Continuous color ramps in SPSS

For graphs in syntax SPSS can specify continuous color ramps. Here I will illustrate a few tricks I have found useful, as well as provide alternatives to the default rainbow color ramps SPSS uses when you don’t specify the colors yourself. First we will start with a simple set of fake data.

INPUT PROGRAM.
LOOP #i = 1 TO 30.
  LOOP #j = 1 TO 30.
    COMPUTE x = #i.
    COMPUTE y = #j.
    END CASE.
  END LOOP.
END LOOP.
END FILE.
END INPUT PROGRAM.
DATASET NAME Col.
FORMATS x y (F2.0).
EXECUTE.

The necessary GGRAPH code to make a continuous color ramp is pretty simple, just include a scale variable and map it to a color.

*Colors vary by X, bar graph default rainbow.
TEMPORARY.
SELECT IF y = 1.
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=x y
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: x=col(source(s), name("x"), unit.category())
  DATA: xC=col(source(s), name("x"))
  DATA: y=col(source(s), name("y"))
  GUIDE: axis(dim(1), null())
  GUIDE: axis(dim(2), null())
  SCALE: linear(dim(2), min(0), max(1))
  ELEMENT: interval(position(x*y), shape.interior(shape.square), color.interior(xC),
           transparency.exterior(transparency."1"))
END GPL.
EXECUTE.

The TEMPORARY statement is just so the bars have only one value passed, and in the inline GPL I also specify that the outsides of the bars are fully transparent. The necessary code is simply creating a variable, here xC, that is continuous and mapping it to a color in the ELEMENT statement using color.interior(xC). Wilkinson in the Grammar of Graphics discusses that even for continuous color ramps he prefers a discrete color legend, which is the behavior in SPSS.

The default color ramp is well known to be problematic, so I will provide some alternatives. A simple choice suitable for many situations is simply a grey-scale chart. To make this you have to make a separate SCALE statement in the inline GPL, and set the aestheticMinimum and the aestheticMaximum. Besides that one additional SCALE statement, the code is the same as before.

*Better color scheme based on grey-scale.
TEMPORARY.
SELECT IF y = 1.
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=x y
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: x=col(source(s), name("x"), unit.category())
  DATA: xC=col(source(s), name("x"))
  DATA: y=col(source(s), name("y"))
  GUIDE: axis(dim(1), null())
  GUIDE: axis(dim(2), null())
  SCALE: linear(dim(2), min(0), max(1))
  SCALE: linear(aesthetic(aesthetic.color.interior), 
         aestheticMinimum(color.lightgrey), aestheticMaximum(color.black))
  ELEMENT: interval(position(x*y), shape.interior(shape.square), color.interior(xC),
           transparency.exterior(transparency."1"))
END GPL.
EXECUTE.

Another option I like is to make a grey-to-red scale ramp (which is arguably diverging or continuous).

*Grey to red.
TEMPORARY.
SELECT IF y = 1.
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=x y
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: x=col(source(s), name("x"), unit.category())
  DATA: xC=col(source(s), name("x"))
  DATA: y=col(source(s), name("y"))
  GUIDE: axis(dim(1), null())
  GUIDE: axis(dim(2), null())
  SCALE: linear(dim(2), min(0), max(1))
  SCALE: linear(aesthetic(aesthetic.color.interior), 
         aestheticMinimum(color.black), aestheticMaximum(color.red))
  ELEMENT: interval(position(x*y), shape.interior(shape.square), color.interior(xC),
           transparency.exterior(transparency."1"))
END GPL.
EXECUTE.

To make an nice looking interpolation with these anchors is pretty difficult, but another one I like is the green to purple. It ends up looking quite close to the associated discrete color ramp from the ColorBrewer palettes.

*Diverging color scale, purple to green.
TEMPORARY.
SELECT IF y = 1.
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=x y
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: x=col(source(s), name("x"), unit.category())
  DATA: xC=col(source(s), name("x"))
  DATA: y=col(source(s), name("y"))
  GUIDE: axis(dim(1), null())
  GUIDE: axis(dim(2), null())
  SCALE: linear(dim(2), min(0), max(1))
  SCALE: linear(aesthetic(aesthetic.color.interior), 
         aestheticMinimum(color.green), aestheticMaximum(color.purple))
  ELEMENT: interval(position(x*y), shape.interior(shape.square), color.interior(xC),
           transparency.exterior(transparency."1"))
END GPL.
EXECUTE.

In cartography, whether one uses diverging or continuous ramps is typically related to the data, e.g. if the data has a natural middle point use diverging (e.g. differences with zero at the middle point). I don’t really like this advice though, as pretty much any continuous number can be reasonably turned into a diverging number (e.g. continuous rates to location quotients, splitting at the mean, residuals from a regression, whatever). So I would make the distinction like this, the ramp decides what elements you end up emphasizing. If you want to emphasize the extremes of both ends of the distribution use a diverging ramp, if you only want to emphasize one end use a continuous ramp. There are many situations with natural continuous numbers that we want to emphasize both ends of the ramp based on the questions the map or graph is intended to answer.

Going along with this, you may want the middle break to not be in the middle of the actual data. To set the anchors according to an external benchmark, you can use the min and max function within the same SCALE statement that you specify the colors. Here is an example with the black-to-red color ramp, but I set the minimum lower than the data are, so the ramp starts at a more grey location.

*Setting the break with the external min.
TEMPORARY.
SELECT IF y = 1.
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=x y
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: x=col(source(s), name("x"), unit.category())
  DATA: xC=col(source(s), name("x"))
  DATA: y=col(source(s), name("y"))
  GUIDE: axis(dim(1), null())
  GUIDE: axis(dim(2), null())
  SCALE: linear(dim(2), min(0), max(1))
  SCALE: linear(aesthetic(aesthetic.color.interior), 
         aestheticMinimum(color.black), aestheticMaximum(color.red), 
         min(-10), max(30))
  ELEMENT: interval(position(x*y), shape.interior(shape.square), color.interior(xC),
           transparency.exterior(transparency."1"))
END GPL.
EXECUTE.

Another trick I like using often is to map discrete colors, and then use transparency to create a continuous ramp (most of the examples I use here could be replicated by specifying the color saturation as well). Here I use two colors and make points more towards the center of the graph more transparent. This can be extended to multiple color bins, see this post on Stackoverflow. Related are value-by-alpha maps, using more transparent to signify more uncertainty in the data (or to draw less attention to those areas). (That linked stackoverflow post wanted to emphasize the middle break for diverging data, but the point remains the same, make things you want to de-emphasize more transparent and things to want to emphasize more saturated.)

*Using transparency and fixed color bins.
RECODE x (1 THRU 15 = 1)(ELSE = 2) INTO XBin.
FORMATS XBin (F1.0).
COMPUTE Dis = -1*SQRT((x - 15)**2 + (y - 15)**2).
FORMATS Dis (F2.0).
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=x y Dis XBin
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: x=col(source(s), name("x"))
  DATA: y=col(source(s), name("y"))
  DATA: Dis=col(source(s), name("Dis"))
  DATA: XBin=col(source(s), name("XBin"), unit.category())
  GUIDE: axis(dim(1), null())
  GUIDE: axis(dim(2), null())
  SCALE: cat(aesthetic(aesthetic.color.interior), map(("1",color.green),("2",color.purple)))
  ELEMENT: point(position(x*y), color.interior(XBin),
           transparency.exterior(transparency."1"), transparency.interior(Dis))
END GPL.

Another powerful visualization tool to emphasize (or de-emphasize) certain points is to map the size of an element in addition to transparency. This is a great tool to add more information to scatterplots.

*Using redundant with size.
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=x y Dis XBin
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: x=col(source(s), name("x"))
  DATA: y=col(source(s), name("y"))
  DATA: Dis=col(source(s), name("Dis"))
  DATA: XBin=col(source(s), name("XBin"), unit.category())
  GUIDE: axis(dim(1), null())
  GUIDE: axis(dim(2), null())
  SCALE: linear(aesthetic(aesthetic.size), aestheticMinimum(size."1"), 
         aestheticMaximum(size."18"), reverse())
  SCALE: cat(aesthetic(aesthetic.color.interior), map(("1",color.green),("2",color.purple)))
  ELEMENT: point(position(x*y), color.interior(XBin),
           transparency.exterior(transparency."1"), transparency.interior(Dis), size(Dis))
END GPL.

Finally, if you want SPSS to omit the legend (or certain aesthetics in the legend) you have to specify a GUIDE: legend statement for every mapped aesthetic. Here is the previous scatterplot omitting all legends.

*IF you want the legend omitted.
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=x y Dis XBin
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: x=col(source(s), name("x"))
  DATA: y=col(source(s), name("y"))
  DATA: Dis=col(source(s), name("Dis"))
  DATA: XBin=col(source(s), name("XBin"), unit.category())
  GUIDE: axis(dim(1), null())
  GUIDE: axis(dim(2), null())
  GUIDE: legend(aesthetic(aesthetic.color), null())
  GUIDE: legend(aesthetic(aesthetic.transparency), null())
  GUIDE: legend(aesthetic(aesthetic.size), null())
  SCALE: linear(aesthetic(aesthetic.size), aestheticMinimum(size."1"), 
         aestheticMaximum(size."18"), reverse())
  SCALE: cat(aesthetic(aesthetic.color.interior), map(("1",color.green),("2",color.purple)))
  ELEMENT: point(position(x*y), color.interior(XBin),
           transparency.exterior(transparency."1"), transparency.interior(Dis), size(Dis))
END GPL.
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Some more value-by-alpha maps for D.C. Census Blocks

I’ve made some more value-by-alpha maps for my dissertation for percent non-white population in comparison to percentage of female-headed households for Census blocks in 2010 in D.C. See my first post for some background. The choropleth classes for the percents are chosen according to quintiles of the distributions and the alpha classes are arbitrary (note the alpha class uses households as the baseline in both maps, even though percent non-white uses the population counts).

When making these maps I’ve found that the Color Brewer sequential styles that range two colors work out much better than those that span one color. What happens with the one color sequential themes is that the faded out colors end up being confounded with the lighter colors in the fully opaque ranges. When using the two sequential color schemes (here showing Yellow to Red and Yellow to Blue) it provides greater discrepancy between the classes.


I did not try out the black background for these maps (I thought perhaps it would be a bit jarring in the document have a swath of black stand out). The CUNY Center for Urban Research has some other example value-by-alpha maps for New York City elections in 2013. After some discussion with Steven Romalewski they decided they liked the white background better for there maps, and my quick attempts for these examples I think I agree.

Cyclical color ramps for time series line plots

Morphet & Symanzik (2010) propose different novel cyclical color ramps by taking ColorBrewer ramps and wrapping them on the circle. All other previous continuous circle ramps I had seen prior were always rainbow scales, and there is plenty discussion about why rainbow color scales are bad so we needn’t rehash that here (see Kosara, Drew Skau, and my favorite Why Should Engineers and Scientists Be Worried About Color? for a sampling of critiques).

Below is a picture of the wrapped cyclical ramps from Morphet & Symanzik (2010). Although how they "average" the end points is not real clear to me from reading the paper, they basically use a diverging ramp and have one end merge at a fully saturated end of the sprectrum (e.g. nearly black) and the other merge at the fully light end of the spectrum (e.g. nearly white).

The original motivation is for directional data, and here is a figure from my paper Viz. JTC lines comparing the original rainbow color ramp I chose (on the right) and an updated red-grey cyclical scale on the left. The map is still quite complicated, as part of the motivation of that map was to show how plotting the JTC the longer lines dominate the graphic.

But I was interested in applying this logic to showing cyclical line plots, e.g. aoristic crime estimates by hour of day and day of week. Using the same Arlington data I used before, here are the aoristic estimates for hour of day plotted seperately for each day of the week. The colors for the day of the week use SPSS’s default color scheme for nominal categories. SPSS does not have anything as far as color defaults to distinguish between ordinal data, so if you use a categorical coloring scheme this is what you get.

The default is very good to distinguish between nominal categories, but here I want to take advantage of the cyclical nature of the data, so I employ a cyclical color ramp.

From this it is immediately apparent that the percentage of crimes dips down during the daytime for the grey Saturday and Sunday aoristic estimates. Most burglaries happen during the day, and so you can see that when homeowners are more likely to be in the house (as oppossed to at work) burglaries are less likely to occur. Besides this, day of week seems largely irrelevant to the percentage of burglaries that are occurring in Arlington.

I chose to make during the week shades of red, the dark color split between Friday-Saturday, and the light color split between Sunday-Monday. This trades one problem for another, in that the more fully saturated colors draw more attention in the plot, but I believe it is a worthwhile sacrifice in this instance. Below are the Hexidecimal RGB codes I used for each day of the week.

Sun - BABABA
Mon - FDDBC7
Tue - F4A582
Wed - D6604D
Thu - 7F0103
Fri - 3F0001
Sat - 878787