Why does a DAG Control Column *have to* impact a Spend Column?

[AnantChandra]

Hi there!

I'm using the PyMC Marketing MMM DAG.

However, I noticed that every control column must impact at least one spend column. Why is this the case?

Works:

causal_dag_str = """
digraph {
   google_performance_max_all_features_spend -> orders_kpi;
   ...
   pr_overall_reach_of_publication_control -> orders_kpi;
   pr_overall_reach_of_publication_control -> google_performance_max_all_features_spend;
}
"""

Doesn't work:

causal_dag_str = """
digraph {
   google_performance_max_all_features_spend -> orders_kpi;
   ...
   pr_overall_reach_of_publication_control -> orders_kpi;
}
"""

Initializing the model this way:

causal_mmm = MMM(
    sampler_config=sample_kwargs,
    date_column='date',
    adstock=GeometricAdstock(l_max=24),
    saturation=MichaelisMentenSaturation(),
    channel_columns=spend_columns,
    control_columns=control_columns,
    outcome_node=sales_col,
    treatment_nodes=treatment_nodes,
    dag=causal_dag_str
)

Working case:

causal_mmm.control_columns --> ['pr_overall_reach_of_publication_control']

Not working case:

causal_mmm.control_columns --> []

What's the way forward if my control is directly impacting the KPI and the KPI only?

[williambdean]

Maybe @cetagostini can shed some light on this

[cetagostini]

Hey @AnantChandra

The code is design to check the causal relationships in the graphical model, and keep the MINIMAL adjustment set, that means, any variable not needed to properly detect the direct effect will be always exclude.

Note

If we were trying to get a MAXIMAL adjustment set, we could include other variables which are not in the path of the variable of interest.

Example, in a structural causal model state as:

a -> b
b -> y
c -> y

c it's not needed to capture the real direct/indirect effect of b or a. Meaning, will be exclude from the regression.

If you want to add c just to explain more variability, then you can use the function to get the MINIMAL adjustment set, create another model manually, without the DAG function and then, add all your variables which are direct.

[AnantChandra]

Got it! Thanks for the detailed answer.

Are there any example notebooks/ public resources available for this approach?

If you want to add c just to explain more variability, then you can use the function to get the MINIMAL adjustment set, create another model manually, without the DAG function and then, add all your variables which are direct.

Since none of my control columns influence the spend columns, causal_mmm.causal_graphical_model.minimal_adjustment_set is always just the spend columns.
Is your suggestion to then build a conventional model with the aforementioned spend columns + all controls?

mmm = MMM(
    model_config=model_config,
    sampler_config=sampler_config,
    date_column=date_column,
    adstock=GeometricAdstock(l_max=4),
    saturation=LogisticSaturation(),
    channel_columns=spend_columns,
    control_columns=control_columns,
    yearly_seasonality=3,
)

[AnantChandra]

Hypothetical follow-up question:

What if a spend column is impacting a control column that's impacting the KPI? (S -> C -> K)
Ex:

casual_dag_str = """
digraph {
    google_performance_max_all_features_spend -> orders_kpi;
    ...
    low_spend -> email_sent_control
    email_sent_control -> orders_kpi;
}
"""

Even then causal_mmm.control_columns = []

Why does this happen?