R: One-Dimensional Scatter Diagram, Spike Histogram, or Density

scat1d {Hmisc} | R Documentation

## One-Dimensional Scatter Diagram, Spike Histogram, or Density

### Description

`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}*\var{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}*\var{w}, \code{jitfrac}*\var{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 (see`tfrac`).

`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 `group`s) 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} <= 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/\var{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 +/- \code{fill}*min(\var{u}-\var{d},\var{d}-\var{l})/2.
`limit` | specifies a limit for maximum shift in jittered values. Duplicate values will be spread within +/- \code{fill}*min(\var{u}-\var{d},\var{d}-\var{l})/2. The default `TRUE` restricts jittering to the smallest \min{(\var{u}-\var{d},\var{d}-\var{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 \var{l}<\var{d}<\var{u}. This is usefull if an existing meaningfull local order would be destroyed by sorting, as in \sin{(π*\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 `NA`s 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 `NA`s
`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`

### 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.

### Value

`histSpike` returns the actual range of `x` used in its binning

### 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.

### Author(s)

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

### See Also

`segments`, `jitter`, `rug`, `plsmo`, `lowess`, `stripplot`, `hist.data.frame`,`Ecdf`, `hist`, `histogram`, `table`, `density`, `stat_plsmo`, `histboxp`

### 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

    ## Not run:
    require(rms)
    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)

    ## End(Not run)

[Package Hmisc version 4.7-0 Index]