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Salanti, G. and Ulm, Kurt (2001): Modelling Under Order Restrictions. Collaborative Research Center 386, Discussion Paper 265
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Abstract

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.