Add tests to test_emuFit_micro comparing closed-form MPLEs to MPLE obtained via numerical optimization

[ailurophilia]

…tained via numerical optimization

[adw96]

@svteichman Do you have time to review? I thought this might be of interest since you've been in the weeds of the optimization. If not, @gthopkins is qualified and capable! Your call

[adw96]

@gthopkins let's save @svteichman 's time for her defense -- can I please ask you to review this? You don't need to review the algebra, just that the test's purpose is clear, well-commented, reasonable, etc. I think this should be straightforward 😸

[gthopkins]

No problem @adw96! I just merged this PR--it all makes sense and it organized well. The only tiny note I have is that the titles of the test_that() functions are not symmetrical:

1. PL fit with categorical predictor matches analytical form of MPLE in this case, and does NOT match MLE
2. PL fit with categorical predictor matches analytical form of MPLE in this case, and does NOT match MLE when group sizes are unequal

For clarity, it would generally make sense to add "when group sizes are equal" to the first title, however this is more of a linguistic note than anything. I figured I would not hold up the PR for such a small detail :)

[adw96]

Thanks so much, @gthopkins!

Quick question -- did you make the changes in line with your linguistic note, or did you just accept the pull request as is? Pull requests aren't just a take-it-or-leave-it -- you can commit to them to make them better. If you didn't make the changes to make this better, would you mind making them now and commiting to main? (a mini PR) I think it's important that we make this repo as good as possible, especially if there are things that are easy to do that add clarity for future maintainers.

Thank you so much!!!

[gthopkins]

Thank you for this reminder, @adw96! I have included this small linguistic edit in PR #92, so it will be changed along with our use of simulate_data in the testing files.