ShiftedBetaGeoModel

class pymc_marketing.clv.models.shifted_beta_geo.ShiftedBetaGeoModel(data=None, *, model_config=None, sampler_config=None)

Modelo Geométrico Beta Desplazado (sBG) para clientes que renuevan contratos durante períodos de tiempo discretos.

El modelo sBG tiene las siguientes suposiciones:

• Dropout probabilities for each cohort are Beta-distributed with hyperparameters alpha and beta.

• Las tasas de retención de cohortes cambian con el tiempo debido a la heterogeneidad de los clientes.

• Los clientes en la misma cohorte comenzaron su contrato en el mismo período de tiempo.

Este modelo requiere que los datos sean resumidos por recencia, T y cohorte para cada cliente. Las suposiciones del modelo requieren 1 <= recencia <= T y T >= 2.

First introduced by Fader & Hardie in [1], with additional expressions and enhancements described in [2] and [3].

Parameters:

dataDataFrame

DataFrame que contiene las siguientes columnas:

• customer_id: Unique customer identifier.

• recency: Time period of last contract renewal. It should equal T for active customers.

• T: Max observed time period in the cohort. All customers in a given cohort share the same value for T.

• cohort: Customer cohort label.

• Any columns listed in dropout_covariate_cols when using covariates.

model_configdict, optional

Diccionario de parámetros previos del modelo:

• alpha: Prior or None (cohort-level). Shape parameter of dropout process. Default is phi * kappa when alpha is not provided directly.

• beta: Prior or None (cohort-level). Shape parameter of dropout process. Default is (1 - phi) * kappa when beta is not provided directly.

• phi: Prior for pooling if alpha and beta are not provided directly; default Prior("Uniform", lower=0, upper=1, dims="cohort").

• kappa: Prior for pooling if alpha and beta are not provided directly; default Prior("Pareto", alpha=1, m=1, dims="cohort").

• dropout_coefficient: Prior for covariate coefficients; default Prior("Normal", mu=0, sigma=1).

• dropout_covariate_cols: Sequence[str]. Column names for customer-level, time-invariant covariates; default [].

sampler_configdict, optional

Diccionario de parámetros del muestreador. Por defecto es Ninguno.

Notes

Example:

Required data format:

customer_id	recency	T	cohort	discrete_covariate	continuous_covariate
1	8	8	2025-02	1	2.172
2	1	5	2025-04	0	1.234
3	4	5	2025-04	1	2.345

Example usage:

from pymc_extras.prior import Prior
from pymc_marketing.clv import ShiftedBetaGeoModel

model = ShiftedBetaGeoModel(
    model_config={
        "alpha": Prior("HalfNormal", sigma=10),
        "beta": Prior("HalfStudentT", nu=4, sigma=10),
    },
    sampler_config={
        "draws": 1000,
        "tune": 1000,
        "chains": 4,
        "cores": 4,
        "nuts_kwargs": {"target_accept": 0.95},
    },
)

# Fit model quickly to large datasets via Maximum a Posteriori
model.fit(method="map")
model.fit_summary()

# Use 'mcmc' for more informative predictions and reliable performance on smaller datasets
model.fit(data=data,method="mcmc")
model.fit_summary()

# Predict probability customers are still active
expected_alive_probability = model.expected_probability_alive(
    active_customers,
    future_t=0,
)

# Predict retention rate for a specific cohort
cohort_name = "2025-02-01"

expected_alive_probability = model.expected_retention_rate(
    future_t=0,
).sel(cohort=cohort_name)

# Predict expected remaining lifetime for all customers with a 5% discount rate
expected_alive_probability = model.expected_residual_lifetime(
    discount_rate=0.05,
)

# Predict expected retention elasticity for all customers in a specific cohort
expected_alive_probability = model.expected_retention_elasticity(
    discount_rate=0.05,
).sel(cohort=cohort_name)

# Example with customer-level covariates
model_with_covariates = ShiftedBetaGeoModel(
    ),
    model_config={
        "dropout_coefficient": Prior("Normal", mu=0, sigma=2),
        "dropout_covariate_cols": ["covariate1", "covariate2"],
    },
)
model_with_covariates.fit(data=covariate_data, method="demz")

References

[1]

Fader, P. S., & Hardie, B. G. (2007). «How to project customer retention.» Journal of Interactive Marketing, 21(1), 76-90. PDF

[2]

Fader, P. S., & Hardie, B. G. (2010). «Customer-Base Valuation in a Contractual Setting: The Perils of Ignoring Heterogeneity.» Marketing Science, 29(1), 85-93. PDF

[3]

Fader, P., & Hardie, B. (2007). «Incorporating Time-Invariant Covariates into the Pareto/NBD and BG/NBD Models.» Note 019

Methods

ShiftedBetaGeoModel.__init__([data, ...])	Inicializar la configuración del modelo y la configuración del muestreador para el modelo.
ShiftedBetaGeoModel.attrs_to_init_kwargs(attrs)	Convierta la configuración del modelo y la configuración del muestreador de los atributos a argumentos de palabra clave.
ShiftedBetaGeoModel.build_from_idata(idata)	Construya el modelo a partir del objeto InferenceData.
ShiftedBetaGeoModel.build_model([data])	Construya el modelo.
ShiftedBetaGeoModel.create_idata_attrs()	Crear atributos para los datos de inferencia.
ShiftedBetaGeoModel.expected_probability_alive([...])	Compute expected probability of contract renewal for each customer.
ShiftedBetaGeoModel.expected_residual_lifetime([...])	Compute expected residual lifetime of each customer.
ShiftedBetaGeoModel.expected_retention_elasticity([...])	Compute expected retention elasticity for each customer.
ShiftedBetaGeoModel.expected_retention_rate([...])	Compute expected retention rate for each customer.
ShiftedBetaGeoModel.fit([data, method, ...])	Infer model posterior.
ShiftedBetaGeoModel.fit_summary(**kwargs)	Calcule el resumen del resultado del ajuste.
ShiftedBetaGeoModel.graphviz(**kwargs)	Obtenga la representación graphviz del modelo.
ShiftedBetaGeoModel.idata_to_init_kwargs(idata)	Cree los kwargs de inicialización a partir de un objeto InferenceData.
ShiftedBetaGeoModel.load(fname[, check])	Crear una instancia de ModelBuilder a partir de un archivo.
ShiftedBetaGeoModel.load_from_idata(idata[, ...])	Cree una instancia de ModelBuilder a partir de un objeto InferenceData.
ShiftedBetaGeoModel.save(fname, **kwargs)	Guarde los datos de inferencia del modelo en un archivo.
ShiftedBetaGeoModel.set_idata_attrs([idata])	Establecer atributos en un objeto InferenceData.
ShiftedBetaGeoModel.table(**model_table_kwargs)	Obtenga la tabla resumen del modelo.
ShiftedBetaGeoModel.thin_fit_result(keep_every)	Devuelva una copia del modelo con un resultado de ajuste reducido.

Attributes

cohort_idx	Cohort indices for each customer.
cohorts	Unique cohort values from data.
default_model_config	Default model configuration.
default_sampler_config	Default sampler configuration.
dropout_covariate_cols	Dropout covariate column names from model_config.
fit_result	Obtenga el resultado de ajuste posterior.
id	Generar un valor hash único para el modelo.
posterior
posterior_predictive
predictions
prior
prior_predictive
version
idata
sampler_config
model_config