Ugh, I made a typo at the very heart of my message:
"when I preprocess each line in R as p<-a/sum(a), occasionally a line will
sum to 0.999, 1.002, or the like"
should be
"when I preprocess each line in R as p<-round(a/sum(a),3) occasionally a
line will sum to 0.999, 1.002, or the like"
Also, the first paragraph should end with "where the other multinomial
functions reside."
Revision 2,
Arni
On Thu, 11 Feb 2010, Arni Magnusson wrote:
I present you with a function that solves a problem that has bugged me
for many years. I think the problem may be general enough to at least
consider adding this function, or a revamped version of it, to the
'stats' package, with the other multinomial functions reside.
I'm using R to export data to text files, which are input data for an
external model written in C++. Parts of the data are age distributions,
in the form of relative frequency in each year:
Year Age1 Age2 ... Age10
1980 0.123 0.234 ... 0.001
... ... ... ... ...
Each row should sum to exactly 1. The problem is that when I preprocess
each line in R as p<-a/sum(a), occasionally a line will sum to 0.999,
1.002, or the like. This could either crash the external model or lead
to wrong conclusions.
I believe similar partitioning is commonly used in a wide variety of
models, making this a general problem for many modellers.
In the past, I have checked every line manually, and then arbitrarily
tweaked one or two values up or down to make the row sum to exactly one,
but two people would tweak differently. Another semi-solution is to
write the values to the text file in a very long format, but this would
(1) make it harder to visually check the numbers and (2) the numbers in
the article or report would no longer match the data files exactly, so
other scientists could not repeat the analysis and get the same results.
Once I implemented a quick and dirty solution, simply setting the last
proportion (Age10 above) as 1 minus the sum of ages 1-9. I quickly
stopped using that approach when I started seeing negative values.
After this introduction, the attached round_multinom.html should make
sense. The algorithm I ended up choosing comes from allocating seats in
elections, so I was tempted to provide that application as well,
although it makes the interface and documentation slightly more
confusing.
The working title of this function was a short and catchy vote(), but I
changed it to round_multinom(), even though it's not matrix-oriented
like the other *multinom functions. That would probably be
straightforward to do, but I'll keep it as a vector function during the
initial discussion.
I'm curious to hear your impressions and ideas. In the worst case, this
is a not-so-great solution to a marginal problem. In the best case, this
might be worth a short note in the Journal of Statistical Software.
Thanks for your time,
Arni
P.S. In case the mailing list doesn't handle attachments, I've placed
the same files on http://www.hafro.is/~arnima/ for your convenience.
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