How can I convert predicted probabilities of a logit model into predicted binary response ? Can I consider 0.5 as cut point to convert probabilities to binary variable (0,1). Or should I use binomial distribution to generate binary variable where predicted probabilities are used as success probability. By the way I am doing it for cross validation of the fitted model.
usually it is feasible to iterate over predicted probabilities with various cut-off points from 0 to 1 with an increment of, say 0.01, and to construct some metric that is of interest to you (i.e. which you want to maximize). Be it accuracy, sensitivity, specificity, K-S score or value of other variable that may be not part of your model.
Then plot the cutoff VS that variable and you will have an idea which cut-off works best for you. And once the cutoff is determined just perform the cross validation with that value.