# Is the decision surface for a Probit model linear?

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.

• 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? – Matthew Drury Jul 30 '18 at 16:02
• Is the model linear in the variables or not? – whuber Jul 30 '18 at 16:13
• 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? – Scott Jul 30 '18 at 18:27
• Then doesn't that answer your question? – whuber Jul 30 '18 at 20:24
• @whuber mind>>blown – Scott Jul 31 '18 at 0:25