[R] Regressions with monotonicity constraints

[Vadim Ogranovich]

This seems to be a recurrent topic, but I don't remember hearing a
definitive answer. I also apologies for cross-posting.

Say I have a numerical response variable and a bunch of multi-level factors
I want to use for modeling. I don't expect factor interaction to be
important so there will be no interactions in the model.
All this would be a perfect job for ANOVA except for one additional
requirement: all factors are ordered, i.e. for any two levels in a factor
one is bigger than the other, and I want the regression to preserve the
ordering, that is to be monotonic.

I can think of two definitions of monotonicity, weak and strong, and in case
it matters I am more interested in the strong one, which I define as
follows:
If L1 < L2 within some factor F than
prediction(L1, other factors) < prediction(L2, other factors)
for ANY SELECTION of 'other factors' levels.
(A weak monotonicity could be defined as prediction(L1) < prediction(L2) on
average).

Any reference to S, R, C code / papers which address this topic will be
highly appreciated.

Similar question could be asked about additive models, i.e. estimate an
additive model with each (or some) functions being monotonic.

Thanks,
Vadim
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