  The paper analyses properties of a large class of "path-based" Data
Envelopment Analysis models through a unifying general scheme. The scheme
includes the well-known oriented radial models, the hyperbolic distance
function model, the directional distance function models, and even permits
their generalisations. The modelling is not constrained to non-negative data
and is flexible enough to accommodate variants of standard models over
arbitrary data.
  Mathematical tools developed in the paper allow systematic analysis of the
models from the point of view of ten desirable properties. It is shown that
some of the properties are satisfied (resp., fail) for all models in the
general scheme, while others have a more nuanced behaviour and must be assessed
individually in each model. Our results can help researchers and practitioners
navigate among the different models and apply the models to mixed data.
