Violin plots

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Screenshot of violin plots generated in example experiment

A violin plot is enhanced form of boxplot that also shows a kernel density estimation of the data. This is useful for bimodal data that are 'concealed' by a boxplot (Hintze & Nelson (1998) The American Statistician 52(2):181-4). The following code comes following a discussion in the forums on how to do this in IgorPro ( The 1D kernel density estimation method used here is Silverman's rule-of-thumb (Bowman & Azzalini (1997) Applied Smoothing Techniques for Data Analysis, OSP). R also uses this, but has options for other smoothing methods. The implementation here is to first make a boxplot. The code then calculates the violins and places them behind the boxplots in ProgBack (see example experiment). This could be turned into a Project to incorporate this into the WavePercentiles.ipf to generate Violin Plots directly, add other options for colour/formatting the boxplot etc.

#pragma rtGlobals=3		// Use modern global access method and strict wave access.
#include <Percentile and Box Plot>
//Before executing, you need to have plotted the boxplots using Percentile and Box Plot
//Plot the box plots into a target window using all waves from a source window
//This is a limitation of the functions, they rely on two graph windows (source and target) for making the violins.
//A width of 0.1 is good for the box plots and the boxplots look better with whiskers going to 0 and 100 rather than 10 and 90 (Igor default)
Menu "Macros"
	"Violin Plot...",  ViolinPlot()
	"Scrub Violins", ClearViolins()
Function ViolinPlot ()
	String sourceWindow	// window with the waves to make boxplot and violins
	String targetWindow	// window with the boxplots to add violins
	Variable trimValue=1	// violins can be trimmed (default) or plotted with long tails
	Variable thickValue=0.1	// this is the width of the boxplot
	Prompt sourceWindow, "What is the source graph?", popup, WinList("*", ";", "WIN:1")
	Prompt targetWindow, "What is the box plot graph?", popup, WinList("*", ";", "WIN:1")
	Prompt  trimValue, "yes=1, no=0"
	Prompt thickValue, "auto=0.1"
	DoPrompt "Pick graphs", sourceWindow, targetWindow, trimValue, thickValue
	String/G gSrcWin = sourceWindow //set global strings and variables
	String/G gTgtWin = targetWindow
	Variable/G gtrim = trimValue
	Variable/G gthick = thickValue
	DoWindow /F $sourceWindow
	String wlist = Wavelist("*",";","WIN:")
	String name
	Variable nWaves = ItemsInList(wlist)
	Variable i
	for(i = 0; i < nWaves; i += 1)
		name = StringFromList(i,wList)	//picks waves from source window and sends them to be plotted as violins in target window
		Wave w0 = $name
	DoWindow /F $targetWindow
	SetAxis/A/N=1/E=1 left
	SetAxis bottom -0.5,(nWaves-0.5)
///		@param	w	1D wave for plotting as violin
///		@param	xpos	variable to describe where violin will go on x-axis
Function Violin(w,xpos)
	Wave w
	Variable xpos
	SVAR srcWin = gSrcWin //set local ref for global strings
	SVAR tgtWin = gTgtWin
	NVAR trim = gtrim
	NVAR thick = gThick
	Variable nPoints = numpnts(w)
	Variable xMin, xMax
	if(trim == 1)
		xMin = wavemin(w)
		xMax = wavemax(w)						// trimmed violins
		Variable bw = ((4 * sqrt(variance(w))^5) / (3 * numpnts(w)))^0.2	// this is Silverman's rule-of-thumb
		xMin = wavemin(w) - (2*bw)
		xMax = wavemax(w) + (2*bw)				// not trimmed, limit kde to 2 bandwidths beyond min/max
	Variable dX = min((xMax - xMin) / 100,1) // delta x for StatsKDE
	StatsKDE/Q/BWM=2/DEST=kdeWave/KT=1/S={xMin,dX,xMax} w
	WAVE/Z w1 = kdeWave
	Variable auc = sum(w1)
	w1 /= auc * (thick / 2)	// omit *thick for a violin=2 i.e. two half-violins that =1
	String wnL = NameofWave(w) + "_kdeL"
	Duplicate/D/O w1 $wnL
	String wnR = NameofWave(w) + "_kdeR"
	Duplicate/D/O w1 $wnR
	String wnLx = NameofWave(w) + "_kdeLx"
	Duplicate/D/O w1 $wnLx
	String wnRx = NameofWave(w) + "_kdeRx"
	Duplicate/D/O w1 $wnRx
	String vwny = NameofWave(w) + "_kdevy"
	String vwnx = NameofWave(w) + "_kdevx"
	KillWaves/Z w1
	Wave wnL1 = $wnL
	Wave wnR1 = $wnR
	Wave wnLx1 = $wnLx
	Wave wnRx1 = $wnRx
	wnLx1 = x					//get x scale
	wnRx1 = x
	if (trim == 1)
		InsertPoints 0,1, wnLx1	//add point, set to same as first point to complete the bottom of a trimmed violin
		InsertPoints 0,1, wnRx1
		wnLx1[0] = wnLx1[1]
		wnRx1[0] = wnRx1[1]
		InsertPoints 0,1, wnL1
		InsertPoints 0,1, wnR1
		wnL1[0] = 0
		wnR1[0] = 0
	wnR1 *= -1										//make the other side of violin
	Reverse wnR1, wnRx1 							//reverse the righthand side of violin
	Concatenate/O/NP {wnL1,wnR1}, $vwny		// form the wave for y position of outline (will be x when vertical)
	Concatenate/O/NP {wnLx1,wnRx1}, $vwnx		// form the wave for x position of outline (will be y when vertical)
	wave vwny1 = $vwny
	wave vwnx1 = $vwnx
	DoWindow/F $tgtWin														//bring target window to the front
	SetDrawLayer ProgBack														// violins are drawn in ProgBack
	SetDrawEnv ycoord=left, xcoord=bottom, fillfgc=(65535,0,0),fillpat=3		// violins are red
	DrawPoly xpos+vwny1[0],vwnx1[0],1,1, vwny1,vwnx1					// draws violin
	KillWaves/Z wnL1,wnR1,wnLx1,wnRx1										// clean-up
	SetDrawLayer UserFront													// set layer back
//Handy function to scrub the violins away
Function ClearViolins()
	SVAR tgtWin = gTgtWin
	DoWindow /F $tgtWin
	SetDrawLayer /K ProgBack // kills ProgBack
	SetDrawLayer UserFront

Edit: updated this procedure to use StatsKDE. Only runs in IP7. Violin Demo file is out of date.

ViolinDemo.pxp79.43 KB

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