Inquiry Regarding Time-based ROI Calculation in lightweightMMM

[shamzos]

I wanted to take a moment to express my appreciation for the exceptional work you've put into developing the lightweightMMM package. It has been an invaluable tool in my work, and I've been thoroughly impressed with its functionality and efficiency.

Recently, I've been exploring the package's capabilities to analyze ROI for various channels over time(steps). While I've managed to grasp the overall equation for ROI calculation, I've encountered a challenge regarding the transformation of media contribution to incorporate time-based factors.
the equation:

roi_hat = sum_unscaled_prediction * media_contribution_hat / unscaled_costs
where :

media_contribution_hat = media_contribution / sum_scaled_prediction
 media_contribution = jnp.einsum(einsum_str, self.trace["media_transformed"],
                                    jnp.squeeze(self.trace["coef_media"]))

Currently, the media contribution transformation utilizes 'einsum_str' with 'stc, sc -> tc'. However, for my analysis, it's crucial to factor in time granularity, which the current transformation doesn't seem to address directly.

I was wondering if it's possible to adapt the transformation process to incorporate time-based calculations, such as 'stc, sc -> tc'. If you could provide any guidance or suggestions on how to implement or achieve this time-based calculation within the lightweightMMM package, I would be immensely grateful. Additionally, if there are any alternative approaches or workarounds you could recommend, I'm eager to explore them further.