Meridian offers multiple ways to parameterize the causal effect of each treatment variable on the KPI. We refer to each option as different model parameterizations. In Bayesian inference, a prior must be set on the parameters of the model. So the model parameterization determines what precisely one is setting a prior on.
The paid_media_prior_type
argument of the
ModelSpec
lets you
specify whether a prior is placed on ROI, mROI, or the coefficient (beta_m
).
The
PriorDistribution
object has arguments for roi_m
, mroi_m
and beta_m
, but only one will be
used depending on the value of paid_media_prior_type
. Likewise, the
PriorDistribution
object has arguments for roi_rf
, mroi_rf
, and beta_rf
,
but only one will be used depending on the value of paid_media_prior_type
.
Each model parameterization has a different default prior distribution. The following tables summarize the default priors under each model parameterization.
Paid media
The following table summarizes the model parameterization and default priors for
the causal effect of paid media on the KPI. These vary based on the
paid_media_prior_type
argument in ModelSpec
. The model parameterization and
default priors also depend on whether outcome
is in terms of revenue. Outcome is in terms of revenue when either the KPI is
revenue or when revenue_per_kpi
is passed to InputData
. Outcome is not in
terms of revenue ("non-revenue") when the KPI is not revenue and
revenue_per_kpi
is not passed to InputData
. The table also includes a column
indicating the corresponding parameter in the PriorDistribution
container that
allows one to customize the prior.
Model Type | Default Prior | ||
---|---|---|---|
paid_media_prior_type |
Outcome | Prior Type | Parameter in PriorDistribution |
'roi' (default) |
Revenue | ROI | roi_m , roi_rf |
'roi' (default) |
Non-revenue | Total Paid Media | roi_m , roi_rf |
'mroi' |
Revenue | mROI | mroi_m , mroi_rf |
'mroi' |
Non-revenue | No default, must set custom | mroi_m , mroi_rf |
'coefficient' |
Revenue | Coefficient | beta_m , beta_rf |
'coefficient' |
Non-revenue | Coefficient | beta_m , beta_rf |
The distribution used as the default prior for each model parameterization is summarized in Default prior distributions.
Under each scenario listed in the table, set a custom prior using the
appropriate PriorDistribution
parameter indicated in the table. When setting
a custom prior, it's important to understand what you are setting a custom
prior on. For more on the definition of ROI and mROI, see ROI and mROI
parameterization. For more
on the definition of a coefficient, see the model specification.
For more on the total paid media contribution prior, see
Custom total paid media contribution prior.
Organic media and non-media treatments
The default prior for treatment effects of organic media and for non-media
treatments are unaffected by the paid_media_prior_type
argument nor are they
affected by whether or not the KPI is revenue. Organic media uses
beta_om
or beta_orf
as its prior parameter and non-media treatments uses
gamma_n
as its prior parameter.