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I am trying to see the relationship between two variables (say A and B) in a plot in RStudio. Both are discrete and range from 1 to 10. However, I have 1000s of data points, so given that there are only 100 possible spaces in which there can be a point, almost every possible place on a graph has a point.

How can I represent 1000s of points on a plot like this, whilst being able to see how many are at each point too?

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  • $\begingroup$ Although nothing in the question implies ordinal variables, the thread specified above is already wide-ranging and well illustrated and would be relevant even if the categories were nominal. $\endgroup$ – Nick Cox Oct 11 '20 at 14:28
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    $\begingroup$ Having thousands of data points is good, but the graphical issue is just to show 100 possible frequencies, some possibly 0. Posting that reduced dataset is a manageable proposition and would allow people to show relevant possibilities. $\endgroup$ – Nick Cox Oct 11 '20 at 15:14
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One potential option is to add a tiny bit of random noise to each observation. In that way fewer points will overlap.

You can either add it directly and use R's basic plotting capabilities or look into the jitter type layer that comes with the GGplot package that adds the noise automatically.

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  • $\begingroup$ I did try to add a jitter to it, but I have that much data that it only made a slight difference to the really lightly dense points. $\endgroup$ – AnoUser1 Oct 10 '20 at 16:16
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    $\begingroup$ Another option to use with the jitter, is setting the alpha value to a small number so that if there are just a few points it is relativity transparent but as more points are stacked upon one another, it gets darker and darker. $\endgroup$ – Dave2e Oct 10 '20 at 20:06
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Mosaic plots are a good way of doing this. https://cran.r-project.org/web/packages/ggmosaic/vignettes/ggmosaic.html

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  • $\begingroup$ Having read the link, I can see why it would be helpful but I don't know how I would apply it myself $\endgroup$ – AnoUser1 Oct 10 '20 at 16:24
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The ggplot2 library should handle something like this. There are example of the specific code out on the internet. I’ll just address the idea, since this is CV.SE, not SO.

I would represent the points in a data frame with three columns. One column would have the x-coordinate, one column would have the y-coordinate, and one column would have the count of how many instances of that x-y pair there are. Then you can use a color to denote the prevalence of a point, which ggplot2 can do.

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    $\begingroup$ Having read on them more, I now understand the concept of them but I still don't understand how I would execute them in R. My GGPlot2 function doesn't have anything to do with mosaic plots inside it $\endgroup$ – AnoUser1 Oct 10 '20 at 17:03
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Similar to what Dave proposes, but in base R: visualize table counts using grayscale, with darker grays for cells with higher counts.

counts

set.seed(1)
nn <- 1e6
aa <- sample(1:10,nn,prob=(1:10)^2-5*(1:10)+20,replace=TRUE)
bb <- sample(1:10,nn,prob=20-(1:10),replace=TRUE)

data_table <- table(aa,bb)

grayscale <- function ( cnt ) paste0("grey",100-3*round(cnt/1000,0))
# this relies on the fact that counts are between 3000 and 30000
# adapt as needed

plot(c(0,12),c(0,11),type="n",las=1,xlab="A",ylab="B")
for ( ii in rownames(data_table) ) {
    for ( jj in colnames(data_table) ) {
        rect(as.numeric(ii)-.5,as.numeric(jj)-.5,as.numeric(ii)+.5,as.numeric(jj)+.5,
            border=NA,col=grayscale(data_table[ii,jj]))
        # optionally, add counts
        # text(as.numeric(ii),as.numeric(jj),data_table[ii,jj],
        #   col=if(data_table[ii,jj]>quantile(data_table,0.7)) "white" else "black")
    }
}
counts_for_legend <- round(seq(min(data_table),max(data_table),length.out=5),0)
legend("right",pch=22,pt.bg=grayscale(counts_for_legend),legend=counts_for_legend,pt.cex=1.5)

Of course, this could be prettified a lot, especially the legend - the question is whether you want to do this by hand (if you want to create this plot only a single time), or programmatically (if this needs to be created often, with different datasets).

Alternatively, if you want a little more color in your life, you could change the grayscale() function above to one that outputs a black body radiation color:

blackbody color counts

lackBodyRadiationColors <- function(x, max_value=1) {
    # x should be between 0 (black) and 1 (white)
    # if large x come out too bright, constrain the bright end of the palette
    #     by setting max_value lower than 1
    foo <- colorRamp(c(rgb(0,0,0),rgb(1,0,0),rgb(1,1,0),rgb(1,1,1)))(x*max_value)/255
    apply(foo,1,function(bar)rgb(bar[1],bar[2],bar[3]))
}

plot(c(0,12),c(0,11),type="n",las=1,xlab="A",ylab="B")
for ( ii in rownames(data_table) ) {
    for ( jj in colnames(data_table) ) {
        rect(as.numeric(ii)-.5,as.numeric(jj)-.5,as.numeric(ii)+.5,as.numeric(jj)+.5,
            border=NA,col=blackBodyRadiationColors(1-data_table[ii,jj]/max(data_table)))
        # optionally, add counts
        # text(as.numeric(ii),as.numeric(jj),data_table[ii,jj],
        #   col=if(data_table[ii,jj]>quantile(data_table,0.7)) "white" else "black")
    }
}
counts_for_legend <- round(seq(min(data_table),max(data_table),length.out=5),0)
legend("right",pch=22,pt.bg=blackBodyRadiationColors(1-counts_for_legend/max(data_table)),
  legend=counts_for_legend,pt.cex=1.5)
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