I am trying to do something that I am not sure it is a possibility, but I would like to ask for some opinions on the matter.
I am predicting the values of sales for every day/product with the information of the previous 30 days.
I use the same variables to obtain the model used for each day/product. It is a 30 days temporal model with random effects at the region level. The values of the coefficients will be different according to the product and day.
What I am trying to figure out is if for the same product I can compare the coefficients for the different days. There is some kind of assessment to do this?
Imagine that we have this model structure, and I want to predict the sales for one day: model_day1<-lmer(y ~ x1 + x2+ x3 + (1|x4) + cos(2*pi*t/7) + sin(2*pi*t/7), data=dados) This is estimated with the 30 previous days, to know the sales of the 31st day.
Then I will use the same model structure to predict the sales of the second day, with the previous 30 days.
model_day2<-lmer(y ~ x1 + x2+ x3 + (1|x4) + cos(2*pi*t/7) + sin(2*pi*t/7), data=dados)
There is a way to know if x1 coefficient of the model of day 1 is the same as x1 of the model of day 2?
Thank you in advance!