How to extract adstock, hill function parameters and final regression coefficients from the model’s inference_data?

[MateSroka]

Hi,
Thanks for your work on this project – I really appreciate it!

I have a question about working with a fitted MMM model. I see that the model object contains a parameter called inference_data, which holds the sampled parameter values after fitting.

I’d like to extract the following parameters from it:

1. Adstock parameters per media variable (e.g. decay rate or retention).

2. Hill function parameters – typically alpha and gamma.

3. Final regression coefficients for media variables after transformation (adstock + hill).

4. Regression coefficients for non-media variables (e.g. pricing, seasonality, trend, etc.).

I’m aware that I can retrieve credible intervals using the method:

analyzer.get_mean_and_ci(mmm.inference_data.posterior.alpha_m, 0.9)

This works great for the adstock parameters (alpha_m). Is there a similar way (or recommended best practice) to extract:

Hill parameters (gamma_m, beta_m or equivalent),

Final coefficients for transformed media and non-media variables?

Also, is there a list of all available parameters within inference_data.posterior, or a preferred way to inspect them programmatically?

Any example or guidance would be much appreciated!

Thanks in advance!

[cpulavarthi]

Hi @MateSroka,

Thank you so much for contacting us.

I would like to inform you that Meridian allows you to access the assessed values of slope of the Hill/ Adstock transformer etc. from the trained model, by channel, in the inference_data attribute of the meridian model object.

Please find the sample code to extract some of the parameters below. You may use similar code to extract any other required parameters similarly. Please find the respective parameter naming conventions followed in Meridian in our documentation on Default Prior Distributions.

• Hill Function Parameters (gamma_m and beta_m)

  gamma_params = analyzer.get_central_tendency_and_ci()(mmm.inference_data.posterior.gamma_m,0.9)
  
  beta_params = analyzer.get_central_tendency_and_ci()(mmm.inference_data.posterior.beta_m,0.9)
  

• Regression coefficients for Transformed Media Variables (coef_media)

  media_coefs = analyzer.get_central_tendency_and_ci()(mmm.inference_data.posterior.coef_media,0.9)
  

The posterior distributions for all other parameters can be accessed in a similar manner. You may also run mmm.inference_data to get a list of all available parameters within inference_data.posterior, example given below:

Please note that the analyzer.get_mean_and_ci() has been renamed get_central_tendency_and_ci() with the inclusion of the median. Hence, kindly follow the updated code as mentioned above.

For more information on how the InferenceData object is organized, please refer to the Arviz documentation linked here. You may also check the API documentation on the Meridian model object here to better understand its attributes and how to extract the necessary information.

Feel free to reach out if you have any questions or suggestions regarding the same.

Thank you

Google Meridian Support Team