i say you're just fine with doing regular OLS multiple regression and treat your DV as 'continuous'. usually discrete variables with 5 options (think a likert scale that goes from 1=completely disagree to 5=completely agree) is OKish if the variables are reasonably symmetric. once it hits 7 points you can handle some non-zero skewness/kurtosis estimates... after 10 points you can pretty much treat it as continuous. you say you have 100 discretization points? i say go for it, run regular OLS

source you can cite: http://psych.colorado.edu/~willcutt/...tulla_2012.pdf