[R] comparative density estimates

[Achim Zeileis]

Michael,

very nice and interesting plots!

One alternative idea to compare the proportion of milestone items
(that does not really answer the bandwith question) in Europe and North
America might be a conditional density plot. After running your R
source code, you could do:
  where <- factor(c(rep("North America", length(sub1)),
                    rep("Europe", length(sub2)))) 
  year <- c(sub1, sub2)
  cdplot(where ~ year, bw = "sj")
showing the decrease in the European proportion.

Internally, this first computes the unconditional density as in
  plot(density(year, bw = "sj"))
and then the density for Europe with the same bandwidth.

Best wishes,
Z


On Thu, 23 Mar 2006 14:25:53 -0500 Michael Friendly wrote:

> I have two series of events over time and I want to construct a graph
> of the relative frequency/density of these events that allows their 
> distributions to
> be sensibly compared.  The events are the milestones items in my
> project on milestones in the history of data visualization [1], and I
> want to compare trends
> in Europe vs. North America.
> 
> I decided to use a graph of two overlaid density estimates with rug 
> plots, but then
> the question arises of how to choose the bandwidth (BW) for the two 
> series to allow them
> to be sensibly compared, because the range of time and total
> frequency differ
> for the two series.  To avoid clutter on this list, I've placed the
> data and R code
> at
> http://euclid.psych.yorku.ca/SCS/Gallery/milestone/Test/kde-bug/mileyears4.R
> 
> I have two versions of this graph, one selecting an optimal BW for
> each separately
> and the other using the adjust= argument of density() to
> approximately equate
> the BW to the value determined for the whole series combined.  The
> two versions
> (done with SAS) are shown at
> 
> http://euclid.psych.yorku.ca/SCS/Gallery/milestone/Test/kde-bug/mileyears32.gif 
> 
> http://euclid.psych.yorku.ca/SCS/Gallery/milestone/Test/kde-bug/mileyears33.gif 
> 
> 
> The densities in the first are roughly equivalent to the R code
> d1 <- density(sub1, from=1500, to=1990, bw="sj", adjust=1)
> d2 <- density(sub2, from=1500, to=1990, bw="sj", adjust=1)
> 
> the second to
> d1 <- density(sub1, from=1500, to=1990, bw="sj", adjust=2.5)
> d2 <- density(sub2, from=1500, to=1990, bw="sj", adjust=0.75)
> 
> The second graph seems to me to undersmooth the more extensive data
> from Europe and undersmooth the data from North America.
> 
> - any comments or suggestions?
> - are there other methods I should consider?
> 
> I did find overlap.Density() in the DAAG package, but perversely, it 
> uses a bw=
> argument to select a B&W/grayscale plot.
> 
> thanks,
> -Michael
> 
> 
> [1] http://www.math.yorku.ca/SCS/Gallery/milestone/
> 
> -- 
> Michael Friendly     Email: friendly at yorku.ca 
> Professor, Psychology Dept.
> York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
> 4700 Keele Street    http://www.math.yorku.ca/SCS/friendly.html
> Toronto, ONT  M3J 1P3 CANADA
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
> http://www.R-project.org/posting-guide.html
>