Allow static covariates in BGNBDModel

[PabloRoque]

Description

Allows static covariates in BetaGeoModel

NOTE: It seems there are convergence issues with the dropout-covariates-related params a|b. Related to similar observations by @juanitorduz here. As a consequence the last two assertions in test_distribution_method are a dubious hack.

Related Issue

• Closes Add Time-Invariant Covariates to ParetoNBD and BG/NBD Models #134
• Related to CLV API Standardization #527

Checklist

• Checked that the pre-commit linting/style checks pass
• Included tests that prove the fix is effective or that the new feature works
• Added necessary documentation (docstrings and/or example notebooks)
• If you are a pro: each commit corresponds to a relevant logical change

Modules affected

• MMM
• CLV
• Customer Choice

Type of change

• New feature / enhancement
• Bug fix
• Documentation
• Maintenance
• Other (please specify):

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📚 Documentation preview 📚: https://pymc-marketing--1390.org.readthedocs.build/en/1390/

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.65%. Comparing base (6ca3a30) to head (dc280d7).
Report is 2 commits behind head on main.

Additional details and impacted files

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+ Coverage   92.59%   92.65%   +0.06%     
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  Files          52       52              
  Lines        6051     6103      +52     
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+ Hits         5603     5655      +52     
  Misses        448      448              

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[ColtAllen]

Merging #1375 has created a merge conflict in clv.distributions.py, but shouldn't be hard to fix. Seems like this branch was created off of that one.

[ColtAllen]

The _extract_predictive_variables internal method for covariates can probably be moved into the Base CLV class to reduce repetition, because static covariates can be included in all CLV models.

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[PabloRoque]

@ColtAllen

OK, the plot kind of thickened.

the poor convergence in distribution_new_customers needs more investigation and plotting of visuals in a notebook.

I added docs/notebooks/dev/clv/dev/bg_nbg_covariates_test_issues.ipynb. Findings:

• We were assuming the tests to be equivalent to the one in ParetoNBD. But this should not be the case.
• Whenever a = b, the Beta distribution is symmetric with E[X]=0.5.
• Under this condition, the only effect of the introduction of covariates is the narrowing of the distribution of E[X] around 0.5.
• I believe this has implications on the results from CLVTools. For them gamma2=gamma3, and thus if a0 = b0 you will have basically a fancy 50/50 coin toss discerning your dropout probability

Generally if a >b, then p increases, and vice-versa. The greater both values are, the narrower the distribution.

This was the whole thing!. I was not taking into account the properties of the Beta dist, and following the ParetoNBD implementation blindly. Working on the notebook, I thought I was going crazy. E["dropout"]~0.5 always, regardless of the covariates I was using. Note that in the test setup we have equal coefficients: dropout_coefficient_a=np.array([3.0]), dropout_coefficient_b=np.array([3.0]). This was meant to be the case from the beginning.

Note however some findings. We are using a|b = pm.Flat("a|b") in distribution_new_customer. If we are not to pass data to the function, we would be having issues because Flat and Beta don't get along too well.

[juanitorduz]

hey! are we missing something here? any blockers :) ?

[ColtAllen]

hey! are we missing something here? any blockers :) ?

Just haven't found time to look at it yet 🤔 Reviewing now.

[PabloRoque]

hey! are we missing something here? any blockers :) ?

It is good to ship on my side, and would allow to work on a clean branch on the addition of covariates to the ModifiedBetaGeoModel

@ColtAllen requested changes a couple of weeks ago related to some tests. I believe I've addressed all the worries he expressed (see dev notebook), but would be good to have the green light on his side.

[ColtAllen]

Note however some findings. We are using a|b = pm.Flat("a|b") in distribution_new_customer. If we are not to pass data to the function, we would be having issues because Flat and Beta don't get along too well.

distribution_new_customer is just boilerplate for sampling from the latent Beta dropout_rate and Gamma purchase_rate distributions. Choice of distributions for a and b are arbitrary because the fitted posteriors from self.fit_result are being used for those parameters.

[ColtAllen]

Do your experiments in the dev notebook confirm this? This seems copy/pasted from the equivalent test for ParetoNBD model.

[PabloRoque]

Modified accordingly to the findings in the notebook

[ColtAllen]

Code looks good! Just some clarifying questions regarding notebook experiments and request to add an additional test condition, and I think this will be good to merge!

[ColtAllen]

Great job! Let's continue to test prior configs w/ covariates and update the docs with our findings.

[juanitorduz]

Thank you @PabloRoque and @ColtAllen 🙌😎🚀