[R] GLM with ranks as response variable

[Jonathan Baron]

>From owner-r-help at stat.math.ethz.ch Sun Dec  2 14:25:42 2001
>I have a survey where customers rank a set of 5 packages for a product,
>so the response variable looks like
>
>a d b c
>a c d b
>d b a c
>
>Predictors variables are 4 socio-economic parameters. I have modelled the FIRST
>choice of each subject as a multinomial model, similar to the housing example in
>MASS ch7.3, , but I would prefer to use the whole rank-set instead.
>
>Can someone give me a hint if a R-package exists for this type of analysis?

I've dealt with data like this, and I think the answer depends a
log on what the packages are, whether you have some prior
hypothesis about the effects of the independent variables, etc.

One way to go is just to translate this into five variables, the
rank of each package, and predict it from a Manova.  I think that
will even work in lm(), but of course the ranks aren't
independent of each other.  Still, I seem to recall being able to
get an overall test of predictability (but I'm not going to try
this again unless I know that this is what you really need).  It
is true that a 1-5 scale will be grainy and violate some
distributional assumptions, but not too badly.

Another way is to reduce the ranks, either by factor analysis or
cluster analysis (both in mva, I think) - or just looking at
their correlations - so that you can devise one or two dependent
measures based on some composite of them.

And of course the best is to have some hypothesis about which
items should be affected by which variables, and then make a
composite of the ranks that is explicitly designed to test your
hypothesis.  Presumably this would not use all of the packages.

Still another approach is something like canonical correlation -
again, blindly empirical.  I think the sem package does this but
I haven't tried it.

Jon Baron

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