# scat1d

##### 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 \(\code{eps}*\var{w}\) 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.

- Keywords
- hplot, distribution, dplot, aplot

##### 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, …)

# S3 method for default
jitter2(x, fill=1/3, limit=TRUE, eps=0,
presorted=FALSE, …)

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

datadensity(object, …)

# S3 method for 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, 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,
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)

##### Arguments

- x
a vector of numeric data, or a data frame (for

`jitter2`

)- 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 \(\max{(.1, 125/\var{n})}\) 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.- 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 \(\pm \code{fill}*\min{(\var{u}-\var{d},\var{d}-\var{l})}/2\).- limit
specifies a limit for maximum shift in jittered values. Duplicate values will be spread within \(\pm\code{fill}*\min{(\var{u}-\var{d},\var{d}-\var{l})}/2\). 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.- …
optional arguments passed to

`scat1d`

from`datadensity`

or to`histSpike`

from`scat1d`

. For`histSpikep`

are passed to the`lines`

list to`add_trace`

.- 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 \(\sin{(\pi*\code{sort}(\code{round}(\code{runif}(1000,0,10),1)))}\).- 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`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.

- 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`

); default is name of input argument`x`

- ylab
y-axis label (

`add=FALSE`

)- 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

##### Details

For `scat1d`

the length of line segments used is
`frac*min(par()$pin)/par()$uin[`

data units, where
`opp`]`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.

##### See Also

`segments`

, `jitter`

, `rug`

,
`plsmo`

, `lowess`

, `stripplot`

,
`hist.data.frame`

,`Ecdf`

, `hist`

,
`histogram`

, `table`

,
`density`

, `stat_plsmo`

, `histboxp`

##### Examples

```
# NOT RUN {
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)
# }
```

*Documentation reproduced from package Hmisc, version 4.3-0, License: GPL (>= 2)*