  Existing ordinal trees and random forests typically use scores that are
assigned to the ordered categories, which implies that a higher scale level is
used. Versions of ordinal trees are proposed that take the scale level
seriously and avoid the assignment of artificial scores. The basic construction
principle is based on an investigation of the binary models that are implicitly
used in parametric ordinal regression. These building blocks can be fitted by
trees and combined in a similar way as in parametric models. The obtained trees
use the ordinal scale level only. Since binary trees and random forests are
constituent elements of the trees one can exploit the wide range of binary
trees that have already been developed. A further topic is the potentially poor
performance of random forests, which seems to have ignored in the literature.
Ensembles that include parametric models are proposed to obtain prediction
methods that tend to perform well in a wide range of settings. The performance
of the methods is evaluated empirically by using several data sets.
