create_bass_model#

pymc_marketing.bass.model.create_bass_model(t, observed, priors, coords, model=None, ds=None)[source]#

Define a Bass diffusion model for product adoption forecasting.

This function creates a Bayesian Bass diffusion model using PyMC to forecast product adoption over time. The Bass model captures both innovation (external influence like advertising) and imitation (internal influence like word-of-mouth) effects in the adoption process.

The model includes the following components:

  • Market potential ‘m’: Total number of eventual adopters

  • Innovation coefficient ‘p’: Measures external influence

  • Imitation coefficient ‘q’: Measures internal influence

  • Adopters over time: Number of new adopters at each time point

  • Innovators: Adopters influenced by external factors

  • Imitators: Adopters influenced by previous adopters

  • Peak adoption time: When adoption rate reaches maximum

Parameters:
tpt.TensorLike

Time points for which the adoption is modeled.

observedpt.TensorLike or xr.DataArray or None

Observed adoption data at each time point. If None, only prior predictive sampling is possible. Axis labels are read from the data itself (an xr.DataArray) or from the model (a pm.Data registered with dims); anything else, such as a plain array or a pm.Data without dims, is labelled positionally in (T, ...) order with the extra dims following their first appearance across the likelihood prior and the dims that m, p and q actually built with, in that order. An array laid out the way the likelihood prior declares it is therefore read the way it is laid out.

priorsBassPriors

Dictionary containing priors or term recipes for: - ‘m’: Market potential prior or term - ‘p’: Innovation coefficient prior or term - ‘q’: Imitation coefficient prior or term - ‘likelihood’: Observation likelihood model

A recipe may carry covariates through Dot when a dataset is passed via ds; pass covariates that vary across a dimension such as product. m, p and q are built in that order, so a recipe may reference an earlier coefficient with Ref; a forward reference fails with an error naming the missing variable.

coordsdict[str, Any]

Coordinate values for dimensions in the model, including ‘date’ for the time dimension and any other dimensions included in the prior specifications.

modelModel, optional

An existing PyMC model to use. If not provided, a new model is created with the given coords.

dsxr.Dataset, optional

Dataset the recipes read covariates from. A recipe references a covariate by name through Dot, and only the variables a recipe names are registered, so passing the full dataset is safe. Omit it when no recipe carries data. A covariate varying over T is rejected for p/q; see the note above.

Returns:
Model

A PyMC model object for the Bass diffusion model, containing the variables m, p, q, adopters, innovators, imitators, peak, and the likelihood y.

Notes

The returned model can be used for prior predictive checks, posterior sampling, and posterior predictive checks to forecast product adoption.

The model implements the following mathematical relationships:

\[\begin{split}\text{adopters}(t) &= m \cdot f(p, q, t) \\ \text{innovators}(t) &= m \cdot p \cdot (1 - F(p, q, t)) \\ \text{imitators}(t) &= m \cdot q \cdot F(p, q, t) \cdot (1 - F(p, q, t)) \\ \text{peak} &= \frac{\ln(q) - \ln(p)}{p + q}\end{split}\]