I a total of 8 Independent Variables (4 continuous - Scales outcomes - and 4 categorical - Demographic and other personality questions) and 2 Dependent Variables (1 continuous and 1 count). The DVs involve data from an Iterated Prisoners' Dilemma - 1)participants mean consumption per game (continuous variable) and 2) the number of cooperations participants played during each game (count variable).
I have tested the DVs for Poisson distributions, but none of them is. Residuals of the continuous variables are not normally distributed.
My main aim is to analyse the main effect of the IVs on the 2 DVs. I am also interested in testing the possible interactions between two of the IVs and their subsequent effects on the outcome variables. What is the best statistical model to use considering that all the variables are not normally distributed? Or at least, what are the first steps I should take knowing that the data is not normally distributed?
I have been looking into Generalized linear models, but how can I run any model if I don't know the exact distribution of my data? Should I try to normalize my data?