LogSaturation

class pymc_marketing.mmm.components.saturation.LogSaturation(priors=None, prefix=None)

Logarithmic saturation for log-log models.

Applies \(\beta \, \log(1 + x)\) to the raw (unscaled) channel input, mapping spend through a concave logarithmic curve with diminishing returns.

When combined with link="log" in the MMM, the model becomes a log-log specification and \(\beta\) is an approximate elasticity – the percentage change in the response per one percent change in spend. For this interpretation to hold, the channel input must not be rescaled: an elasticity is dimensionless, so dividing spend by an arbitrary channel_scale would change \(\beta\) (because \(\log(1 + x)\) is not invariant under multiplicative rescaling of \(x\)). This class therefore sets requires_unscaled_input to True, which makes the MMM feed raw spend to the saturation and force channel_scale = 1 for the affected channels.

log(1 + x) (rather than log(x)) is used so that the transform is finite at x = 0 – common for paused or cold-start channels – while remaining numerically indistinguishable from log(x) once spend is large, where the elasticity interpretation is exact in the limit \(\partial \log y / \partial \log x \to \beta\).

(Source code, png, hires.png, pdf)

Methods

LogSaturation.__init__([priors, prefix])
LogSaturation.apply(x, *[, core_dim, idx])	Call within a model context.
LogSaturation.from_dict(data)	Reconstruct a saturation transformation from a dict.
LogSaturation.function(x, beta, *[, dim])	Logarithmic saturation function: beta * log(1 + x).
LogSaturation.plot_curve(curve[, n_samples, ...])	Plot curve HDI and samples.
LogSaturation.plot_curve_hdi(curve[, ...])	Plot the HDI of the curve.
LogSaturation.plot_curve_samples(curve[, n, ...])	Plot samples from the curve.
LogSaturation.sample_curve([parameters, ...])	Sample the curve of the saturation transformation given parameters.
LogSaturation.sample_prior([coords])	Sample the priors for the transformation.
LogSaturation.set_dims_for_all_priors(dims)	Set the dims for all priors.
LogSaturation.to_dict([_orig])	Convert the transformation to a dictionary.
LogSaturation.update_priors(priors)	Update the priors for a function after initialization.
LogSaturation.with_default_prior_dims(dims)	Return a copy with default prior dims (dims=None) set to dims instead.
LogSaturation.with_updated_priors(priors)	Return a copy with updated priors.

Attributes

combined_dims	Get the combined dims for all the parameters.
default_priors
function_priors	Get the priors for the function.
model_config	Mapping from variable name to prior for the model.
prefix
priors	Get the priors for the function.
requires_unscaled_input	Whether the saturation must receive raw (unscaled) channel inputs.
variable_mapping	Mapping from parameter name to variable name in the model.