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
>
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