I have about 80 predictor variables (with some multicollinearity, I assume) and a non-normal count data response variable (n=570) which is arranged into groups (n=34). I need to reduce the number of predictors for the use of GLM and/or GLMM. Ideally, the number for regression model in this case would be about 4 or 5 predictor variables.
Spearman's correlation, linear or curvilinear trend line in excel would be an easy way (for me as a student) for looking the most obvious predictors, but I think I need to do that for each group separately, and that obviously will result in a large number of coefficients. Is it appropriate to use the highest correlation coefficient average to "judge" the best predictors for later use? So I would be comparing coefficient averages (got from a single grouped variable) of different variables.
I'm sure there are plenty of better ways to choose the best predictors and feel free to suggest methods. Just to mention every one of those 80 predictors could be important.