + sex, p, d)

# colors <- c('red', 'blue')
# p <- plot_ly(x=x, y=y, color=g, colors=colors, mode='markers')
# histSpikep(p, x, y, z, color=g, colors=colors)

w <- data.frame(x1=rnorm(100), x2=exp(rnorm(100)))
g <- c(rep('a', 50), rep('b', 50))
ecdfpM(w, group=g, ncols=2)
} # }