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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.

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    $\begingroup$ Using 0.5 is a good "default". However, if your two misclassifications have different costs or implications, another number might be better. What is the context? $\endgroup$ – Peter Flom - Reinstate Monica Dec 18 '13 at 12:49
  • $\begingroup$ what is cost? how can i define it? context labor force participation \... $\endgroup$ – Mazumder Dec 18 '13 at 15:12
  • $\begingroup$ Cost is how bad each type of misclassification is. You would have to figure it out on substantive basis. $\endgroup$ – Peter Flom - Reinstate Monica Dec 18 '13 at 15:33
  • $\begingroup$ this is an overly complex introduction to this topic, but should give you the basics to produce cost/utility function if you want: ncbi.nlm.nih.gov/pubmed/17099194 $\endgroup$ – charles Dec 19 '13 at 0:02
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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.

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