Handling missing data in zero-inflated models because data doesn't exist

Modeling
,
1

I have a dataset where I am looking at how many customers a store receives per hour (Customers). When there are customers, I am also interested in understanding how much each individual customer has spent. There are some hours where there are no customers, which I am trying to study using a hurdle model. However, this means that in those cases there is no money spent, so the column Spent would be NA. My data looks something like this:

Hour Spent Customers
1       20         1
1       10         2
2       NA         0
3       NA         0
4       10         2
5       15         1
6       10         3
7       NA         0

I’m trying to fit a model of this type:

model <- brms(bf(Customers ~ Hour + Spent,
                 hu ~ Hour + Spent),
                 data = df,
                 family = hurdle_poisson())

However I’m not sure how to handle these NAs. Technically they are not missing data as there was no data to collect at that time, so I’m not sure if imputation or handling it with the mi function are appropriate ways to handle it.

I would appreciate any suggestions that may come up.

2

It looks like your model’s trying to predict customers based on hour and amount spent.

I doubt that hour is going to be a linear effect if this is store hours, so I’d suggest using an hour random effect rather than a fixed effect. I think that’s 1 | Hour but I’m not 100% sure not being a brms or lme4 user.

I don’t know brms, but my guess is that you want to change those NA to 0. The dollar amount spent isn’t unknown, it’s zero. Is it possible there is 1 or more customers and 0 dollars spent? If it were NA, it might be 0, 10, 20, or some other value.

Assuming you have a bunch of days, I’d suggest plotting the number of customers for each hour as a bar plot (multiple plots, one per hour) and seeing if they’re consistent with a Poisson distribution or if they need zero inflation of some kind (hurdle or direct).