[R] Fitting a choice model (Bradley-Terry generalization)

[Achim Zeileis]

On Wed, 15 Jun 2011, David Scott wrote:

> I have some data I would like to model which involves choice of food by 
> dung beetles.
>
> There are a number of experiments where in each case, there are five 
> choices. Overall there are more than 5 different foods being compared 
> (including a placebo) and different experiments use different 
> comparisons.
>
> The problem is a generalization of Bradley-Terry but it differs from 
> some generalizations in that the comparisons are not pairwise, and they 
> don't produce a full ordering, just that one is preferred to the other 
> four possibilities.

In some cases such comparisons are coded with "undecided" for those 
comparisons that are not fully ranked. Alternatively, sometimes they are 
also coded with NAs.

For example, if A is preferred over B and C, this may be coded as:
"A > B, A > C, B = C" or "A > B, A > C, NA".

> I have had a look at the BradleyTerry2, eba, pmr and MLCM packages, none 
> of which appear to provide the required functionality.

That depends what you think the required functionality is. If it is 
"dealing with NAs", then some certainly have the functionality. Similarly, 
"dealing with undecided" is provided in several implementations.

Additionally, to the packages above, the "prefmod" package provides a 
Bradley-Terry models as well as pattern models which might be interesting 
for you. The "VGAM" package can estimate Bradley-Terry models, see
http://www.jstatsoft.org/v32/i10/. Finally, the "psychotree" package 
provides a class "paircomp" for representing paired comparison data, to
estimate Bradley-Terry models, and in particular to assess the influence 
of covariates on such a model by recursive partitioning (see 
example("bttree", package = "psychotree")).

hth,
Z

> I have also looked at a 
> number of papers (Hunter, 2004; Firth, 2005; Huang Weng and Lin, 2006; and 
> Fujimoto, Hino and Murata 2011). I think fitting using maximum likelihood 
> should be possible, but would welcome any pointers to useful code,  relevant 
> ideas, or similar analyses.
>
> David Scott
>
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