How to set prior on none-media treatment variables?

[Aminshnn]

Consider a case that we have incentive as our non-media treatment. The default prior for incentive is HalfNormal or Truncated Normal(0,0.1,0.1). Im my case, the incentive variable is categorical variable which takes 5 levels. So, I use one-hot encoding and will get 4 new columns. Now, my first question is how I should set prior for each new column?
if I set the prior on the each new column like Truncated Normal(0,0.1,0,1), it will be like increasing the possible contribution of the original incentive variable in the prior distribution. What is the best approach to set the prior for each column corresponding to each level?

Another concern is that when we use one hot encoding, each level would take 1 only for a fraction of observations. I think when we set the prior Truncated Normal(0,0.1,0,1) for a variable, the assumption is that it will take non-zero values often. How should we incorporate the fact that each level of incentive can take 1 for p fraction of times? Do we need to consider the fraction p in the prior? For example, if the prior is the default prior and a level takes 1 only 20% of time, the contribution in active periods can be so high, like 50%, and at the end, the total contribution of that level is still reasonable and low.

[dattatreyam23]

Hi @Aminshnn ,

Thank you for contacting us!

Here is how to address priors interacting with one-hot encoded variables and sparsity both in Meridian.

1. Setting Priors for One-Hot Encoded Columns

You are correct that applying a single 1D prior to all 4 columns would broadcast the same expected contribution across each, which could artificially inflate the overall expectation. Passing a multi-dimensional prior array is the correct approach to distribute the total expected contribution.

• Baseline Choice: When one-hot encoding, the choice of your dropped baseline variable is very important. It will be much easier to interpret your results if your baseline represents the state where all categories of incentives are inactive.
• Prior Distribution: The prior means in your array do not have to be equal. Since each category represents a different incentive type, it is highly recommended to set different values based on your prior business intuition of how effective each specific tier or type is.
• You can learn more about setting parameter dimensionality in the Configure the model documentation.

2. Handling Sparsity and Frequency ($p$)

You actually do not need to adjust your prior to account for the fraction of time ($p$) a level is active.

• Historical Execution: In Meridian, a "contribution" prior is defined as the contribution at historical execution. This means if an incentive was active 20% of the time in your dataset, the contribution prior you provide already represents the expected contribution of that incentive being active 20% of the time. No mathematical scaling is required.
• Addressing Sparsity: While the prior doesn't need adjustment, high sparsity can still affect the model's ability to get good estimates. You can use Meridian's EDA module to diagnose if this is happening. To alleviate severe sparsity, consider combining smaller categories to increase their frequency. Alternatively, if your incentives are sequential (e.g., Tier 1, Tier 2, Tier 3), consider treating the incentive as an ordinal variable using integer encoding rather than one-hot encoding.

Hope this helps you set up your model accurately!

Thank you,

Google Meridian Support Team