Channel Contributions Monotonically Increasing

[janweyers]

Hello,
I have a question regarding an issue I encountered using the inference data of my mmm model.

Suppose I want to examine the channel contributions. Using a geometric adstock transformation, a logistic saturation transformation and the presence of positive channel coefficients, I would expect my channel contributions to be monotonically increasing as adstocked spending increases.

If I take the mean / median values for alpha (for the geometric adstock) over all chains and draws from the posterior, take the mean / median lambda (for the logisitic saturation), perform the transformations with it on my original data and then multiply the result of the transformations with my mean / median channel coefficients, I get channel contribution values that show the expected behavior (monotonically increasing as adstocked spend increases).

But when I access the mean / median channel contributions directly from the posterior across all chains and draws, I don't find this monotonic behavior. I sometimes find discontinuities in my data points so no monotonically increasing behavior with increasing adstocked spend.

This is the way I proceed when I talk about drawing mean / median values across chains and draws directly from the posterior.

mmm.fit_result['channel_contributions'].median(dim=['chain', 'draw']

This is what my response curves (response = channel contribution) look like. The manually calculated contribution is shown in red, and in blue is shown if I take it directly from the channel contribution posterior.

Zoomed in.

I wonder why this is the case?
Am I wrong in any of my assumptions?
Am I missing something?
Is my approach of "manual" calculation of the channel contributions the correct procedure?
Is it wrong to simply draw the channel contributions from the posterior using the mean / median across all chains and draws?

I would highly appreciate an answer to gain clarity.
Thanks a lot!