Fix bug in likelihood caused by #278.

[peisenha]

Current Behavior

The likelihood function is wrong as we currently evaluate the average of the log smoothed choice probabilities instead of the log of the average smoothed choice probabilities.

The bug was implemented in #278 and the lines are:

https://github.com/OpenSourceEconomics/respy/pull/278/files#diff-7d9b0e9ef0d4224d6a91d036420079b0L406-L410

Desired Behavior

• We want the correct likelihood function.
• logsumexp.pdf shows that the problem boils down to two logsumexp functions which is better than the softmax.

Todo

• update docstrings
• investigate the failure of our test battery to detect the change in likelihood evaluation

[tobiasraabe]

I am fine with the changes, now. The speed is almost back to levels before #278 (+0.2s for 40k obs with kw_94_one). But, the function is more robust.

[tobiasraabe]

@peisenha I cannot assign a review to you, but you should go over the changes again. Afterwards, I will hit approve.

[peisenha]

Thanks, it looks good and it is much faster now. What is our way forward for adding more sensitive regression tests? Are we going to create a new PR for that?

[tobiasraabe]

At least the clipping PR in #286 will change the regression tests and then I will create different ones as proposed by Janos.

[tobiasraabe]

Thanks for finding the bug, @peisenha!