CLV calculation when the average transaction values change over time for individuals.

[wleopach]

I’m trying to calculate the CLV for a dataset where the transaction values for some individuals look like this:

The Gamma-Gamma model does not converge, and the CLV estimates are poor. I suspect the issue lies in the data violating a key assumption of the Gamma-Gamma model:

“Average transaction values vary across customers but do not vary over
time for any given individual.”

Is there a way to handle this type of data?

[ColtAllen]

Hey @wleopach,

A few questions:

• Are you using GammaGammaModel or GammaGammaModelIndividual?
• Can you share the error trace indicating the model is not converging?

[wleopach]

Hey @ColtAllen ,

I am using the GammaGammaModel

This is the error trace:

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 129 seconds.
Chain 1 reached the maximum tree depth. Increase `max_treedepth`, increase `target_accept` or reparameterize.
Chain 3 reached the maximum tree depth. Increase `max_treedepth`, increase `target_accept` or reparameterize.
The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details
The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details
           mean            sd                         hdi_3%  ...   ess_bulk  ess_tail   r_hat
p  1.400000e-01    4.700000e-02     0.097  ...       5.0           11.0         2.29
q  3.416761e+12   5.615817e+12    5.157  ...       5.0           20.0         2.30
v  3.310748e+15   5.467989e+15    2328.450  ... 5.0           12.0         2.19

The r_hat is too high

Thanks in advance for your help.

[ColtAllen]

Thanks; that's helpful.

How many customers are in this dataset? Also have you looked at the avg spend distribution for the entire customer population? If there's a lot of variability, you may be better off segmenting the dataset with rfm_segments and fitting a separate Gamma-Gamma model to each segment.

[wleopach]

There are 395 customers in the dataset.
This is the kde plot of the monetary_value

I will try with the segmentation, thank you very much, @ColtAllen !!

[ColtAllen]

There are 395 customers in the dataset. This is the kde plot of the monetary_value

That's a very small dataset. I'd try more informative priors in the model config, or even GammaGammaModelIndividual.

I will try with the segmentation, thank you very much, @ColtAllen !!

Looks like you have a few outlier customers in that KDE plot. Segmentation would be useful for better understanding the dataset, but since it's so small I don't know if it'd help much for modeling purposes.

[wleopach]

I switched to using the GammaGammaFitterIndividual model, and now the sampling is converging properly. Looks like that solved the issue!

Thanks a lot @ColtAllen!