TST: check and add unit tests for one parameter models

[josef-pkt]

see #8780 (comment)

AFAIK, we have almost no unit tests if len(params) is 1.

The smallest exog that I usually use has 2 columns, e.g. for 2 independent sample case.

There might be problems and bugs mainly in generic code, as in the approx_fprime case.

[jkriv]

I would be willing to work on this issue if it is still available!

[josef-pkt]

It's still available.
However, it's not really clear where and how to add those, because we want some kind of parametrized unit tests or reuse existing unit tests.

For example,
I think at test like this https://github.com/josef-pkt/statsmodels/blob/main/statsmodels/discrete/tests/test_predict.py#L348
could include smoke or shape tests for all which in get_prediction(which=xxx)
Where available model specific which would have to be collected, for example in a dictionary, then we could just run the tests for all which in a loop.

aside: hurdle and truncated models are missing in that parametrized list of models.

[josef-pkt]

You don't need to be assigned to an issue to open a pull request. We usually don't assign.