Allow covariates in plot_expected_purchases

[PabloRoque]

Description

Includes covariates when calculation the unconditional frequency expectation. Allows the estimation of future purchases for the "average customer" just after first order for models with covariates.

Additionally:

• Introduces a new dataset apparel_trans.csv and accompanying apparel_static_cov.csv. These datasets are extracted from R's CLVTools package.
• A new notebook bg_nbd_covariates.ipynb shows an example of the new functionality using the new dataset.

Related Issue

• Closes #
• Related to Allow static covariates in BGNBDModel #1390. That PR should be merge before this one.

Checklist

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

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📚 Documentation preview 📚: https://pymc-marketing--1430.org.readthedocs.build/en/1430/

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Codecov Report

Attention: Patch coverage is 75.00000% with 7 lines in your changes missing coverage. Please review.

Project coverage is 91.51%. Comparing base (f88c98d) to head (9abe758).

Files with missing lines	Patch %	Lines
pymc_marketing/clv/utils.py	75.00%	7 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1430      +/-   ##
==========================================
- Coverage   91.59%   91.51%   -0.08%     
==========================================
  Files          60       60              
  Lines        6782     6802      +20     
==========================================
+ Hits         6212     6225      +13     
- Misses        570      577       +7     

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[ColtAllen]

I'll review this in detail later, but it looks like there may be merge conflicts with #1390

[PabloRoque]

@ColtAllen Feel free to have a look at this PR whenever you have some spare time. It is ready for review from my side.

[ColtAllen]

Introduces a new dataset apparel_trans.csv and accompanying apparel_static_cov.csv. These datasets are extracted from R's CLVTools package.

Is there documentation available for these datasets? I wasn't able to find anything in the R library.

A new notebook bg_nbd_covariates.ipynb shows an example of the new functionality using the new dataset.

Is it possible to consolidate this into the existing BG/NBD notebook?

[PabloRoque]

Is there documentation available for these datasets? I wasn't able to find anything in the R library.

Link to apparelTrans and apparelStaticCov

Is it possible to consolidate this into the existing BG/NBD notebook?

Do you propose to add this new dataset, or use the synthetic covariates that we are using in the ParetoNBD notebook?

[ColtAllen]

Link to apparelTrans and apparelStaticCov

Nice, so this dataset is simulated, then.

Do you propose to add this new dataset, or use the synthetic covariates that we are using in the ParetoNBD notebook?

The Pareto/NBD notebook is using real data available here. I think using the same dataset would make for a good comparison in resolving #1496. That said, let's just remove the apparel datasets for now and do the notebook consolidation in a separate PR. No need for any additional changes to the dev notebook here unless you want to test visualizations.

[ColtAllen]

Let's use the covariate data already being saved in a fitted model rather than require the user to add this to the transaction data (see my comment for more details). This should cut down on the additional code/testing requirements and also be more efficient.

One of these days I'd like to refactor _expected_cumulative_transactions to eliminate the FOR loop, but this would require xarray support in the predictive methods.

[ColtAllen]

There's a customer_id dimension for the covariates in the fitted model idata. Rather than requiring covariates be added to be transaction dataframe, we can obtain the covariates from the model directly and merge them with repeated_and_first_transactions.

[juanitorduz]

@PabloRoque can we bring this one to the finish line?