Hi Stan experts, I am new to Bayesian and brms. I am trying to run multivariate regression using Bayesian.
I am working on a marketing mix problem using Bayesian. I am working with a data of 200k records which is at customer x month level for year 2019. Which means, for each customer I have 12 records. I have sales as the dependent variable and various marketing channels as the independent variable. I am trying to estimate the betas of these marketing channels using Bayesian models.
There are few issues I am facing:

Prior selection: I have Beta estimates of different channels from 2018 data, can I use these betas as the prior for my 2019 Bayesian model? If yes, then if I run the model with 2018 betas as priors for my entire 200k records 2019 data, then due to large number of records, effect of priors is going to wash away anyway. How can I utilize the previous 2018 information? Also, I have to include all the 200k records in my model as we cannot drop any customer from our analysis.

I understand each customer would have different purchasing behavior, so I have alrerady bucketed them in the order of there sales or rather say deciles 0,1,2,3,4 with decile 4 for the customers with maximum sales. Since I was still not clear on point 1 above, I used 2018 priors with just few observation to check the approach.
I ran below model for 100 customer from decile 4:
bmod1 < brm(Sales ~ Comp + FTO + CPL + SPL
+ CC + ENG + IMP + PSO+ (1decile)+ (0+FTOdecile)
+ (0+Compdecile)+(0+SPLdecile)+(0+CCdecile)
+ (0+ENGdecile) + (0+IMPdecile) +(0+PSOdecile) ,
data = mdb_14, family = gaussian(),prior=prior2,
warmup = 1000, iter = 5000, chains = 4,
control = list(adapt_delta = 0.9999), seed=150, thin=2,
cores = parallel::detectCores()
)
But for the fit of bmod1 I am getting a very poor fit below:
I think I have added all the relevant details but please feel free to ask any clarification. I would really appreciate if you could first look into issue no.1 and give your qualitative suggestions and second look into the issue no.2 and let me know if there is any other distribution or any other tweaks I should make with bmod1 to improve my fit.
Thanks in advance.