Modelling Under Order Restrictions

Order restricted effects of predictors can be represented in models
by the monotonic transformation fitted by the pooled adjacent
violators algorithm as described by T. Robertson et al. In the
context of multivariate modelling, this paper aims to introduce
next to additive monotonic models a multidimensional approach. The
corresponding permutations test to assess significance for the
predictors is described and some feeble points of the approach are
discussed. We also introduce a procedure to improve the parsimony
of the model by reducing the resulting level sets. The use of
monotonic regression in connection with the threshold value
estimation problematic is outlined and two similar approaches to
assess it are discussed.