For example, if we threshold our classification on $0.5$, is the decision surface necessarily linear? It is linear for Multinomial Logit models, but it's not obvious to me that it is for Probit models.

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    $\begingroup$ The decision surface would have a huge discontinuity if you set any threshold, in what sense do you say it is linear? Do you mean the decision boundary? $\endgroup$ – Matthew Drury Jul 30 '18 at 16:02
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    $\begingroup$ Is the model linear in the variables or not? $\endgroup$ – whuber Jul 30 '18 at 16:13
  • $\begingroup$ I mean the surface, in feature space, upon which the output of the model is $0.5$... Is that what you mean by decision boundary? $\endgroup$ – Scott Jul 30 '18 at 18:27
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    $\begingroup$ Then doesn't that answer your question? $\endgroup$ – whuber Jul 30 '18 at 20:24
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    $\begingroup$ @whuber mind>>blown $\endgroup$ – Scott Jul 31 '18 at 0:25

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