[R] OT : sensible analysis of censored rank data

John Aitchison jaitchis at hwy.com.au
Thu Nov 7 02:18:10 CET 2002

This is more of a conceptual/methodological question than
"how to do it in R", so anyone who cares to reply might 
want to do it off list.

I have censored rank order data .. electors have been asked
to rank the 4 most important issues out of a list of 20. For each 
individual we therefore have a vector of 20 measurements 1..5, 
where 1..4 are ranks and 5 = not ranked/less important than the 
nominated 4.
I would like to be able to use the full information in the ranking,
not just rely on first preferences. Nor do I want to average ranks,
which appears to be common practice.

I would like to make statements of the sort 'I am at least 80% 
confident that the most important issue is "B" '.  

The immediate thought is some sort of simulation/bootstrapping, 
which should be straightforward enough if I use just the first rank to 
denote "most important"... but that seems to ignore the information 
contained in the lower ranks.

My next thought is that I should attempt some form of ordination ..
some unidimensional scaling using perhaps a 1 dimensional 
cmdscale solution .. this rests on the ability to build a suitable 
distance matrix, which I think is possible. Or maybe a form of 
Thurstone scaling. If I wrapped this in the function called by boot .. 
a unique ordination solution for each sample draw, mapped to 1="B 
has highest value"/ 0 otherwise .. then perhaps I might be on the 
right track. (I guess I would have to do something about scale 
flip/flop, indeterminacy).

If this floundering around makes any sense to anyone .. perhaps 
someone who has worked with such data .. I'd appreciate some 


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