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Some days ago, I learned in a lecture that the intersection of Sensitivity and Specificity provides an optimal compromise for choosing a classification threshold for logit or probit models. However, no one told me in which sense it is optimal. Is there some criterion which is minimized or maximized by doing it? I think there are several different approaches for choosing a threshold. So, I doubt the intersection of Sensitivity and Specificity is the only one.

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This overall approach is inconsistent with the theory of optimum decision making. The goal of a logit or probit model is to accurately estimate the probability of an event - nothing more, nothing less. Risk estimation nicely avoids the multitude of problems that arise from seeking thresholds, and avoids the use of improper accuracy scoring rules such as sensitivity and specificity.

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  • $\begingroup$ Is there no other possible answer for my problem? This was just introduced in the context of logit and probit models. However, this is not the important point for me here. What I am trying to find is an explanation in what sense it can be seen as an optimal threshold, regardless of the underlying model. $\endgroup$ – random_guy Jan 15 '15 at 17:35
  • $\begingroup$ There is no threshold, so no need to search for one, unless you known the loss/utility function and work backwards from there. $\endgroup$ – Frank Harrell Jan 15 '15 at 22:36
  • $\begingroup$ Okay, I see, but isn't their some sort of quick and dirty way if one has no knowledge about it and wants to do it anyway? And does this intersection somehow correspond to some optimal quick and dirty procedure, where only some sort of error criterion is minimized and a loss function? $\endgroup$ – random_guy Jan 16 '15 at 19:00
  • $\begingroup$ Expected loss is minimized by jointly considering the estimated risk (continuously) and the loss function. $\endgroup$ – Frank Harrell Jan 16 '15 at 19:46
  • $\begingroup$ Does this mean my Professor taught me something wrong? $\endgroup$ – random_guy Jan 16 '15 at 20:56

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