Bug in setting the number of nests in generalized_nested_logit

[timokau]

See #118 (comment) for details. Should be resolved after merging #118 to avoid conflicts.

[timokau]

Continuing the discussion in #118 (comment) here for better visibility (since that PR is merged). CC @prithagupta @kiudee

While GenNestedModel, says every object to some extend is a part of a nest, there is some literature which suggests still the number of nests should be less than number of objects in the choice set.

I am not sure I understand your point. Could you clarify? Do you agree that we should replace

if n_nests is None:
    self.n_nests = self.n_objects_fit_ + int(self.n_objects_fit_ / 2)

by

if n_nests is None:
    self.n_nests = int(self.n_objects_fit_ / 2)

in generalized_nested_logit.py ?

[prithagupta]

In nested logit, we are taking default number of nests to be
self.n_objects = n_objects
if n_nests is None:
self.n_nests = int(n_objects / 2)
else:
self.n_nests = n_nests
, while in generalized_nested_logit,
its
self.n_nests = n_objects + int(n_objects / 2)

The nested logit model divides the objects into a mutually exclusive set so the nests should be less than the number of objects if n_nests=n_objects, then it becomes a logit model.
While GenNestedModel, says every object to some extend is a part of a nest, there is some literature which suggests still the number of nests should be less than the number of objects in the choice set. So, in principle, it is a good idea to get the number of objects in a choice set.
So for both NLM and GLM we can set the default number of nests to be half of the number of objects.