Adding a variable taking both negative and positive values

[Aminshnn]

In my model, I extracted the seasonality from Prophet and I want to include it in my model as a non-media treatment variable to get its contribution. Since it has cycles, it gets both positive and negative values. Now, I want to set a prior on this seasonality variable. I am wondering if I should restrict its prior contribution to be positive, free or negative? I am using contribution to set the priors.
Also, I need to specify the non-media baseline value for this variable. I am wondering if it should have 0 as the baseline or the minimum value which is a negative value. I want to find the actual contribution not just relative contributions compared to the a specific value/level.
the main issue is that the model diverges.

[dattatreyam23]

Hi @Aminshnn ,

Thanks for reaching out. We appreciate you exploring potential variations on how to approach the estimation of seasonality.

Meridian already offers a way to adjust for seasonality that you could use instead of Prophet (see Set Knots). We strongly recommend you consider using knots before trying to figure out how to use Prophet to estimate seasonality. The Meridian adjustments for seasonality (knots) are estimated in conjunction with the media effects and other model parameters, thus working to avoid potential bias that can be introduced by estimating seasonality independently in a 2-step process. For example, if a media channel spend is seasonal, estimating the seasonality independently and before estimating media effects can bias the results and give credit that should go to the channel to the pre-estimated seasonality terms or baseline. This can actually result in a Prophet-derived estimate of the seasonality that is biased and taking credit away from actual media channels. Estimating them jointly in Meridian provides safeguards against this issue. For further reading, one non-Google blog that discusses this can be found at https://getrecast.com/seasonality/.

If you still want to continue trying to incorporate the Prophet-estimated seasonality, here are a couple suggestions in response to your questions.

1. Since your KPI is positive and you are using the Prophet estimates as a non-media treatment variable, any seasonality should be expected to contribute a value greater than 0. It would seem prudent to adjust the Prophet estimates to be positive (possibly a shift or transformation) and to set the prior for those terms to be positive.
2. Once again, since you would expect the seasonality to have a contribution to your positive KPI values, setting a baseline to 0 or greater seems most appropriate.

We have not spent time troubleshooting how to make use of Prophet estimates in Meridian since our preferred solution was to model the seasonality and media effects jointly to avoid some pitfalls we felt needed to be addressed. However, if you find that using Prophet estimates works well for you, we'd love to hear back from your experience.

Hope this helps. Feel free to reach out to us with any further queries regarding Meridian.

Thank you,

Google Meridian Support Team

[Aminshnn]

Thank you so much for your reply.

Meridian determines the location of knots before training the model and it ignores media channels and those are determined based on peaks and valleys. So, during the sampling process, media channels and baseline are competing for the contribution which will be similar to what we have using Prophet’s outputs.

The issue with knots is that it uses a non parametric model to show seasonality, trend which is not appropriate for future predictions and setting a target for future. What do you recommend to use to have seasonality and trend in closed-form format?

One of the features of Prophet library is that it replaces holidays and campaign variables (which are categorical) by numerical values. So, we can have different values for different holidays (can have negative and positive values for different holidays). What is the best strategy to add holidays? Should I treat all holidays the same by using binary values where 1 indicates holiday; otherwise, 0. Or, I should use one column for each holiday (many new columns).
Similarly for campaigns. What is the best strategy to include campaigns when we have different levels (categorical variables)? For example, we offer gift cards with different monetary values over time (one level), loyalty points with different monetary values over time (another level), and so on.

[dattatreyam23]

Thanks for the follow up.

As you know, Meridian uses a flexible knot-based spline approach to model the time-varying baseline effects, capturing trend and seasonality jointly while fitting the model. You are correct that this is a non-parametric approach. While powerful for fitting complex patterns, it is not as straightforward for extrapolation or setting targets as a model with explicit parametric forms for trend and seasonality, and understandably might not be the best approach for your use case.

Meridian's focus is on providing causal estimates for intervenable media. Prophet's seasonality outputs represent underlying temporal patterns, however, these are not "treatments" in the sense of intervenable variables like pricing or promotions. If used in Meridian, the seasonality and temporal estimates should be considered control variables, not non-media treatment variables. Non-media treatments are for factors you can actively change and want to measure the causal impact of. See Organic media and non-media treatment variables and Control variables.

I understand your interest in estimating the contribution from the seasonality to the KPI, however, Meridian is set up to best estimate the causal impact of intervenable media and effects, and thus does not offer contribution breakdowns for controls, seasonality, or baseline. See Reasons controls don't have causal inference or baseline breakdown. If you want to get a sense of the strength of a control's impact, you could look at the distributions of the posterior control coefficients ((\gamma_c)) to get a sense of strength from the magnitude of the coefficient. You can include your Prophet estimates of seasonality as a control in that way.

To directly address you question on including holidays and promotions as control variables, using binary control variables for each holiday individually or group of holidays that you expect identical effects (strong assumption) from is recommended. Generally we suggest one binary variable for each individual holiday. For variables that have numerical levels, like gift cards of $5, $10, $25 values, we recommend using individual one-hot encoded variables for each level unless you feel strongly the effect would be linear. For a control you feel has a legitimate linear effect, you can use a numerical control value, however that is a very strong assumption and should be considered carefully.

Additionally, instead of creating binary controls for each holiday, you can also manually choose the location of all knots, setting some knots at the holidays of interest. See "Manually Adjust Knots" in Set Knots

Hope this helps. Feel free to reach out to us with any further queries regarding Meridian.

Thank you,

Google Meridian Support Team