Understanding the MaxAbsScaler and Channel Contribution Discrepancy in PyMC Marketing Models

[stdp95]

I'm currently using PyMC Marketing for a Marketing Mix Modeling project and noticed a potential issue related to scaling and contribution attribution in the final model. Here's the situation:

1. Issue:

• I see that channels with very low spend are contributing disproportionately to sales in the final model, whereas high-spend channels are underperforming in terms of their contribution. For instance:
• A high-spend channel is ranked 5th out of 9 in terms of contribution to sales.
• Meanwhile, a low-spend channel is ranked 1st in contribution to sales.

2. Scaling Context:

• I noticed that the MaxAbsScaler is applied independently at the channel level during preprocessing (as per the default max_abs_scale_channel_data function in the codebase). This scales each channel by its own maximum absolute value, which means the total spend proportions across channels are not preserved.

3. Question:

• Could the independent scaling of channels (via MaxAbsScaler) be causing a distortion in the contribution estimates, especially for channels with very low spend?
• If so, how should I modify the scaling approach to ensure that the percent share of spend across channels is preserved and reflected in the contribution estimates?
• Would switching to global scaling (e.g., scaling relative to the highest spend across all channels or total spend across all channels) improve the interpretation and reliability of the contributions?

4. Example Data:
   Here’s a simplified snapshot of my original spend data vs. scaled spend data:
   Original Spend

• Cost_CTV 3,058,184
• Cost_Display 2,426,354
• Cost_E-Commerce 815,907
• Cost_OLV 9,671,693
• Cost_Paid_Search 938,310
• Cost_Streaming_Audio 667,339
• Cost_Social 15,844,830
• Cost_OOH 2,248,606
• Cost_Radio 79,950

Scaled Spend Values (MaxAbsScaler):

• Cost_CTV 25.77
• Cost_Display 24.08
• Cost_E-Commerce 64.73
• Cost_OLV 41.73
• Cost_Paid_Search 41.76
• Cost_Streaming_Audio 6.96
• Cost_Social 37.56
• Cost_OOH 17.98
• Cost_Radio 2.58

This discrepancy seems to disproportionately impact low-spend channels, amplifying their contributions while diminishing the role of high-spend channels.

Your expertise and guidance would mean a lot as I try to better understand this behavior. Thank you for your time and support!

[AnantChandra]

You're right about the scaling issue. Independent MaxAbsScaler application distorts the relative spending between channels. The solution is to implement global scaling instead.

Scale all channels relative to the global maximum spend across channels. Instead of the default max_abs_scale_channel_data when preprocessing your data, implement a method along these lines:

def global_scale_channel_data(df, channel_cols):
    global_max = df[channel_cols].abs().max().max()
    df_scaled = df.copy()
    for col in channel_cols:
        df_scaled[col] = df[col] / global_max
    return df_scaled

[JnsLns]

I think the biasing effect of per-channel scaling is somewhat alleviated by setting the width of coefficient priors depending on the share each channel has on the total spend (as shown in the MMM example notebook). It tends to make low spend channels contribute less. One advantage of this approach would be easier interpretation of the coefficient estimates in terms of all of them living on a similar scale; the same may apply to other parameters (e.g. saturation).