Add FrequencyReachAdditiveEffect

[PabloRoque]

Description

Add Frequency/Reach support via the MuEffect interface.
Similar, but slightly different (see below) to the implementation described here

Notes:

1) The formulation is not strictly equivalent. Notice that our frequency_sat: Tensorvariable already applies the multiplicative Beta coefficient. If we want a fully equivalent implementation we need to call , but then we cannot rely on .apply to do dim_handling.

1. Introduced HillShapeSaturation to make the formulation equivalent

2. This is a very drafty feature. No support for optimization whatsoever.

Related Issue

• Closes #
• Related to #

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

---

📚 Documentation preview 📚: https://pymc-marketing--1968.org.readthedocs.build/en/1968/

[codecov]

Codecov Report

❌ Patch coverage is 21.73913% with 108 lines in your changes missing coverage. Please review.
✅ Project coverage is 91.12%. Comparing base (539f32c) to head (c32abed).
⚠️ Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
...ting/mmm/additive_effect/frequency_reach_effect.py	17.69%	107 Missing ⚠️
pymc_marketing/mmm/components/saturation.py	80.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1968      +/-   ##
==========================================
- Coverage   92.18%   91.12%   -1.07%     
==========================================
  Files          67       69       +2     
  Lines        8147     8424     +277     
==========================================
+ Hits         7510     7676     +166     
- Misses        637      748     +111     

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[williambdean]

Shall we change additive_effect.py into additive_effects/ submodule and has this as a file?

[williambdean]

All can added to __init__ so that the import is kept

[cetagostini]

I like this idea!

[PabloRoque]

I am happy to move things around, but for me the main question of this PR is:

• Should we somehow modify SaturationTransformation to offer strong separation between saturation asymptote and lambda, c, slope, etc?

[juanitorduz]

Amazing!