I am interested in smoking_ads effect on smoking_rate. I also have two categorical confounders in the data: town and year.
Possible DAG shows two backdoors that need to be closed in conditioning. Each town may have different characteristics that possibly have an effect on ads (laws) or smoking rate (habitational factors).
However, my data is a bit tricky as its detailedness is limited. Smoking_ads is calculated for each town by study year: the values of "smoking_ads" are very similar for each town. For example, town "C" values range between 22-24 and town D between 233-257.
To illustrate, a stupid analogy of this is would be the following model:
weight ~ sex + breast_size
1) Should I adjust for town or not? It seems, et adding town kills the effect. How you handle such situations?
2) How does it differ if "town" is added as a another level into model + (1 |town)?