List of Continuous, Non-Contractual clv Models to Consider Adding

[ricardoV94]

https://github.com/mplatzer/BTYDplus

[ColtAllen]

Model List

1. Modified BG/NBD: Implement Modified BetaGeo Model #94
2. BG/CNBD-k: http://www.reutterer.com/papers/reutterer&platzer&schroeder_2021.pdf
3. Modified )BG/CNBD-k: http://www.reutterer.com/papers/reutterer&platzer&schroeder_2021.pdf
4. Abe variant of Pareto/NBD: [1],[2],[3],[4]
5. Pareto/GGG: http://www.reutterer.com/papers/platzer&reutterer_pareto-ggg_2016.pdf
6. Gamma/Gompertz/NBD: free PDF available
7. Gamma/Gompertz/NBD w/ covariates: https://pubsonline.informs.org/doi/epdf/10.1287/mksc.2020.1254
8. Pareto/NBD w/ time-varying covariates: https://www.zora.uzh.ch/id/eprint/197236/1/mksc.2020.1254.pdf
9. BG/NBD w/time-varying covariates: https://www.brucehardie.com/notes/040/time-varying_covariates_in_BGNBD.pdf
10. Periodic Death Opportunity: [1] & [2]
11. Gaussian Processes: https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfiles/26107/ansari_Bayesian_Nonparametric.pdf

Notes on Implementation

• The papers for Models 4 & 5 provide MCMC sampling strategies.
• Models 5 & 9 require raw transactions as inputs. All other models follow the frequency/recency/T format.
• Should cite the R libraries where appropriate: https://github.com/mplatzer/BTYDplus & https://github.com/bachmannpatrick/CLVTools
• On that note, CLVTools contains C++ code for model 8. Consider adapting those scripts with a python binding, because this model is by far the most complex on this list. The likelihood function alone sprawls across 2 pages in the research paper!
• Models 6 & 7 utilize a Gompertz distribution, which is not currently provided in pymc. The likelihood function also contains an infinite integral, which I'm not sure how to code out in pytensor.
• The papers for models 5 & 7 cite even more options we could add to this list.
• The paper for model 9 also includes a section on incorporating seasonality which could implemented in any model, which I would prefer to do in lieu of model 8.

[zwelitunyiswa]

@ColtAllen The Gamma/Gompertz/NBD model with time-invariant contextual factors (Näf, Bachmann & Meierer 2020) paper is here: https://pubsonline.informs.org/doi/epdf/10.1287/mksc.2020.1254

I also have the Standard Gamma/Gompertz/NBD (Bemmaor & Glady 2012) paper. I can give it to you via email or DM.

[zwelitunyiswa]

@ColtAllen Check your LinkedIn inbox.

[ColtAllen]

Thanks @zwelitunyiswa!

[ColtAllen]

Pinning this because it's a good list of models to add to the clv module and research reference. Also added a link to another paper comparing the Pareto/NBD, BetaGeo/NBD, PDO and Bayesian Pareto/NBD Abe models.

[larryshamalama]

There's a lot of models that seem available, each with a different paper. Perhaps it would be good to find a way to harmonize all the models in a table or some sort of documentation? On top of other models (discrete, contractual, etc.)

[ColtAllen]

There's a lot of models that seem available, each with a different paper. Perhaps it would be good to find a way to harmonize all the models in a table or some sort of documentation? On top of other models (discrete, contractual, etc.)

That's a good idea. Do you think it's worth adding to the official documentation?

[larryshamalama]

That's a good idea. Do you think it's worth adding to the official documentation?

If I can find a clever and intuitive way of summarizing the models 😅 Something that I will have to think about...

[ColtAllen]

That's a good idea. Do you think it's worth adding to the official documentation?

If I can find a clever and intuitive way of summarizing the models 😅 Something that I will have to think about...

I edited my OP so it's more coherent. For the official documentation, use case recommendations would be the best way to summarize these models methinks, preferably after some real-world application.

[ColtAllen]

Updated OP to add issue link for generalized seasonality.