I'm running a logistic regression with a selection of categorical predictors. I have split my data into a training and testing set to evaluate my model. One of these predictors is "employment" which has over 50 levels. For some of the levels of this factor, the amount of observations are extremely limited, as low as 1. the range of observations in each variable is also very large (1 - 2011). I have two questions regarding this issue:
1) It's not possible to represent all levels of employment in the training and the testing set due to the fact that for some levels there is only one observation. I don't want to exclude these levels because those categories are necessary. How can I include then in the model? I suspect that I should possibly create some more observations which include those categories that just consist of noise. If that is the solution, how many of such observations would be required?
2) How does the model deal with those categories that have such few observations including those with 1, 2 or 4? Their associated standard errors are inflated and their p values are far from significant, however their estimates can be relatively large. Will they have weird effects on my model or are they dealt with automatically?
Below is a sample of the frequency of observations per each level of the category.