StatsPlots

Original author: Thomas Breloff (@tbreloff), maintained by the JuliaPlots members

This package is a drop-in replacement for Plots.jl that contains many statistical recipes for concepts and types introduced in the JuliaStats organization.

• Types:
  • DataFrames
  • Distributions
• Recipes:
  • histogram/histogram2d
  • groupedhist
  • boxplot
  • dotplot
  • violin
  • marginalhist
  • corrplot/cornerplot
  • andrewsplot
  • MDS plot

It is thus slightly less lightweight, but has more functionality. Main documentation is found in the Plots.jl documentation (https://juliaplots.github.io).

Initialize:

#]add StatsPlots # install the package if it isn't installed
using StatsPlots # no need for `using Plots` as that is reexported here
gr(size=(400,300))

Table-like data structures, including

DataFrames

IndexedTables

DataStreams

@df

plot

Arrays

julia
using DataFrames, IndexedTables
df = DataFrame(a = 1:10, b = 10 .* rand(10), c = 10 .* rand(10))
@df df plot(:a, [:b :c], colour = [:red :blue])
@df df scatter(:a, :b, markersize = 4 .* log.(:c .+ 0.1))
t = table(1:10, rand(10), names = [:a, :b]) # IndexedTable
@df t scatter(2 .* :b)

Inside a

@df

cols

@df df plot(:a, cols(2:3), colour = [:red :blue])

or to refer to a column whose symbol is represented by a variable:

s = :b
@df df plot(:a, cols(s))

cols()

In case of ambiguity, symbols not referring to

DataFrame

^()

julia
df[:red] = rand(10)
@df df plot(:a, [:b :c], colour = ^([:red :blue]))

The

@df

using Query, StatsPlots
df |>
    @filter(_.a > 5) |>
    @map({_.b, d = _.c-10}) |>
    @df scatter(:b, :d)

The

@df

using RDatasets
school = RDatasets.dataset("mlmRev","Hsb82")
@df school density(:MAch, group = :Sx)

To group by more than one column, use a tuple of symbols:

@df school density(:MAch, group = (:Sx, :Sector), legend = :topleft)

To name the legend entries with custom or automatic names (i.e.

Sex = Male, Sector = Public

group = {Sex = :Sx, :Sector}

=

=

The old syntax, passing the

DataFrame

plot

Visualizing a table interactively

A GUI based on the Interact package is available to create plots from a table interactively, using any of the recipes defined below. This small app can be deployed in a Jupyter lab / notebook, Juno plot pane, a Blink window or in the browser, see here for instructions.

import RDatasets
iris = RDatasets.dataset("datasets", "iris")
using StatsPlots, Interact
using Blink
w = Window()
body!(w, dataviewer(iris))

marginalhist with DataFrames

using RDatasets
iris = dataset("datasets","iris")
@df iris marginalhist(:PetalLength, :PetalWidth)

marginalscatter with DataFrames

using RDatasets
iris = dataset("datasets","iris")
@df iris marginalscatter(:PetalLength, :PetalWidth)

marginalkde

x = randn(1024)
y = randn(1024)
marginalkde(x, x+y)

• levels=N

  can be used to set the number of contour levels (default 10); levels are evenly-spaced in the cumulative probability mass.

• clip=((-xl, xh), (-yl, yh))

  (default

  ((-3, 3), (-3, 3))

  ) can be used to adjust the bounds of the plot. Clip values are expressed as multiples of the

  [0.16-0.5]

  and

  [0.5,0.84]

  percentiles of the underlying 1D distributions (these would be 1-sigma ranges for a Gaussian).

corrplot and cornerplot

This plot type shows the correlation among input variables. The marker color in scatter plots reveal the degree of correlation. Pass the desired colorgradient to

markercolor

seriescolor

gr(size = (600, 500))

then

julia
@df iris corrplot([:SepalLength :SepalWidth :PetalLength :PetalWidth], grid = false)

julia
@df iris corrplot(cols(1:4), grid = false)

A correlation plot may also be produced from a matrix:

M = randn(1000,4)
M[:,2] .+= 0.8sqrt.(abs.(M[:,1])) .- 0.5M[:,3] .+ 5
M[:,3] .-= 0.7M[:,1].^2 .+ 2
corrplot(M, label = ["x$i" for i=1:4])

cornerplot(M)

cornerplot(M, compact=true)

boxplot, dotplot, and violin

import RDatasets
singers = dataset("lattice", "singer")
@df singers violin(string.(:VoicePart), :Height, linewidth=0)
@df singers boxplot!(string.(:VoicePart), :Height, fillalpha=0.75, linewidth=2)
@df singers dotplot!(string.(:VoicePart), :Height, marker=(:black, stroke(0)))

Asymmetric violin or dot plots can be created using the

side

:both

:right

:left

singers_moscow = deepcopy(singers)
singers_moscow[:Height] = singers_moscow[:Height] .+ 5
@df singers violin(string.(:VoicePart), :Height, side=:right, linewidth=0, label="Scala")
@df singers_moscow violin!(string.(:VoicePart), :Height, side=:left, linewidth=0, label="Moscow")
@df singers dotplot!(string.(:VoicePart), :Height, side=:right, marker=(:black,stroke(0)), label="")
@df singers_moscow dotplot!(string.(:VoicePart), :Height, side=:left, marker=(:black,stroke(0)), label="")

Dot plots can spread their dots over the full width of their column

mode = :uniform

mode = :density

mode = :none

Equal-area histograms

The ea-histogram is an alternative histogram implementation, where every 'box' in the histogram contains the same number of sample points and all boxes have the same area. Areas with a higher density of points thus get higher boxes. This type of histogram shows spikes well, but may oversmooth in the tails. The y axis is not intuitively interpretable.

a = [randn(100); randn(100) .+ 3; randn(100) ./ 2 .+ 3]
ea_histogram(a, bins = :scott, fillalpha = 0.4)

AndrewsPlot

AndrewsPlots are a way to visualize structure in high-dimensional data by depicting each row of an array or table as a line that varies with the values in columns. https://en.wikipedia.org/wiki/Andrews_plot

using RDatasets
iris = dataset("datasets", "iris")
@df iris andrewsplot(:Species, cols(1:4), legend = :topleft)

Distributions

using Distributions
plot(Normal(3,5), fill=(0, .5,:orange))

dist = Gamma(2)
scatter(dist, leg=false)
bar!(dist, func=cdf, alpha=0.3)

Quantile-Quantile plots

The

qqplot

Distribution

qqnorm

x = rand(Normal(), 100)
y = rand(Cauchy(), 100)

plot(
 qqplot(x, y, qqline = :fit), # qqplot of two samples, show a fitted regression line
 qqplot(Cauchy, y),           # compare with a Cauchy distribution fitted to y; pass an instance (e.g. Normal(0,1)) to compare with a specific distribution
 qqnorm(x, qqline = :R)       # the :R default line passes through the 1st and 3rd quartiles of the distribution
)

Grouped Bar plots

groupedbar(rand(10,3), bar_position = :stack, bar_width=0.7)

This is the default:

groupedbar(rand(10,3), bar_position = :dodge, bar_width=0.7)

The

group

groupedbar

ctg = repeat(["Category 1", "Category 2"], inner = 5)
nam = repeat("G" .* string.(1:5), outer = 2)

groupedbar(nam, rand(5, 2), group = ctg, xlabel = "Groups", ylabel = "Scores",
        title = "Scores by group and category", bar_width = 0.67,
        lw = 0, framestyle = :box)

Grouped Histograms

using RDatasets
iris = dataset("datasets", "iris")
@df iris groupedhist(:SepalLength, group = :Species, bar_position = :dodge)

@df iris groupedhist(:SepalLength, group = :Species, bar_position = :stack)

Dendrograms

using Clustering
D = rand(10, 10)
D += D'
hc = hclust(D, linkage=:single)
plot(hc)

The

branchorder=:optimal

hclust()

using Clustering
using Distances
using StatsPlots
using Random

n = 40
mat = zeros(Int, n, n)
create banded matrix
for i in 1:n
    last = minimum([i+Int(floor(n/5)), n])
    for j in i:last
        mat[i,j] = 1
    end
end
randomize order
mat = mat[:, randperm(n)]
dm = pairwise(Euclidean(), mat, dims=2)
normal ordering
hcl1 = hclust(dm, linkage=:average)
plot(
    plot(hcl1, xticks=false),
    heatmap(mat[:, hcl1.order], colorbar=false, xticks=(1:n, ["$i" for i in hcl1.order])),
    layout=grid(2,1, heights=[0.2,0.8])
    )

Compare to:

# optimal ordering
hcl2 = hclust(dm, linkage=:average, branchorder=:optimal)
plot(
    plot(hcl2, xticks=false),
    heatmap(mat[:, hcl2.order], colorbar=false, xticks=(1:n, ["$i" for i in hcl2.order])),
    layout=grid(2,1, heights=[0.2,0.8])
    )

Dendrogram on the right side

using Distances
using Clustering
using StatsBase
using StatsPlots

pd=rand(Float64,16,7)
dist_col=pairwise(CorrDist(),pd,dims=2)
hc_col=hclust(dist_col, branchorder=:optimal)
dist_row=pairwise(CorrDist(),pd,dims=1)
hc_row=hclust(dist_row, branchorder=:optimal)
pdz=similar(pd)
for row in hc_row.order
    pdz[row,hc_col.order]=zscore(pd[row,hc_col.order])
end
nrows=length(hc_row.order)
rowlabels=(1:16)[hc_row.order]
ncols=length(hc_col.order)
collabels=(1:7)[hc_col.order]
l = grid(2,2,heights=[0.2,0.8,0.2,0.8],widths=[0.8,0.2,0.8,0.2])
plot(
    layout = l,
    plot(hc_col,xticks=false),
    plot(ticks=nothing,border=:none),
    plot(
        pdz[hc_row.order,hc_col.order],
        st=:heatmap,
        #yticks=(1:nrows,rowlabels),
        yticks=(1:nrows,rowlabels),
        xticks=(1:ncols,collabels),
        xrotation=90,
        colorbar=false
    ),
    plot(hc_row,yticks=false,xrotation=90,orientation=:horizontal)
)

GroupedErrors.jl for population analysis

Population analysis on a table-like data structures can be done using the highly recommended GroupedErrors package.

This external package, in combination with StatsPlots, greatly simplifies the creation of two types of plots:

1. Subject by subject plot (generally a scatter plot)

Some simple summary statistics are computed for each experimental subject (mean is default but any scalar valued function would do) and then plotted against some other summary statistics, potentially splitting by some categorical experimental variable.

2. Population plot (generally a ribbon plot in continuous case, or bar plot in discrete case)

Some statistical analysis is computed at the single subject level (for example the density/hazard/cumulative of some variable, or the expected value of a variable given another) and the analysis is summarized across subjects (taking for example mean and s.e.m), potentially splitting by some categorical experimental variable.

For more information please refer to the README.

A GUI based on QML and the GR Plots.jl backend to simplify the use of StatsPlots.jl and GroupedErrors.jl even further can be found here (usable but still in alpha stage).

Ordinations

MDS from

MultivariateStats.jl

using MultivariateStats, RDatasets, StatsPlots

iris = dataset("datasets", "iris")
X = convert(Matrix, iris[:, 1:4])
M = fit(MDS, X'; maxoutdim=2)
plot(M, group=iris.Species)

PCA will be added once the API in MultivariateStats is changed. See https://github.com/JuliaStats/MultivariateStats.jl/issues/109 and https://github.com/JuliaStats/MultivariateStats.jl/issues/95.

Covariance ellipses

A 2×2 covariance matrix

Σ

Σ

covellipse([0,2], [2 1; 1 4], n_std=2, aspect_ratio=1, label="cov1")
covellipse!([1,0], [1 -0.5; -0.5 3], showaxes=true, label="cov2")