Data with too many categories
I am not sure if I understand by "automatically". However, instead of plotting (which can be a hard task if you have many attributes for each sample), you can try to automatically group your samples using clustering techniques such as K-Means, Hierarchical clustering, SOM (or any clustering technique that fits to your problem). Then, for each group, you may extract any statistical information of interest.
I hope to know a general approach when do data engineering.
I have a data set with some variables with too many categories, and including these variables into a predictive model definitely would increase the complexity of the model, thus leads to overfit.
While normally I would group those categories into fewer groups by drawing plots to see if the response variable is significantly different among these groups. Is there a more efficient way dealing with this issue, like automatically carry out some statistical test?
ADDED: In a nutshell, I hope to group or bin values in a variable  so that the response variable in each group has very different distribution.