Media mix models with negative coefficient of trend t

1

Hi everyone,

Recently i used pymc marketing to build a media mix model for budget optimization. One thing that got me confused is that the actual y (revenue) as well as channel costs are in uptrend whereas I got a negative coefficient for trend variable t meaning that the trend variable is in its downtrend.

My question for this is that how we interpret this downtrend t coefficient whereas observed data (both revenue and costs) are in uptrend?

Thank you for your insight in advance.

Kelvin

2

Hi Kelvin,

Can you share the model initialization for your MMM? Do you have any time varying parameters in your model configuration?

Will

3

Hi Will,

This is the same model initialization in my question regarding negative intercept

dummy_model = DelayedSaturatedMM(date_column="", channel_columns="", adstock_max_lag=4)

my_sampler_config = {"progressbar", True}

mmm = DelayedSaturatedMMM(
    model_config=dummy_model.default_model_config,
    sampler_config=my_sampler_config,
    data=column="date_week",
    channel_columns=cost_channel,
    control_columns=event_column_names + ['t'],
    adstock_max_lag=8,
    yearly_seasonality=2,

)

mmm.fit(X=X, y=y, target_accept=0.95, chains=8, nuts_sampler="numpyro", random_seed=rng)

and the only time varying parameters I used are

control_columns=event_column_names + ['t']

Thank you for your insight in advance.

Kelvin

4

Hi everyone,

Sorry that there is a missing information regarding this question is that both costs and revenue are time series data from 20230101 to 20240630 and both the costs and revenue are in up trend. The slope of costs’ time series is large than the slope of revenue’s time series.

Given the missing information above, is it possible to interpret that “Since both costs and revenue are in up trend, and the slope of costs’ time series is larger than the slope of revenue’s time series, meaning the costs trend up higher than the revenue. In order to average out the difference in slope, the model will have a negative coefficient of trend t?”

Kelvin