  Threshold methods are popular for ordinal regression problems, which are
classification problems for data with a natural ordinal relation. They learn a
one-dimensional transformation (1DT) of observations of the explanatory
variable, and then assign label predictions to the observations by thresholding
their 1DT values. In this paper, we study the influence of the underlying data
distribution and of the learning procedure of the 1DT on the classification
performance of the threshold method via theoretical considerations and
numerical experiments. Consequently, for example, we found that threshold
methods based on typical learning procedures may perform poorly when the
probability distribution of the target variable conditioned on an observation
of the explanatory variable tends to be non-unimodal. Another instance of our
findings is that learned 1DT values are concentrated at a few points under the
learning procedure based on a piecewise-linear loss function, which can make
difficult to classify data well.
