I plan to fit a GAM or GAMM. There is one categorical variable which I think is important for explaining Y (or Y*), but it is not in my dataset - it is measurable but has not been measured.
Can I use a mixture model (GAMM) to compensate for the omission of this variable? If I had this variable, I would have just used a GAM.
Can you recommend some software for me to use? Do you have examples? Is the gamm4 R package "the way to go"?
Other details: Y is count data, so I plan to use a Negative Binomial model or "family". The purpose of this taks is to investigate the relationships between the variables. Although the dataset, with N rows, fits into memory of my machine, a matrix with NxN rows will not fit into memory.