ModifiedBetaGeoModel#

class pymc_marketing.clv.models.modified_beta_geo.ModifiedBetaGeoModel(data=None, *, model_config=None, sampler_config=None)[source]#

Modified Beta-Geometric Negative Binomial Distribution (MBG/NBD) model for a non-contractual customer population across continuous time.

Based on proposed modifications to the BG/NBD model by Battislam, et al. in [1], and Wagner & Hoppe in[Rd9315d94a886-2]_, which remove the BG/NBD assumption that all non-repeat customers are still active.

The MBG/NBD model assumes dropout probabilities for the customer population are Beta distributed, and time between transactions follows a Gamma distribution while the customer is still active.

This model requires data to be summarized by recency, frequency, and T for each customer, using clv.utils.rfm_summary() or equivalent. Modeling assumptions require T >= recency.

Predictive methods have been adapted from the ModifiedBetaGeoFitter class in the legacy lifetimes library (see CamDavidsonPilon/lifetimes).

Parameters:

dataDataFrame

DataFrame containing the following columns:

customer_id: Unique customer identifier
frequency: Number of repeat purchases
recency: Time between the first and the last purchase
T: Time between the first purchase and the end of the observation period

model_configdict, optional

Dictionary of model prior parameters:

alpha: Scale parameter for time between purchases; defaults to Prior("HalfFlat")
r: Shape parameter for time between purchases; defaults to Prior("HalfFlat")
a: Shape parameter of dropout process; defaults to phi_purchase * kappa_purchase
b: Shape parameter of dropout process; defaults to (1 - phi_dropout) * kappa_dropout
phi_dropout: Nested prior for a and b priors; defaults to Prior("Uniform", lower=0, upper=1)
kappa_dropout: Nested prior for a and b priors; defaults to Prior("Pareto", alpha=1, m=1)
purchase_covariates: Coefficients for purchase rate covariates; defaults to Normal(0, 1)
dropout_covariates: Coefficients for dropout covariates; defaults to Normal.dist(0, 1)
purchase_covariate_cols: List containing column names of covariates for customer purchase rates.
dropout_covariate_cols: List containing column names of covariates for customer dropouts.

sampler_configdict, optional

Dictionary of sampler parameters. Defaults to None.

References

[1]

Batislam, E.P., M. Denizel, A. Filiztekin (2007), “Empirical validation and comparison of models for customer base analysis.” International Journal of Research in Marketing, 24 (3), 201-209. https://works.bepress.com/meltem-denizel/2/download/

[2]

Wagner, U. and Hoppe D. (2008), “Erratum on the MBG/NBD Model,” International Journal of Research in Marketing, 25 (3), 225-226. https://www.researchgate.net/profile/Udo-Wagner/publication/274894157_Customer_Base_Analysis_The_Case_for_a_Central_Variant_of_the_BetageometricBND_Model/links/55c3728608aeca747d5f6658/Customer-Base-Analysis-The-Case-for-a-Central-Variant-of-the-Betageometric-BND-Model.pdf

Examples

from pymc_extras.prior import Prior
from pymc_marketing.clv import ModifiedBetaGeoModel, rfm_summary

# customer identifiers and purchase datetimes
# are all that's needed to start modeling
data = [
    [1, "2024-01-01"],
    [1, "2024-02-06"],
    [2, "2024-01-01"],
    [3, "2024-01-02"],
    [3, "2024-01-05"],
    [4, "2024-01-16"],
    [4, "2024-02-05"],
    [5, "2024-01-17"],
    [5, "2024-01-18"],
    [5, "2024-01-19"],
]
raw_data = pd.DataFrame(data, columns=["id", "date"])

# preprocess data
rfm_df = rfm_summary(raw_data, "id", "date")

# model_config and sampler_configs are optional
model = ModifiedBetaGeoModel(
    model_config={
        "r": Prior("HalfFlat"),
        "alpha": Prior("HalfFlat"),
        "a": Prior("HalfFlat"),
        "b": Prior("HalfFlat"),
    },
    sampler_config={
        "draws": 1000,
        "tune": 1000,
        "chains": 2,
        "cores": 2,
    },
)

# The default 'mcmc' fit_method provides informative predictions
# and reliable performance on small datasets
model.fit(data=rfm_df)
print(model.fit_summary())

# Maximum a Posteriori can quickly fit a model to large datasets,
# but will give limited insights into predictive uncertainty.
model.fit(data=rfm_df, fit_method="map")
print(model.fit_summary())

# Predict number of purchases for current customers
# over the next 10 time periods
expected_purchases = model.expected_purchases(future_t=10)

# Predict probability customers are still active
probability_alive = model.expected_probability_alive()

# Predict number of purchases for a new customer over 't' time periods
expected_purchases_new_customer = model.expected_purchases_new_customer(t=10)

Methods

`ModifiedBetaGeoModel.__init__`([data, ...])	Initialize model configuration and sampler configuration for the model.
`ModifiedBetaGeoModel.attrs_to_init_kwargs`(attrs)	Convert the model configuration and sampler configuration from the attributes to keyword arguments.
`ModifiedBetaGeoModel.build_from_idata`(idata)	Build the model from the InferenceData object.
`ModifiedBetaGeoModel.build_model`([data])	Build the model.
`ModifiedBetaGeoModel.create_idata_attrs`()	Create attributes for the inference data.
`ModifiedBetaGeoModel.distribution_new_customer`([...])	Compute posterior predictive samples of dropout, purchase rate and frequency/recency of new customers.
`ModifiedBetaGeoModel.distribution_new_customer_dropout`([...])	Sample the Beta distribution for the population-level dropout rate.
`ModifiedBetaGeoModel.distribution_new_customer_purchase_rate`([...])	Sample the Gamma distribution for the population-level purchase rate.
`ModifiedBetaGeoModel.distribution_new_customer_recency_frequency`([...])	BG/NBD process representing purchases across the customer population.
`ModifiedBetaGeoModel.expected_probability_alive`([data])	Compute the probability a customer with history frequency, recency, and T is currently active.
`ModifiedBetaGeoModel.expected_probability_no_purchase`(t)	Probability a customer with frequency, recency, and T will have 0 purchases in the period (T, T+t].
`ModifiedBetaGeoModel.expected_purchases`([...])	Compute the expected number of future purchases across future_t time periods given recency, frequency, and T for each customer.
`ModifiedBetaGeoModel.expected_purchases_new_customer`([...])	Compute the expected number of purchases for a new customer across t time periods.
`ModifiedBetaGeoModel.fit`([data, method, ...])	Infer model posterior.
`ModifiedBetaGeoModel.fit_summary`(**kwargs)	Compute the summary of the fit result.
`ModifiedBetaGeoModel.graphviz`(**kwargs)	Get the graphviz representation of the model.
`ModifiedBetaGeoModel.idata_to_init_kwargs`(idata)	Create the initialization kwargs from an InferenceData object.
`ModifiedBetaGeoModel.load`(fname[, check])	Create a ModelBuilder instance from a file.
`ModifiedBetaGeoModel.load_from_idata`(idata)	Create a ModelBuilder instance from an InferenceData object.
`ModifiedBetaGeoModel.save`(fname, **kwargs)	Save the model's inference data to a file.
`ModifiedBetaGeoModel.set_idata_attrs`([idata])	Set attributes on an InferenceData object.
`ModifiedBetaGeoModel.table`(**model_table_kwargs)	Get the summary table of the model.
`ModifiedBetaGeoModel.thin_fit_result`(keep_every)	Return a copy of the model with a thinned fit result.

Attributes

`covariate_cols`	All covariate column names.
`default_model_config`	Default model configuration.
`default_sampler_config`	Default sampler configuration.
`dropout_covariate_cols`	Dropout covariate column names from model_config.
`fit_result`	Get the posterior fit_result.
`id`	Generate a unique hash value for the model.
`posterior`	Access the 'posterior' attribute of the InferenceData object.
`posterior_predictive`	Access the 'posterior_predictive' attribute of the InferenceData object.
`predictions`	Access the 'predictions' attribute of the InferenceData object.
`prior`	Access the 'prior' attribute of the InferenceData object.
`prior_predictive`	Access the 'prior_predictive' attribute of the InferenceData object.
`purchase_covariate_cols`	Purchase covariate column names from model_config.
`version`
`idata`
`sampler_config`
`model_config`