I have an experiment that produces a decimal score representing quality, and a bunch (5-30) of variables that each take on one of a set of discrete states. - The states are not meaningfully contiguous - the states are just a set of unrelated discrete values ("foo", "bar") - The set of states is about 10-40 for each variable. - There may be correlation between the values of different variables. - The states for one variable may overlap with another variable, but we can treat them independently. There is also noise unrelated to the variables, but lets assume that the noise is much smaller than the effect of the variables.
What approach can I use to correlate or cluster good scores with specific states?
I'm looking for a result along the lines of "a good score is mostly correlated with variable X = state foo, and variable Y = state bar"
I'm relatively new to this area and every method I'm familiar with deals with relationships between continuous variables. There seem to be methods based on binary states, and I suppose I could translate my variables into mutually exclusive binary states, but I'm still not sure where to go from there.
(possibly similar to Similarity between objects based on tags (binary features) but I haven't figured it out yet)