Suppose I want to investigate the impact of some binary independent variables (let’s say: sex and height [tall/short]) on my binary response (alcohol consumption for instance). The distribution of my variables is as following (number of observations - 419):
Dependent variable: # FALSE TRUE #0.8400955% 0.1599045% Some independent variables: FALSE TRUE 0.97374702% 0.02625298% FALSE TRUE 0.9451074% 0.0548926% FALSE TRUE 0.96420048% 0.03579952%
Logistic Regression in Rare Events Data Predictive Performance of Logistic Regression for Imbalanced Data with Categorical Covariate
However, they both regard to dependent variable, while I have unbalanced the independent ones. I know, that my model will have low predictive power because of such unbalance, since it may not capture the characteristics of population (I mean that the distribution in population may differ).
But I am not sure whether I may use my independent variables to make any statistical inferences about the impact of independent variables on my dependent one? I am looking for a rule regarding the distribution/size of binary independent variables (e.g. 97% of FALSE and 3% of TRUE cases).